DISCRETIZED MODEL AND EXPERIMENTAL STUDY OF VISCOELASTIC 
FLUIDS IN SCALABLE SPINNING AND SPRAYING PROCESSES  
 
 
 
 
 
 
 
A Thesis 
Presented to the Faculty of the Graduate School 
of Cornell University 
In Partial Fulfillment of the Requirements for the Degree of 
Doctor of Philosophy 
 
 
 
 
 
 
by 
Mounica Jyothi Divvela 
August 2019 
 
 
 
 
 
 
 
 
 
 
 
 
© 2019 Mounica Jyothi Divvela 
 
 
DISCRETIZED MODEL AND EXPERIMENTAL STUDY OF VISCOELASTIC 
FLUIDS IN SCALABLE SPINNING AND SPRAYING PROCESSES  
 
Mounica Jyothi Divvela, Ph. D. 
Cornell University 2019 
 
Polymer nanomaterials have been of scientific and industrial interest due to their 
applications in filtration, energy storage, and biomedical engineering. The 
electrospinning and electrospray processes can produce functional nanofibers and nano-
coatings respectively. In these processes, the liquid solution is ejected out of a nozzle 
and the liquid jets or droplets travel towards the collector under an electric field. There 
have been numerous experimental studies on these processes where the behavior of 
different viscoelastic polymer systems at various process conditions are studied. The 
theoretical studies are limited due to the mathematical complexity of the polymer 
rheology and also the non-linear effects of the process.  In this thesis, a discretized 
model for spinning and spraying process is discussed. In the model, the polymer jet is 
considered to be made up of discrete beads attached with massless springs. The jet 
trajectory is obtained by following a Lagrangian approach and applying conservation of 
mass and momentum equations to each bead. In addition, the whipping and 
axisymmetric instabilities on electrically driven jets are also discussed.   
In the electrospinning process, the whipping instability causes the jet to undergo 
non-axisymmetric motion and leads to uncontrolled deposition of the jet on the 
collector. To reduce the whipping motion of the fiber, the spinning solution is 
electrospun in a liquid medium and this modified system is called as the immersed 
electrospinning system. This modified system allows the electrically driven jets to 2D 
or 3D print on the substrate and form ordered fiber mats. In our printing approach, the 
nozzle system is stationary, and the fiber is electrically maneuvered for printing on the 
substrate. However, in this setup, there is no proper contact between the printing jet and 
the substrate to form 3D structures. Therefore, we studied the motionless printing 
method in electrohydrodynamic jet printing and melt electrospinning. In these two 
setups, first, we studied the onset position of whipping instability at different applied 
voltage conditions to obtain controlled deposition. Later, for the melt electrospinning 
setup, we studied the formation of 3D square pattern with motionless printing approach. 
The axisymmetric instability is responsible for the modulations in the radius of the 
polymer jet. In the presence of an electric field, the growth rate of the instability 
increases, and the jet breaks up to form droplets. The electrically driven droplets 
electrosprays and forms a coating on the collector. When coaxial air flow is applied to 
the viscoelastic polymer jets in the electrospray process, it is called as the air controlled 
electrospray process. The comparison of the droplet size distribution from simulations 
and experiments for the cases: i) air spray, ii) electrospray and iii) air controlled 
electrospray is studied. The three spray processes are used to coat cathodes in lithium 
sulfur batteries and the electrochemical performance of the batteries are compared. In 
addition, the effect of air flow on the surface morphology of the coating on the substrate 
is also discussed. Finally, the discretized model is used to study an industrial scale rotary 
bell spray process that is used in the automobile industry to coat the car body.  
BIOGRAPHICAL SKETCH 
Mounica Divvela was born on February 9, 1993 to Prasad Divvela and Lakshmi 
Garuda in Visakhapatnam, India. During childhood, Mounica has developed interest in 
mathematics and its applications which led her to pursue engineering. She did her 
schooling in India at St. Francis and later at Narayana College. In school, she earned 
first place in the subjects of mathematics and sciences. Later, she was determined to 
pursue engineering in India’s prestigious university Indian Institute of Technology. To 
achieve this, she prepared for an immense competitive entrance exam and after 
qualifying the exam, she joined Chemical engineering program at Indian Institute of 
Technology Madras in July 2010. During her undergraduate studies, she was involved 
in both academics and extracurricular club activities. After finishing undergraduate 
studies in 2014 she joined Master of Science program in Chemical and Biomolecular 
Engineering at Cornell University. Later, wanting to pursue a career in research she 
joined the Doctorate program in the Chemical and Biomolecular Engineering 
department in Cornell University in 2016. She defended her Ph.D. thesis in May 2019 
and will move to Hilsboro, Oregon to join the Computational Lithography group in 
Intel.  
ii i 
 
 
 
 
 
 
 
 
To my dear mother, Lakshmi, for being very understanding and giving me all the love 
and support in the world. 
To my dear father, Prasad, for being an exemplar hard working individual, role model 
and inspiration. 
To my dear sister, Sruthi, the closest person to me and for always being there for me.  
To all my family and friends, who are always there to fill my life with love and joy, to 
support and believe in me. 
iv  
 
ACKNOWLEDGMENTS 
I would first like to thank my family; my parents and sister for all their support 
and encouragement. I appreciate the constant love and care they provide which made it 
easier staying away from home. I would also like to thank all my friends in India for 
constantly being in touch and greeting me with open arms every time I went home. 
I would like to express my gratitude towards my advisor Prof. Yong L. Joo for 
believing in me and joining me in his group. I am also grateful for his constant help and 
guidance throughout my Doctorate thesis research. I would also like to thank my 
committee Prof. Paul Steen and Prof. Margaret Frey for their time and support. 
I would like to thank all the Joo research group members for their discussions 
and advice during my research and providing an inclusive work environment. I would 
like to specially thank Dr. An-cheng Ruo who shared his work on discretized model 
with me and was constantly helping me through emails even after finishing his post doc 
from Cornell University. I would also like to thank Dr. Colman P. Carroll for sharing 
his work on electrospinning and all his research papers and his thesis have been a useful 
guide for my research. I would like to thank Larissa Shepherd, PhD student from Fiber 
science department for collaborating with me and working on experiments on 
immersion electrospinning system. I would also like to thank Yevgen Zhmayev for 
providing me with an internship opportunity in Summer 2018 in BASF Coatings, 
Münster, Germany.  
I gratefully acknowledge the funding for various projects from E.I. du Pont de 
Nemours and Company, Buckingham Manufacturing Ltd. and BASF Coatings. The 
Cornell Center for Materials Research (CCMR) has provided funding and experimental 
facilities, and special gratitude goes to Malcolm Thomas and Don Werder for their help 
in my research and in equipment training.  
v  
 
I would finally like to thank all the friends I made in Ithaca and for the wonderful 
time I had with them during my graduate studies. 
v i 
 
TABLE OF CONTENTS 
Biographical Sketch                                                                                                          iii 
Dedication                                                                                                                      iv 
Acknowledgements                                                                                                         v 
Table of Contents                                                                                                          vii 
List of Figures                                                                                                                 x 
List of Tables                                                                                                               xiv 
 
Chapter 1: Introduction 
1.1 Introduction                                                                                                                  1 
1.2 The scope of investigated problems                                                                                                    5 
      References                                                                                                                       9 
 
Chapter 2: Discretized modeling motionless printing based on retarded bending 
motion and deposition control of electrically driven jet   
2.1 Introduction                                                                                                             12 
2.2 Immersion electrospinning experiment                                                                   14 
 2.2.1 Experimental fluids                                                                                   14 
 2.2.2 Experimental setup                                                                                      15 
2.3 Discretized model                                                                                                    16 
2.4 Results and discussion                                                                                                20 
 2.4.1 Bending instability study                                                                           20 
 2.4.2 Electrically controlled patterning of the fiber                                            22 
2.5 Conclusions                                                                                                               28 
      References                                                                                                                        30 
 
vi i 
 
Chapter 3: Whipping instability study of viscoelastic and conducting fluids in 
electrohydrodynamic jet printing system 
3.1 Introduction                                                                                                               34 
3.2 Experimental procedure                                                                                             36 
 3.2.1 Experimental fluids                                                                                                          36 
 3.2.2 Experimental setup                                                                                   37 
3.3 Simulation procedure                                                                                                38 
3.4 Results and discussion                                                                                                41 
 3.4.1 Jetting behavior of the spinning solutions                                                  41 
 3.4.2 Onset position of the whipping instability                                                 42 
3.5 Conclusions                                                                                                              53                           
      References                                                                                                                      54 
 
Chapter 4: Controlled deposition of the jet and motionless printing of 3D patterns 
using melt electrospinning system 
4.1 Introduction                                                                                                               56 
4.2 Experimental procedure                                                                                           58 
4.3 Simulation procedure                                                                                               59 
4.4 Results and discussion                                                                                                63 
 4.4.1 Jet behavior in melt electrospinning system                                             63 
 4.4.2 Onset of whipping motion                                                                          65 
 4.4.3 Motionless printing with melt electrospinning system                                72 
4.5 Conclusions                                                                                                              75 
      References                                                                                                                       76 
 
vi ii 
 
Chapter 5: Discretized modeling of whipping motion during wet electrospinning of 
poly acrylonitrile/dimethyl formamide fibers 
5.1 Introduction                                                                                                                 77 
5.2 Electrospray experiment                                                                                          80 
 5.2.1 Experimental fluids                                                                                    80 
 5.2.2 Experimental setup                                                                                     81 
5.3 Discretized model                                                                                                        83 
5.4 Results and discussion                                                                                               87 
 5.4.1 Electrospray and air spray                                                                         88 
 5.4.2 Air controlled electrospray                                                                       92 
5.4.3 Controlling coating topology, morphology and nanoparticle dispersion 
via AC electrospraying                                                                            93 
5.4.4 Lithium sulfur battery performance with air controlled electrospray 
coated electrodes                                                                                     99 
5.5 Conclusions                                                                                                           104 
      References                                                                                                             106 
 
Chapter 6: Jet spraying behavior and coating deposition of viscoelastic liquid in 
rotary bell spray process 
6.1 Introduction                                                                                                             109 
6.2 Experimental procedure                                                                                                                   111 
6.3 Simulation procedure                                                                                       112 
6.4 Results and discussion                                                                                             115 
6.5 Conclusion                                                                                                             126 
      References                                                                                                                   127 
 
ix  
 
LIST OF FIGURES 
 
Figure 2.1. Immersion electrospinning setup                                                                       16 
Figure 2.2. Jet trajectory obtained from a) experiments at 5 kV b) experiments at  
10 kV c) comparing simulations and experiments at 5 kV and 10 kV                                      21 
Figure 2.3. a) Radius of the jet measured along the length, from simulation  
and experiment, b) SEM image of the fiber                                                                     22 
Figure 2.4. The fiber pattern formed with voltage switching from simulation  
and experiment                                                                                                                  24 
Figure 2.5. 3D structure and Top view of the 3D print at different switching times  
and resolutions                                                                                                                             26 
Figure 2.6. Circle pattern at different switching times and resolutions obtained  
from simulations                                                                                                                          27 
Figure 3.1. Electrohydrodynamic jet system schematic                                                           37 
Figure 3.2. Radius thinning profile of: a) PIB/PB b) Silver ink c) PEO/water               42 
Figure 3.3. Experimental imaging of PIB/PB solution at a) 8 kV and 3 cm  
b) 8 kV and 1 cm                                                                                                           43 
Figure 3.4. High speed camera image of the experimental result at voltage  
and spinning distance a) 6 kV and 1cm b) 8 kV and 1 cm c) 6 kV and 0.5 cm  
d) 8 kV and 0.5 cm                                                                                                           45 
Figure 3.5. Comparing the position of the onset of the whipping from simulations  
and experiments at different electric fields for silver ink solution                                   46 
 
x  
 
Figure 3.6. High speed camera images of PEO/water solution at voltage and  
spinning distance a) 8 kV 3 cm b) 12 kV 3 cm c) 16 kV 3 cm d) 6 kV 1 cm  
e) 8 kV 1 cm                                                                                                                        48 
Figure 3.7. Effect of voltage on the jet trajectory of PEO/water                                     49 
Figure 3.8. Comparing the position of the onset of the whipping from simulations  
and experiments at different electric fields for PEO/water solution                                 50 
Figure 3.9. ℇE Vs PeE' plot for silver ink and PEO/water solution                                  52 
Figure 3.10. ℇE Vs PeE' linear regression plot for experimental and simulation  
results for silver ink and PEO/water solutions                                                                                     52 
Figure 4.1. Experimental setup for motionless printing with melt electrospinning       59 
Figure 4.2. Radius thinning profile of the jet at different nozzle temperatures              63 
Figure 4.3. Jet temperature profile at different nozzle temperatures                               64 
Figure 4.4 Radius thinning profile at different air temperatures                                      65 
Figure 4.5. Jet trajectory in the XZ plane for cases: a) different voltages  
b) different air temperatures                                                                                                           66 
Figure 4.6. High speed camera images of jet trajectory to observe whipping motion  
near collector at air temperature a) 25 oC, and b) 80 oC [16]                                            68 
Figure 4.7. Onset of whipping motion position comparison between simulations  
and experiments at a) different voltages b) different air temperatures                             69 
Figure 4.8. ℇE Vs PeE' for melt electrospinning system                                                     70 
Figure 4.9. ℇE' Vs PeE' for melt electrospinning system to study the effect  
of air temperature                                                                                                           71 
 
x i 
 
Figure 4.10. Simulation of motionless printing of 3D square pattern at different  
switching times and resolution                                                                                        74 
Figure 5.1 Schematic of a) Electrospray b) Air spray c) Air controlled (AC)  
electrospray                                                                                                                              82 
Figure 5.2. a) Effect of voltage on average droplet radius for electrospray process  
b) Effect of air velocity on average droplet radius for air spray process                           91 
Figure 5.3. Air controlled electrospray at air flow a) 0 m/s b) 7.5 m/s c) 15 m/s           92 
Figure 5.4. Effect of air flow on average droplet radius for air controlled  
electrospray process                                                                                                           93 
Figure 5.5. AFM images of AC electrospray surface of PVA/H2O at air flow  
a) 0 m/s b) 15 m/s c) 60 m/s and d) Effect of air flow on surface roughness  
of the coating                                                                                                                                   94 
Figure 5.6. Effect of air flow on coating efficiency of the AC electrospray of  
PVA/H2O                                                                                                                        95 
Figure 5.7. SEM images of macro/micro/nano-topology of 3% PVA solution with  
CB (15 vol% to PVA) coatings deposited via a) 0 m/s, b) 30 m/s, c) 55 m/s and  
d) 70 m/s sheath layer air flow AC electrospray                                                                       97 
Figure 5.8. Surface morphology and cross-section of air controlled electrospray of  
GO at air flow a) 0 m/s b) 50 m/s c) 100 m/s                                                                       99 
Figure 5.9. SEM images of cathodes via a) slurry coating, b) electrospray,  
c) air spray and d) air controlled electrospray                                                                     101 
 
 
xi i 
 
Figure 5.10. a) Discharge capacity at 0.5C, and b) Rate capability of lithium  
sulfur battery cathode fabricated with air controlled electrospray, air spray  
and electrospray                                                                                                           103 
Figure 6.1. a) Schematic of the rotary bell spray setup b) Experimental image of  
the rotary bell spray setup                                                                                                           112 
Figure 6.2. Comparing initial diameter of jets from simulation and experiments  
at different a) flowrates b) rotational speed                                                                              116 
Figure 6.3. High speed camera images of rotary bell spray process at a) 15000 rpm  
and 50 ml/min b) 30000 rpm and 250 ml/min c) 45000 rpm and 250 ml/min                   117 
Figure 6.4. The droplet trajectories and droplet diameter for a) 150 ml/min and  
15000 rpm and b) 150 ml/min and 25000 rpm                                                               119 
Figure 6.5. The droplet trajectories and droplet diameter for a) 150 ml/min and  
20000 rpm and b) 250 ml/min and 20000 rpm                                                                  120 
Figure 6.6. a) Brush size b) Brush thickness c) Deposited coating profile at  
150 ml/min and 15000 rpm                                                                                                            122 
Figure 6.7. a) Brush size b) Brush thickness c) Deposited coating profile at  
150 ml/min and 25000 rpm                                                                                                           123 
Figure 6.8. a) Brush size b) Brush thickness c) Deposited coating profile at  
150 ml/min and 20000 rpm                                                                                                           124 
Figure 6.9. a) Brush size b) Brush thickness c) Deposited coating profile at  
250 ml/min and 20000 rpm                                                                                                           125 
 
 
xi ii 
 
LIST OF TABLES 
 
Table 2.1. Material properties of 10.5 wt% of PAN & DMF solution and mineral  
oil and chloroform mixture                                                                                                         15 
Table 3.1. Material properties of the model fluids                                                                           36 
Table 5.1. Material properties of 5 wt% of PVA & H2O solution                                    80 
xi v 
 
CHAPTER 1 
INTRODUCTION 
1.1 Introduction 
 
Polymeric materials are essential components of the modern nanotechnology due 
to their unique properties, and a wide range of products with polymeric nanomaterials 
became a vital part of our daily lives. Polymeric fibers are utilized in such areas as 
advanced electronics, catalysis, protective clothing, filtration, drug delivery, and 
biomedical engineering [1-11]. In general, polymeric fibers are manufactured by 
extrusion of the polymer solution, with this, the polymer chains align and orient along 
the axis of the fiber which increases the mechanical strength, stiffness, and continuity 
of the fiber [12-14]. In addition, functional polymer coatings are utilized for the 
fabrication of superhydrophobic materials, encapsulation, biomedical devices and 
energy storage materials [15-25]. However, the fabrication of these nanomaterials 
requires high control of the dimensions, control of the morphology and topology, and 
efficient production [17, 22]. Therefore, in recent years a lot of attention has been gained 
for the development of various process techniques for the fabrication of polymer fibers 
and coatings [1-25]. 
The conventional mechanical spinning techniques like wet spinning and melt 
spinning cannot produce diameters smaller than micrometers without an additional step 
[26-30]. An alternative spinning approach, called electrospinning technique can produce 
fibers in the submicron range with the use of the electric field. Morton[31] and 
Cooley[32] discovered the electrospinning process in 1902, and they later filed US 
patents on the process. However, it was in the late 1990s that this process started to get 
1  
 
more recognition in the context of nanofiber production [33]. In this process, the 
polymer solution is released from a nozzle at a constant flowrate and the presence of an 
electric field in the spinning gap accelerates the polymer jet and forms thin fibers due 
to the extension of the jet. However, in this process, the presence of the electric field 
leads to instabilities in the system. The whipping instability leads to a chaotic motion of 
the fiber and leads to uncontrolled deposition and results in the formation of unordered 
fiber mats. However, in the electrospinning process, the initial region of the jet near the 
nozzle is stable and then at a position downstream of the jet, the onset of the whipping 
instability is observed. Therefore, in this thesis, we study the onset position of the 
whipping instability and the effect of the process conditions on the whipping motion of 
the jet from simulations and experiments. The ordered fibers can be formed from 2D 
and 3D printing methods. For instance, the conventional printing methods use the 
movement of the nozzle or the collector to obtain a pattern, but this method leads to 
noise, error and long printing time [34-38]. Alternatively, we attempted a pattern 
formation from simulations and experiments with a different printing approach called 
motionless printing. In this printing process, the electric field is used to steer the 
direction of the jet for the print formation.  
In general, several functional nano-coatings are obtained through air spray and 
electrospray processes [20-25]. However, the spray deposition via these methods leads 
to poor control of surface topology, low deposition efficiency and low coverage of the 
coating [17, 22]. Therefore, in this thesis, to address these issues we explored a novel 
technique called air controlled electrospray by combining electric field and air flow 
which are the driving forces in electrospray and air spray process respectively. We 
2  
 
studied the droplet size distribution in the three spraying processes from simulations and 
experiments and with air-controlled electrospray process we can obtain a uniformly 
sized large number of droplets. Hence, the air controlled electrospray technique offers 
a ten-fold increase in production rate per spinneret. In addition, rigorous control of 
dimensions, topologies, and morphologies of resulting nanocomposites, as well as a 
possibility to uniformly coat convoluted architecture can be achieved, which makes this 
process much more attractive and promising for industrial applications. The additional 
extensional deformation through the sheath-layer air in the process can effectively 
control the placement and spatial distribution of various active nanoinclusions, which 
obviates both nanoparticle functionalization and a multi-step process for desired 
nanocomposite fabrication [11, 39–41].  
In this thesis, we also studied the rotary bell spray process, in which the rotational 
force and air flow are the driving forces. This process is commercially used by the 
automobile industry to paint the car’s exteriors. However, there are not many theoretical 
studies on this process to obtain the effects of process conditions and paint rheology. 
This leads to high cost in the industry during the formulation of the coating. The coatings 
are adjusted to different values of viscosity, surface tension and relaxation time and 
tested on car panels and the formulation with best appearance and properties of the 
coating is chosen for the paint. This tedious process of testing can be avoided if we can 
obtain a starting point for the formulation of the paint if we have a prediction tool and 
can understand the fundamental behavior of the process. Therefore, we developed a 
computational model for the rotary bell spray process to study the effect of various 
process conditions on the atomization behavior and coating deposition profile. 
3  
 
The spinning and spraying processes mentioned above were studied from 
simulations by solving the equations of motion driving the process. Generally, for the 
modeling of a transport process, a continuum analysis is used by solving the continuity 
and conservation of momentum equations [42]. These are differential equations, usually 
solved using differential equation calculators, which can solve the boundary value 
problems or initial value problems [43, 44]. However, solving both simultaneously is 
more complex due to nonlinearities among the variables. To overcome this, techniques 
like asymptotic analysis [45] and Fourier series analysis [46] have been used.  
Alternatively, various numerical techniques can be used by converting the 
computational domain into a grid structure with various node points. The derivative at 
a certain node point is defined locally based on the variable values at the neighboring 
node points. In this way, the solution for the governing equations is calculated at these 
discrete node points. The different numerical methods are finite difference method, 
finite volume method and finite element method [47]. However, the grid size affects the 
accuracy of the solution, the smaller the grid size the more accurate is the method. 
Hence, there is a trade-off between accuracy and computational time. In this thesis, a 
different approach can be used where the polymer jet can be divided into discrete 
elements and solve the conservation of mass and momentum for each element. The 
polymer fiber is analogous to a bead-spring system where the discrete beads are 
connected to each other with springs [48-50]. This method is in a Lagrangian frame 
where we apply Newton’s second law to each of these beads (discrete elements) to 
obtain the trajectory of the fiber. This approach does not involve solving differential 
equations and can work easily with polymers of complex rheology.  
4  
 
1.2 The scope of Investigated Problems 
As mentioned in the previous section, in this thesis we studied the spinning and 
spraying processes of polymer and viscoelastic solutions using simulations and 
experiments.  
In Chapter 2, we studied a modified electrospinning process called immersed 
electrospinning process in which the polymer solution is electrospun in a liquid medium. 
Unlike the conventional electrospinning setup, the immersed electrospinning setup can 
obtain a controlled deposition of the jet.   In this setup, the drag and dielectric effects 
from the liquid medium reduce the acceleration and whipping motion of the jet. We 
studied the whipping instability behavior at different voltage conditions from 
simulations and experiments. The discretized model is modified from the 
electrospinning study to incorporate the drag force due to the liquid medium. In 
addition, we also demonstrated the printing of a square pattern from both simulations 
and experiments. The square pattern is obtained by using a motionless printing 
approach, in which, the collector is designed with conducting points and the voltage at 
these conducting points is switched ON and OFF based on the desired pattern. The 
change in the direction of the electric field by this switching of the voltage steers the 
printing jet direction. Also, we also attempted the formation of 3D structures and 
printing of circular pattern from the simulations which use bead spring-model 
mentioned in the previous section. 
In the immersed electrospinning setup, the liquid spinning media makes it difficult 
for the printed jet to adhere to the collector or substrate. However, this problem is not 
5  
 
observed for electrospinning and melt electrospinning processes. Therefore, we studied 
the onset of whipping instability and motionless printing for electrospinning and melt 
electrospinning in Chapters 3 and 4 respectively. In the electrospinning process, 
however, the whipping motion is very rapid and chaotic and is difficult to control. To 
address this issue, we studied the electrospinning process at a lower spinning distance 
(0.5 cm to 5 cm), similar to the electrohydrodynamic printing process. With this, the 
spinning length is reduced, and the utilization of the stable jet region can be maximized. 
Therefore, in chapter 3, we studied the onset of whipping motion in 
electrohydrodynamic process for three different model fluids. The model fluids are 
chosen based on the electrical conductivity and viscoelasticity properties of the fluid. 
We analyzed the behavior of the onset of whipping motion for these fluids at different 
applied voltage conditions. In addition, the onset of the whipping positions is studied 
based on the time scales of the electric field and convection to obtain an empirical 
relation between the electric field and instability onset position. This relation can be 
used for the prediction of whipping instability behavior at different applied voltage. 
In chapter 4, the melt electrospinning process is studied for printing application. 
Unlike the electrospinning process, the melt electrospinning setup follows a non-
isothermal behavior. In the melt electrospinning process, the polymer resin is melted in 
a reservoir at high temperature and then extruded out of the nozzle. Apart from the 
electric field, there is cooling air in the spinning gap to cool the high-temperature 
polymer jet which also determines the jet behavior. The heat transfer between the jet 
and the surrounding air changes the jet temperature and the rheological properties of the 
jet that are temperature dependent. To model this system, the simulations using the 
6  
 
discretized model are modified to incorporate the temperature change in the jet by 
including energy balance equations. In addition, the rheological behavior of this non-
isothermal jet is modeled using non-isothermal Giesekus model. In this chapter, first, 
the process is also studied for the onset of whipping instability to obtain the effect of 
process conditions on the controlled deposition of the jet. Similar to the analysis in 
chapter 3, the empirical relation between the whipping onset or the stable jet length with 
electrostatic force parameter is obtained. In addition, as the temperature of the cooling 
air is also an important factor in whipping instability, the relation between the instability 
onset position and temperature dependent force factor is obtained. Finally, 3D structure 
formation from motionless printing approach is studied in the melt electrospinning setup 
at different switching times and print resolutions. 
In chapter 5, we studied the novel air controlled electrospray process for the 
production of polymer coating with nano inclusions. In general, the droplets in the spray 
process are formed from two phenomena; i) atomization at the nozzle, and ii) 
axisymmetric instability growth on the jet leads to jet-breakup into droplets. In general, 
the spray process of viscoelastic liquids follows the second phenomenon, i.e., the jet 
extends and breaks into droplets because of axisymmetric instability. Therefore, the 
modeling of the spray process used in this chapter is an extension of the axisymmetric 
instability model for the electrospinning process [50]. As the axisymmetric instability 
grows a breakup criterion is added in the model which determines when the jet breaks 
up, in our model, when the jet radius becomes negligible the jet breaks into droplets. 
We first compared the droplet size distribution from experiments and simulations for 
air spray and electrospray processes with air controlled electrospray process. Later, the 
7  
 
effect of air flow on the deposition of nano inclusions in the air controlled electrospray 
process is studied. This process is then used to obtain conductive coating on the cathode 
of Lithium sulfur battery. The electrochemical performance of the battery is compared 
with cathodes coated with air spray, electrospray, and air controlled electrospray 
process. 
The rotary bell spray process is studied in chapter 6, and in this process, the jet 
breakup behavior depends on the rotational force and air flow. The modeling approach 
for the jet breakup behavior in this process is similar to the air controlled electrospray 
model. However, instead of the electric field force, the rotational force acts as the main 
driving force. The droplet trajectories and size distribution are obtained at different 
process conditions. In addition, the coating deposition profile is also studied to obtain 
the thickness and the size of the deposited coating. 
 
 
 
 
 
 
8  
 
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11  
 
 
1CHAPTER 2 
DISCRETIZED MODELING OF MOTIONLESS PRINTING BASED ON 
RETARDED BENDING MOTION AND DEPOSITION CONTROL OF 
ELECTRICALLY DRIVEN JET   
2.1 Introduction 
The electrospinning process is widely used to produce fibers with diameters in the 
sub-micron range1,2. These fibers have been of interest due to their high surface area, 
and have applications in filtration, catalysis, tissue engineering, drug delivery, energy 
storage systems, and microencapsulation2-9. In this process, the polymer solution or melt 
is slowly extruded out of the nozzle and accelerated towards the collector under an 
electric field12-14. There have been several theoretical studies on the electrospinning 
process12-32, most of which were done by using one-dimensional slender jet models13-18. 
In general, in the electrospinning process, the polymer jet undergoes a chaotic bending 
or whipping motion due to the electrohydrodynamic instability.   
Electrically driven fibers have been of interest in the area of 2D and 3D printing to 
fabricate ordered fiber mats33-39. Melt electrospinning has been widely used for this 
purpose36-39. However, there are several shortcomings in this process36: (i) only limited 
materials can be melt spun, (ii) mechanical motion of the nozzle head and/or collector 
results in long print time and poor resolution, and (iii) the electrostatic forces between 
collected fibers restrict the controlled deposition of the 3D constructs to 1 mm. On the 
                                               
This chapter is adapted from M. J. Divvela, L. M. Shepherd, M. W. Frey and Y. L. 
Joo, 3D Printing and Additive Manufacturing 5 248-256 (2018). 
12 
 
 
other hand, in the immersed electrospinning, where the electrically driven jet is ejected 
into a liquid medium can be a better alternative because: i) it potentially increases the 
collection depth profile due to reduced charge build-up on the jet40-42, and ii) the drag 
force due to the surrounding liquid retards the motion of the jet, which makes it possible 
to form a controlled pattern on the collector without the movement of nozzle head and 
collector.  
In the current work, the bending instability of the fiber is studied as it affects the 
fiber trajectory during its deposition on the collector. The complexity of solving the 
equations for the rapid, chaotic motion of the jet limited the theoretical study on the 
bending instability. Therefore, the discretized model with bead-spring approach19,24-32 
has been used in this study to model the bending motion of the fiber in the immersed 
electrospinning setup. This model simplifies the equations of motion and makes it easy 
to solve and apply the stability analysis. In the current study, the bead-spring model is 
modified to incorporate the drag and dielectric effects. The reduced chaotic motion of 
the jet in this setup makes it easier to take visualization images at a low frame rate and 
high exposure time, because of which, the lighting and the depth of field are not 
compensated. This can then be used to test the validity of the discretized model. Finally, 
for the 3D printing application, the bead-spring model is employed to form a pattern on 
the collector. This is achieved by applying a temporal boundary condition on the voltage 
on the collector, and the simulation results are then compared with the experiments. 
With suppressed bending motion and guided deposition of the jet, the print resolution is 
limited only by the material delivery system.  
13 
 
 
2.2 Immersion electrospinning experiment 
2.2.1 Experimental fluids 
The spinning solution is 10.5 wt% of Polyacrylonitrile (PAN) in 99.8% anhydrous 
N, N-Dimethylformamide (DMF). PAN (150,000 g/mol) and DMF are purchased from 
Sigma-Aldrich. This solution is spun into a coagulation medium of 2:1 chloroform and 
mineral oil mixture. Mineral oil is purchased from Fischer Scientific and chloroform is 
from Macron Fine Chemicals. The material properties of the spinning solution (PAN & 
DMF solution) and coagulation medium (Mineral oil and chloroform) are presented in 
Table I. The dielectric constant and the conductivity of the PAN & DMF solution, and 
viscosity of DMF are taken from literature43-45. The viscosity of the coagulation medium 
is obtained from the Gambill method for the viscosity of liquid mixtures45. The rest of 
the properties are taken from our previous work42. 
 
 
 
 
 
 
 
 
14 
 
 
Table 2.1. Material properties of 10.5 wt% of PAN & DMF solution and mineral 
oil and chloroform mixture 
Material properties of 10.5 wt% of PAN in DMF 
Density, ρ (kg/m3) 964.5 
Viscosity, μ (Pa.s) 1.109 
Relaxation time, λ (s) 0.1 
Conductivity, K (S/m) 0.005 
Surface tension, γ (N/m) 0.00538 
Solvent viscosity, μs (Pa.s) 0.009 
Material properties of mineral oil and chloroform mixture 
Density, ρ (kg/m3) 1263 
Viscosity, μ (Pa.s) 0.00279 
Relative permittivity, εr 3.94 
 
2.2.2 Experimental setup 
The experimental setup for the immersed electrospinning is illustrated in Fig. 2.1. 
The coagulation bath contains a mixture liquid of chloroform and mineral oil. The 
PAN/DMF solution is pumped out of a 25-gauge needle at a flowrate of 0.5 ml/hr by 
using a programmable PHS Ultra syringe pump (Harvard Apparatus). The voltage 
difference in the spinning gap is obtained by connecting the needle to the ground and 
applying the desired voltage to the collector with a Gamma High Voltage Research 
voltmeter. The experiments are conducted at 5, 7 and 10 kV voltage differences, and the 
spinning distance is ~ 9.5 cm.  
15 
 
 
The spinning behavior of the polymer fiber is visualized using a high-speed camera 
(RedLake MotionPro HS-3 with Nikon MICRO NIKORR 60mm 1:2:8 lens). The 
images are taken at 100 frames per second with a shutter time of 400 μs. Finally, the 
images are digitized using MotionStudio x64 software and are analyzed using ImageJ. 
 
Figure 2.1. Immersion Electrospinning setup 
 
2.3 Discretized model 
The immersed electrospinning system is modeled using the bead-spring model; the 
jet is assumed to be a series of beads attached with springs. The modeling approach is 
similar to the model used previously in the electrospinning and centrifugal spinning 
systems29-32. However, in the current study, the drag and dielectric effects on the polymer 
fiber are incorporated into the model to describe the interaction between the electrically 
driven jet and the coagulation liquid medium.  
 
16 
 
 
For each bead ‘i’, the radius 𝑟" is obtained from conservation of mass equation (Eq. 
(2.1)). 
 𝑟" =
%
$ & ,																																																																												(2.1) '()&
The equations of motion for a bead ‘i’ of mass 𝑚", length 𝑙" and radius 𝑟" are 
obtained by applying Newton’s second law (Eq. (2.2)). The position vector 𝒙𝒊 is 
obtained from the forces acting on the bead ‘i’, which are surface tension 𝑭𝒔𝒕,𝒊, 
viscoelastic force 𝑭𝒗,𝒊, drag force 𝑭𝒅,𝒊, electric force 𝑭𝒆,𝒊 and gravitational force 𝑭𝒈,𝒊.  
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒔𝒕,𝒊 + 𝑭𝒗,𝒊 + 𝑭𝒅,𝒊 + 𝑭𝒆,𝒊 + 𝑭𝒈,𝒊,																																										(2.2) 
The surface tension force and viscoelastic force are obtained from the work by 
Divvela et al.30,32. The surface tension force has two components: i) capillary force ii) 
bending force due to local curvature of the fiber. In Eq. (2.3), 𝑘A is the local curvature 
of the fiber and 𝛾 is the surface tension coefficient. 
𝑎
𝑭 = 𝛾𝜋 D F"
+ 𝑎G" 𝒆𝒅𝒊 − 𝒆𝒖𝒊
𝒔𝒕,𝒊 2 H 𝑘A D|𝒆 − 𝒆 |H + 2𝜋𝛾
(𝑎F"𝒆𝒅𝒊 − 𝑎G"𝒆𝒖𝒊),												(2.3) 
𝒅𝒊 𝒖𝒊
The viscoelastic force is due to the stress from the solvent and polymer; the solvent 
is a Newtonian fluid, and the polymer stress is obtained from the Giesekus model32. In 
Eq. (2.4), 𝜏F" and 𝜏G" are viscoelastic stress for downstream and upstream beads 
respectively.  
𝑭 = 𝜋(𝑎=𝒗,𝒊 F"𝜏F"𝒆 =𝒅𝒊 − 𝑎G"𝜏G"𝒆𝒖𝒊),																																													(2.4) 
17 
 
 
The drag force due to the coagulation medium (mineral oil and chloroform mixture) 
is obtained by considering the average of the drag effects on the upstream and the 
downstream elements. The drag force has two components as shown in Eq. (2.5): i) 
friction drag due to shear stress on the surface of the fiber 𝑭𝒇,𝒊 and ii) pressure drag due 
to pressure difference radial to the fiber 𝑭𝒑,𝒊. 
𝑭𝒅,𝒊 = 𝑭𝒇,𝒊 + 𝑭𝒑,𝒊 = 𝑐R𝜌)"T𝜋𝑟"𝑙"U𝑉W,"U𝑽𝒕,𝒊 + 𝑐Y𝜌)"T𝑟"𝑙"U𝑉Z,"U𝑽𝒏,𝒊,								(2.5) 
In which, 𝜌)"T is the density of the surrounding liquid, 𝑐R is the friction drag 
coefficient and 𝑐Y is the pressure drag coefficient. 𝑉W and 𝑉Z are the tangential and 
normal components of the relative velocity of the bead with the liquid. 
The friction drag coefficient 𝑐R is obtained from the shear stress due to the flow of 
the surrounding liquid in a thin boundary layer, which forms a concentric annulus 
around the fiber. At the surface of this boundary layer, the liquid is stagnant and it is not 
affected by the motion of the fiber. The velocity of the liquid in the boundary layer is in 
the axial direction and it is radially dependent with no slip condition at the surface of 
the fiber. The frictional drag force is caused by the shear stress on the surface of the 
fiber due to the radial gradient of the velocity. In Eq. (2.6), the variable r is the radial 
distance from the axis of the fiber. The pressure drop along the length of the fiber, ]Y, 
]^
is neglected in the boundary layer. 
1 𝜕𝑝 𝑟=
𝑉 = 𝜇 𝜕𝑧 2 + 	𝑘c𝑙𝑛𝑟 + 𝑘=,																																																																	(2.6) )"T
The constants 𝑘c and 𝑘= are obtained from the boundary conditions: i) Vz = 0 at the 
boundary layer with 𝛿 thickness, and ii) Vz = U at the radius of the fiber, 𝑅, where U is 
18 
 
 
the axial velocity of the fiber. Furthermore, the pressure drag coefficient is obtained 
from the cross flow on the cylinder48.  
The electric force on a bead ‘i’ is given in Eq. (2.7). The electric field on the element 
i, has two terms: i) gradient of the applied voltage 𝑉h with the spinning length ℎ, and ii) 
Coulombic interaction with the rest of the beads j with charge 𝑞k at a distance 𝑥"k from 
bead ‘i’ in a liquid medium with relative permittivity 𝜖n. The surface charges are 
conserved by considering the convection and conduction currents, as given by Divvela 
et al.32. In this case,  𝜖n>1 for the liquid medium, this reduces the electric field force on 
the jet reducing the acceleration and bending motion of the jet. 
𝑉 1 𝑞
𝑭𝒆,𝒊 = 𝑞"𝑬𝒆,𝒊 = 𝑞" p
h
ℎ 𝒆𝒛 +
k
4𝜋𝜖 𝜖 s𝑥 t 𝒙𝒊𝒋w,																														(2.7) r n kv" "k
The bending motion is induced in the system by applying the non-axisymmetric 
normal mode perturbations at the nozzle to the x and y coordinates (Eqs. (2.8) and 
(2.9))19,29. The terms 𝑥y and 𝑦y are the coordinates of the stable jet, 𝐴r is the amplitude, 
and 𝑓 is the frequency of the perturbation.  
𝑥 = 𝑥y + 𝐴r cos(𝑓𝑡),																																																																									(2.8) 
𝑦 = 𝑦y + 𝐴r sin(𝑓𝑡),																																																																										(2.9) 
 
 
19 
 
 
The growth rate of the perturbation 𝜔 is measured from the growth of the spiral 
radius 𝑅(𝑡) or bending amplitude of the fiber with time 𝑡 in Eq. (2.10). The spiral radius 
𝑅(𝑡) is the radial distance of the jet measured from the axis. 
ln†𝑅(𝑡)‡ − ln†𝑅(0)‡
𝜔 = 𝑡 	.																																																																		(2.10) 
 
2.4 Results and discussion 
2.4.1 Bending instability study 
The PAN/DMF solution is spun at 5 kV and 10 kV (Fig. 2.2)42, and all the other 
conditions are same as mentioned in Section 2.2. The non-axisymmetric motion of the 
jet is higher for 10 kV (Fig. 2.2(b)). This behavior from experiments is similar to the 
results predicted from the model as shown in Fig. 2.2(c), the coordinate axes are scaled 
with the radius of the nozzle. The magnitude of the surface charges on the jet increases 
with the voltage, which leads to large Coulombic repulsions between them. These large 
repulsions amplify the bending motion of the fiber, forming a spiral with a larger radius. 
Therefore, from Eq. (2.8), the growth rate is observed to increase with the voltage (and 
thus electric field at the same spinning distance) from experiments and simulation. This 
shows that the instability is the conducting mode, as it is electrically driven. 
20 
 
 
   1 mm    1 mm 
 
Figure 2.2. Jet trajectory obtained from a) experiments at 5 kV b) experiments at 
10 kV c) comparing simulations and experiments at 5 kV and 10 kV 
Figure 2.3(a) shows the variation of the jet radius along the length of the jet when 
7 kV is the applied voltage difference. A rapid thinning of the jet is observed at the 
nozzle, and the jet radius varies from 130 microns (radius of the nozzle) to 15 microns 
at the collector. The radius of the jet obtained at different jet lengths from experiments 
is also plotted in Fig. 2.3(a). The field emission electron microscopy (FESEM) image 
of the fibers collected on the collector at 9.5 cm distance from nozzle during immersion 
electrospinning is shown in Fig. 2.3(b). The average fiber radius is measured to be 34 
microns from the experiment, which is comparable to the simulation result (Fig. 2.3(a)).  
21 
 
 
 
Figure 2.3. a) Radius of the jet measured along the length, from simulation and 
experiment, b) SEM image of the fiber 
2.4.2 Electrically controlled patterning of the fiber 
The current setup of the immersed electrospinning retards the acceleration of the 
fiber, which makes it easy to control its motion. The collector in this setup is a black 
thick art paper, this material does not dissolve in the chloroform, and it is nonconductive 
to the electric field. Four copper plates of size ~ 4 X 6 mm are attached to this collector, 
and the voltage is conducted through these points on the collector. As the fiber reaches 
a copper plate, the voltage is switched OFF at that location, and the voltage at the next 
copper plate is switched ON. Hence, for obtaining the square pattern, the order of 
switching ON of the collector plates is 1→ 2 → 3 → 4 → 1, based on the numbering in 
Fig. 2.4. This electrically controlled motion of the fiber forms a square pattern of size 1 
cm as shown in Fig. 2.4. The voltage applied to the copper plates is 1 kV and the 
collector is at a distance ~1.8 cm from the nozzle. The size and the structural 
arrangement of these copper plates determine the accuracy of the pattern. In this way, 
the voltage is applied to a particular point on the collector at a certain time. Therefore, 
22 
 
 
in the bead-spring model, a temporal boundary condition is applied on the voltage on 
the collector to simulate the guided patterning similar to the experiments. 
The pattern formed from experiments exhibits departure from the predicted near 
square path as there are only four collector points used. This coarse resolution of the 
lattice points on the collector is not enough to obtain an exact square pattern. In addition, 
the switching of the electric fields is done manually, so as soon as the fiber reached one 
collector point the electric field at the next point is switched on. On an average, the pulse 
duration is around 5.5 s and the rise time is around 0.5 s. As there is no rise time in the 
simulation, this manual switching is mainly responsible for the discrepancy in the 
simulation and experimental result. If the duration of the applied voltage is longer than 
needed then the jet will overshoot its position from the actual pattern. If the rise time is 
longer then the response to changing the fields may not be quick enough to steer the 
fiber towards the direction of the next switched ON point on the collector.  
23 
 
 
 
Figure 2.4. The fiber pattern formed with voltage switching from simulation and 
experiment 
Dispite the discrepancy, both experiments and simulation of immersion 
electrospinning with electrically guided collector demonstrate that the controlled 
deposition of an electrically driven jet can be done without any movement of nozzle 
head and collector. The accuracy of the pattern can be improved with microscale 
electrode arrays and using MOSFETs for switching the electric field. In addition, we 
can achieve pattern formation in a regular electrospinning setup (with air as spinning 
medium) by reducing the spinning distance so that we can obtain jet deposition when it 
24 
 
 
is in the stable region. With this, we can reduce the bending instability of the jet and 
achieve controlled deposition on the collector for the pattern formation. 
The 3D structure of the pattern is obtained from the simulations and the square 
pattern is observed to be repeated for different layers on the collector. The pattern is 
formed by considering four collector points on the collector but the dimension of the 
square formed is 0.1 cm (Fig. 2.5). The simulation results for four cases i) shorter 
switching time (0.13 ms) and resolution (1 mm distance between adjacent collector 
plates) ii) longer switching time (0.32 ms) and resolution (1 mm distance between 
adjacent collector plates) iii) optimized switching time (0.2 ms) resolution (1 mm 
distance between adjacent collector plates) iv) improved switching time (0.1 ms) and 
resolution (0.5 mm distance between adjacent collector plates). Initially when the 
switching time is shorter or longer from the actual switching time and the resolution is 
poor, the formed fiber pattern is underpredicting or overpredicting respectively 
compared to the desired pattern. Therefore, when the switching time is optimized, in 
this case it is 0.2 ms and keeping the resolution same, the pattern formed is closer to the 
square pattern but with few discrepencies. When the resolution is improved to 0.5 mm 
(distance between adjacent collector plates) by adding 8 collector plates instead of 4, 
the fiber forms a square pattern with higher accuracy. In the third case, we can observe 
that with increase in resolution the switching time decreased (from 0.2 ms to 0.1 ms). 
This is because with increase in the number of collector plates, the distance between the 
plates reduced therefore, it takes less time to reach the next switching plate. 
25 
 
 
 
Figure 2.5. 3D structure and Top view of the 3D print at different switching times 
and resolutions 
 
 
26 
 
 
The circle pattern obtained from simulations is studied for two layers of printing in 
Fig. 2.6. The index of sphericity (Is) for the two layers formed at different printing 
conditions is also shown in Fig. 2.6. When the switching time is not optimized the 
second layer was less circular (high Is). In addition, with increase in resolution i.e. 
decrease in distance between the collector points from 1.53 mm to 1.04 mm (from 8 
collector points to 12 collector points) the pattern was more circular (low Is). 
 
Figure 2.6. Circle pattern at different switching times and resolutions obtained 
from simulations  
27 
 
 
Therefore, with the discretized model we can simulate the fiber motion for 
motionless 3D printing application and the model also incorporates the different 
switching times and resolutions of the desired pattern. In addition, the predictions from 
the discretized model can be used to decide the process conditions for the 3D printing 
of various other patterns. 
 
2.5 Conclusion 
In this study, simple 3D printing with the immersed electrospinning setup is studied 
experimentally and theoretically. To account for the liquid coagulation medium, the 
drag and the dielectric effects on the polymer are incorporated in the bead-spring model. 
In addition, to study the bending instability, normal mode perturbations are applied on 
the jet at the nozzle. The jet trajectory visualized with the high-speed camera is similar 
to the prediction by the model. From these results, we confirmed that the bending 
instability is electrically driven, as the growth rate is increased with the applied voltage. 
In addition, the fiber collection is controlled by switching the electric fields among the 
four copper plates on the collector to form a square pattern. The bead-spring model also 
predicted a square pattern formation of the deposited jet by applying a temporal 
boundary condition. However, an exact square pattern is not formed as the manual 
switching of the electric fields is difficult to effectively steer the fiber. The simulations 
were also used to study the 3D prints of a square and circular pattern at different 
switching times and resolutions of the collector plates. This approach for 3D printing 
can be further developed by using electrode arrays with MOSFETs for switching the 
28 
 
 
voltage at the lattice points. In addition, this approach can be applied to regular 
electrospinning setup by reducing the spinning distance to obtain a controlled 
deposition. Furthermore, as the predictions from the discretized model are similar to the 
experimental observations, and it can be used for designing complex motionless 3D 
printing. 
ACKNOWLEDGEMENTS 
Cornell Center for Materials Research Shared Facilities supported through the NSF 
MRSEC program (DMR-1120296). Cornell University Glass Shop for the fabrication 
of coagulation bath vessel, and Yevgen Zhmayev for his help with the flow visualization 
study. 
 
  
29 
 
 
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33 
 
 
CHAPTER 3 
WHIPPING INSTABILITY STUDY OF VISCOELASTIC AND CONDUCTING 
FLUIDS IN ELECTROHYDRODYNAMIC JET PRINTING SYSTEM 
3.1 Introduction 
Electrohydrodynamic (EHD) jet printing is a high (submicron) resolution inkjet 
printing technology as it can be used to fabricate functional devices with submicrometric 
resolution [1-3]. This process has gained attention as it is a non-contact, direct-write, 
low cost and environmentally friendly process [4-7]. In addition, using EHD printing 
process, we can control the generation and deposition of the print without adversely 
affecting the chemical properties of the deposited material or the substrate. In the EHD 
jet printing, there are two methods of printing based on the ejection of the ink: 
Continuous inkjet (CIJ), where jet emerges from the nozzle and Drop-On-Demand (D-
O-D) wherein the droplets are ejected out from the nozzle [8-10]. In both the methods 
of printing, the jet or droplet is ejected out of a cone-shaped liquid meniscus called 
Taylor cone when high voltage is applied to the liquid [11-13]. In this paper, we study 
the continuous inkjet method in the EHD process. 
This continuous inkjet method is similar to the electrospinning process, however, 
in the conventional electrospinning process the distance between the nozzle and the 
substrate is in the order of ~10 cm [14-18] and in the EHD printing approach the distance 
is 100 μm - 1 cm [4-13]. The large spinning distance in the electrospinning process leads 
to uncontrolled deposition due to whipping instability resulting from electrical repulsive 
force on the jet [19]. In general, in the electrospinning process, there is a stable jet region 
34 
 
 
near the nozzle and then onset of the whipping motion occurs downstream of the jet. 
Therefore, the whipping instability can be reduced by shortening the spinning distance 
(distance between the nozzle and the collector) for maximum utilization of the stable jet 
region. However, the applied voltage difference in the spinning gap should also be 
reduced to have a controlled electric field in the spinning gap. To obtain good quality 
patterns with controlled deposition, it is essential to study how the different process 
parameters affect the whipping motion of the jet.   
In the current work, we study the onset of the whipping motion of the jet in the 
EHD jet system from simulations and experiments. There have been several works in 
predicting the diameter of the jet but there have not been many studies on predicting the 
stable jet length. In this work, we studied the behavior of 3 different fluids in the EHD 
jet system. These different fluids vary in their viscoelasticity and conductivity as 
follows: i) Polyisobutylene/polybutene – high viscoelasticity and low conducting ii) 
Silver nanoparticle ink – low viscoelasticity and high conducting iii) Polyethylene 
oxide/water – high viscoelasticity and high conducting. We first compare the Taylor 
cone behavior and the stable jet radius of the three model fluids. Later, we study the 
effect of viscoelasticity and conductivity on the onset of whipping motion for the model 
fluids and compare the simulation predictions with experiments.   
 
 
 
 
35 
 
 
3.2 Experimental procedure 
3.2.1 Experimental fluids 
The solutions used for the electrohydrodynamic setup are: i) 4000 ppm 
polyisobutylene (PIB) in polybutene (PB) ii) 2.5 wt% polyethylene oxide (PEO) in 
water iii) Silver ink. The PIB/PB solution is prepared using PIB with Mw ~ 106 (Aldrich) 
and PB solvent (Aldrich) with Mn ~ 320. The solution is prepared by using 
Trichloroethylene (TCE) as an intermediate solvent. PIB is first dissolved in TCE and 
later the solution is diluted to the desired concentration by adding PB. The resulting 
solution is stored in vacuum and at slight heating for a week to remove TCE solvent. 
The silver ink solution (Aldrich) used in the current study is a 30 wt% of silver 
nanoparticles in ethylene glycol solvent. The PEO/water solution was prepared by 
mixing PEO with Mw ~ 2x106 (Aldrich) in water. The electrical conductivity and 
relaxation time of the spinning solutions are shown in Table 1. 
Table 3.1. Material properties of the model fluids 
Electrical 
Spinning solution conductivity Relaxation Debye 
(micro S/cm) time (ms) length (nm) 
Polyisobutylene in Low conducting and 0.0003 3 NA 
polybutene viscoelastic 
Silver High conducting 
nanoparticle ink and non-viscoelastic 3.21 0.145 25 
Polyethylene High conducting 
oxide in water and viscoelastic 140 200 2 
 
 
 
36 
 
 
3.2.2 Experimental setup 
The experimental setup for the electrospinning is illustrated in Figure 3.1. The 
spinning solutions is pumped out of a 20-gauge needle at a flowrate of 0.2 ml/min by 
using a programmable PHS Ultra syringe pump (Harvard Apparatus). The voltage 
difference in the spinning gap is obtained with a Gamma High Voltage Research 
voltmeter. The experiments are conducted for 3-8 kV voltage differences and the 
spinning distance is at ~ 1-5 cm. The voltage difference is applied to a flat plate near the 
nozzle and the collector as shown in the Fig. 3.1. The spinning behavior of the polymer 
fiber is visualized using a high-speed camera (RedLake MotionPro HS-3 with Nikon 
MICRO NIKORR 60mm 1:2:8 lens). The images are taken at 1000 frames per second. 
Finally, the images are digitized using MotionStudio x64 software and are analyzed 
using ImageJ. 
 
Figure 3.1. Electrohydrodynamic jet system schematic 
 
37 
 
 
3.3 Simulation procedure 
In the current work, we use a discretized model to study the whipping motion 
behavior of the jet in the electrohydrodynamic printing system. The discretized model 
used is a bead-spring model, in which, the jet is assumed to be a series of beads attached 
with springs [17-20]. This model has been previously used to model the whipping 
motion and 3D printing using the electrospinning system [19]. However, in this study 
we study the onset of whipping, which is the axial position at which the whipping starts 
to occur. The onset of whipping is studied for 3 solutions: i) polyisobutylene/polybutene 
(low conducting and viscoelastic), ii) Silver nanoparticle ink (high conducting and non-
viscoelastic), and iii) polyethylene oxide/water (high conducting and viscoelastic) 
In the model, the equations of motion are applied to the beads which solves for the 
trajectory vector of the beads from the forces in the system. The whipping motion of the 
jet is studied by applying a normal mode perturbation to the position vector of the bead 
in the nozzle [19].  
The simulation begins with introducing a bead ‘i’ of mass 𝑚", length 𝑙" and radius 
𝑟" in the nozzle. The forces acting on the bead ‘i’ are surface tension 𝑭𝒔𝒕,𝒊, viscoelastic 
force 𝑭𝒗,𝒊, drag force 𝑭𝒅,𝒊, electric force 𝑭𝒆,𝒊 and gravitational force 𝑭𝒈,𝒊. We obtain the 
position vector of the bead from Newton’s second law of motion (Eq. (3.1)).  
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒔𝒕,𝒊 + 𝑭𝒗,𝒊 + 𝑭𝒅,𝒊 + 𝑭𝒆,𝒊 + 𝑭𝒈,𝒊,																																(3.1) 
The surface tension force, viscoelastic force, drag force and gravitational force are 
obtained from the motionless printing using electrospinning work by Divvela et al 
38 
 
 
[19,21]. The electric field force used in this model is different from the previous model 
used in electrospinning. Most of the electrospinning studies use uniform applied electric 
field V0/h, with V0 as the applied voltage difference and h as the spinning distance. 
However, in reality a highly divergent field is expected at the needle tip [22]. As the 
distance between the needle and the collector is lower in the current system, it is 
important to incorporate the effect of the diverging field. Therefore, the electric field 
equation as given in Eq. (2) is used to give a more realistic expression of the divergent 
field near the needle. This electric field result was compared with numerical results from 
boundary element simulations and it provides a good approximation to the electric field. 
2𝑉
𝐸Š(𝑧) = (𝑎 + 2𝑧 − 𝑧=/ℎ)ln	(1 + 4ℎ/𝑎 ),																																			(3.2) r r
Where, 𝐸Š is the electric field due to the voltage difference in the spinning gap,	𝑧 
is the axial distance from the needle, 𝑉 is the voltage applied to the needle, ℎ is the 
spinning gap, and 𝑎r is the radius of the needle. 
The jet in the electrospinning studies act as a leaky dielectric where the charges in 
the jet separate at the surface of the jet and the electric field interacts only with the 
surface charges. However, this is valid for liquids with are not highly conducting and 
also not very insulating. For high conducting liquids, all the charges will not separate 
on the jet surface and the electric field interacts only with a fraction of the charges 
depending on the Debye length of the liquid [17]. The equation for Debye length for an 
electrolyte or colloidal suspension is in Eq. (3.3) [23]. 
39 
 
 
𝜀 𝜀 𝑘 𝑇
𝜆 = Ž
n r 
2 × 10t𝑁 𝑒=𝐼 	,																																																												(3.3) ”
Where, 𝜆 is the Debye length, 𝜀n is the relative permittivity of the solution, 𝜀r is 
the permittivity of free space, 𝑘 is the Boltzmann constant, 𝑇 is the temperature, 𝑁” is 
the Avogadro number and 𝑒	is the elementary charge. 
The electric force on a bead ‘i’ is given in Eq. (3.4). For highly conducting liquids, 
as the electric field interacts only with the charges within the Debye length, the Debye 
length (𝜆) is multiplied with charge and electric field. The electric field on the element 
i, has two terms: i) Electric field due to the applied voltage on the needle, and ii) 
Coulombic interaction with the rest of the beads j with charge 𝑞k within the Debye 
length (𝜆) at a distance 𝑥"k from bead ‘i’. The surface charges are conserved by 
considering the convection and conduction currents, as given by Divvela et al. [18,19].  
1 𝜆	𝑞𝑭𝒆,𝒊 = 𝑞"𝑬𝒆,𝒊 = 𝜆	𝑞" p𝐸Š(𝑧)𝒆𝒛 + 4𝜋𝜖 s
k
𝑥 t 𝒙𝒊𝒋w,																				(3.4) r kv" "k
The onset of whipping motion in the system is studied by introducing a non-
axisymmetric normal mode perturbation at the nozzle to the x and y coordinates (Eqs. 
(3.5)-(3.6)) [19]. We consider the mode of the perturbation with maximum growth rate. 
The amplitude of the perturbation is 𝛿 and 𝑓 is the frequency of the perturbation. The 
terms 𝑥y and 𝑦y are the stable jet coordinates. 
𝑥 = 𝑥y + 𝛿 cos(𝑓𝑡),																																																														(3.5) 
𝑦 = 𝑦y + 𝛿 sin(𝑓𝑡),																																																															(3.6) 
40 
 
 
3.4 Results and Discussion 
3.4.1 Jet behavior of the spinning solutions 
In this section, the radius thinning profile for three spinning solutions: i) PIB/PB, 
ii) Silver ink, and iii) PEO/water are obtained from experiments and simulations.    
The radius thinning profile of PIB/PB solution from Fig. 3.2(a) shows the formation 
of Taylor cone. The electric field makes the liquid meniscus of the needle unstable and 
the meniscus forms a cone shape and the jet extends from this Taylor cone. The radius 
of the jet in the stable region is around 60 microns.  
The simulation and experimental result of the radius profile for silver ink is shown 
in Fig. 3.2(b). The Taylor cone formation is observed even for the silver ink case. 
However, the shape of the Taylor cone is different from the PIB/PB solution. The initial 
thinning in the silver ink case is higher compared to PIB/PB solution. This difference is 
due to the difference in the conductivity of the solutions. The high conductivity of the 
silver ink solution causes it to undergo higher thinning compared to PIB/PB solution. In 
addition, the viscoelasticity causes rapid thinning in the jet due the jet extension. The 
stable jet radius of the jet is around ~ 25 microns. 
The radius thinning profile of PEO/water solution from Fig. 3.2(c) shows a rapid 
thinning near the nozzle. Unlike PIB/PB or silver ink system PEO/water solution does 
not form Taylor cone at the nozzle. The high viscoelasticity and conductivity of the 
PEO/water solution results in instantaneous thinning of the jet at the nozzle. In addition, 
the jet undergoes slower thinning downstream of the jet due to high polymeric stress 
within the jet which resist the extensional flow. The radius of the stable jet for 
41 
 
 
PEO/water solution is around 40 microns, which is lower than the stable jet radius of 
silver ink solution as the high viscoelasticity of PEO/water solution causes strain 
hardening downstream of the jet and inhibits the extensional flow. 
 
Figure 3.2. Radius thinning profile of: a) PIB/PB b) Silver ink c) PEO/water 
 
3.4.2 Onset of whipping study 
The jet trajectory of PIB/PB solution is observed through high speed imaging at 
two spinning distances 3 cm and 1 cm and the applied voltage is kept constant at 8 kV. 
The radius of the jet for Fig. 3.3(a) when the spinning distance is 3 cm is lower (50 
microns) compared to the jet radius when the spinning distance is 1 cm (20 microns). 
This is because, when the voltage is kept constant the electric field is higher at lower 
spinning distance, which leads to increase in the extension of the jet.  
42 
 
 
We can observe from the experimental results in Fig. 3.3 that there is no onset of 
whipping observed for PIB/PB solution. The low conducting PIB/PB solution is not 
affected by the surface charges on the jet under the electric field. We obtained the 
trajectory of the jet in the XZ plane from the simulations to compare with the 
experimental observation. Even from the simulations we can observe that there is no 
whipping motion observed for PIB/PB solution. As PIB/PB solution has low 
conductivity, the onset of whipping is not observed. The whipping motion under electric 
field is in conducting mode and depends on the conductivity of the solution as it occurs 
due to Coulombic repulsion between the surface charges of the jet.  
a)                                                           b) 
1 mm 1 mm 
  
Figure 3.3. Experimental imaging of PIB/PB solution at a) 8 kV and 3 cm b) 8 kV 
and 1 cm 
 
43 
 
 
The onset of the whipping for silver ink solution is observed from the high speed 
camera images of the experiments at two different spinning distances (1 cm and 0.5 cm) 
and voltage conditions (6 kV and 8 kV) (Fig. 3.4). We can observe earlier onset of 
whipping (by ~0.6 mm earlier for 0.5 cm compared to 1 cm) for lower spinning distance. 
The high electric field at lower spinning distance is responsible for the earlier onset of 
the whipping motion. In addition, the amplitude of the whipping instability increases 
with increase in the electric field.  
  
 
 
 
 
 
 
 
 
 
 
 
44 
 
 
 
Figure 3.4. High speed camera image of the experimental result at voltage and 
spinning distance a) 6 kV and 1cm b) 8 kV and 1 cm c) 6 kV and 0.5 cm d) 8 kV and 
0.5 cm 
45 
 
 
We can observe from Fig. 3.5 that with increase in the electric field, the onset of 
the whipping position is predicted to be lower from simulations. The simulation 
predictions agree with the experimental results obtained from high speed camera 
images. The whipping motion of the jet is closer to the needle and the stable jet region 
is smaller at shorter spinning distance. In addition, at lower spinning distance the onset 
of whipping distance from the needle is smaller due to high electric field in the spinning 
region at lower spinning distance and constant applied voltage. 
5
4.5
4
3.5 y	=	-0.2668x	+	4.7179
3
2.5
2 y	=	-0.246x	+	4.6778
1.5
1 Experiment
0.5 Simulation
0
0 2 4 6 8 10 12
Electric	field	(kV/cm)  
Figure 3.5. Comparing the position of the onset of the whipping from simulations and 
experiments at different electric fields for silver ink solution 
The high speed camera images for PEO/water solution are obtained for two 
different spinning distances 3 cm and 1 cm. The voltage conditions used for 3 cm 
spinning distance are 8 kV,12 kV and 16 kV and for 1 cm spinning distance the voltage 
conditions are 6 kV and 8 kV. At 8 kV and 3 cm there is no whipping observed in the 
captured length of the frame in the high speed camera image. However, with increase 
46 
 
Onset	of	whipping
 
in the applied voltage from Fig. 3.6(a)-(c) we can observe that the onset of the whipping 
occurs closer to the nozzle. At 1 cm spinning distance, the whipping is more chaotic as 
observed from Fig. 3.6(d), and the effect of the spinning distance and voltage is more 
prominent for PEO/water compared to PIB/PB solution. The high conductivity of the 
PEO/water solution makes it is more susceptible to the electric field. 
47 
 
 
  
Figure 3.6. High speed camera images of PEO/water solution at voltage and spinning 
distance a) 8 kV 3 cm b) 12 kV 3 cm c) 16 kV 3 cm d) 6 kV 1 cm e) 8 kV 1 cm 
48 
 
 
The simulation result of the jet trajectory for three different voltages (6 kV, 7 kV 
and 8 kV) and at spinning distance of 1 cm is shown in the Fig. 3.7. From the simulation 
result, the jet trajectory for 8 kV shows an earlier onset of whipping compared to 6 kV 
and 7 kV as observed from the high speed camera images. The whipping amplitude for 
8 kV is larger than for 7 kV and 6 kV. In the simulation the perturbation is applied at the 
nozzle and it grows as it travels along the length of the jet. The growth of the 
perturbation depends on the forces that are applied on the jet. 
0
-0.2 -0.1 -2 0 0.1 0.2
-4
-6
-8
6	kV
-10 7	kV
-12 8	kV
-14 X  
Figure 3.7. Effect of voltage on the jet trajectory of PEO/water 
The onset of the whipping motion from simulations is compared with experiments 
and we can observe that the onset occurs earlier at higher voltage and the stable jet 
region is smaller. At lower spinning distance the onset occurs even earlier.  
 
 
 
 
49 
 
Z
 
8
7 Experiment
6 Simulation
5
4
3
2
1
0
0 10 20 30 40
Electric	field	(kV/cm)  
Figure 3.8. Comparing the position of the onset of the whipping from simulations and 
experiments at different electric fields for PEO/water solution 
The onset position of the whipping motion is analyzed for the silver ink and 
PEO/water cases using dimensionless parameters using the time scales of the of the 
main driving processes of the system (Eqs. (3.7) & (3.8)). The dimensionless parameters 
considered in the system are electrostatic force parameter (ℇE) and electric field Péclet 
number (PeE). The electrostatic force parameter is the ratio of characteristic times for 
electric field and inertia. In Eq. (3.7), the characteristic electric field (E0) is obtained 
from the ratio of total current to conductive current in the jet (𝐸r = 𝐼/𝜋𝐾𝑟r𝜆) [14]. 
Debye length (𝜆) is included in the conductive current as the conduction of the charges 
to the jet surface within the Debye length region is significant for high conducting fluids. 
The electric field Péclet number is the ratio of time scales for electrical conductivity and 
convection of charges [14].   
50 
 
Onset	of	whipping	(mm)
 
𝜀 𝐸= 𝑡
𝜀 =  r™ = =
›)›A
𝑡 ,																																																											(3.7) 𝜌𝑣r "Z›nW"œ
2𝜀 𝑣 𝑡
𝑃𝑒 =  r = ›)›AžAhZF™ 𝐾𝜆 𝑡 ,																																																					(3.8)  AhZŠ
In Eqs. (3.7) & (3.8), 𝜀 is the permittivity of free space, 𝜌 is the density of the 
spinning jet, 𝑣r is the characteristic velocity, 𝐾 is the electrical conductivity and 𝜆 is 
the Debye length. 
In the Fig. 3.9, a modified PeE is used taking into account the convection of the 
instability along the axis of the jet. The modified 𝑃𝑒™ is given in Eq. (3.9) and 𝑟r is the 
radius and ℎ is the stable jet length. 
𝑟
𝑃𝑒Ÿ r™ = 𝑃𝑒™ × ℎ ,																																																																			(3.9) 
The ℇE Vs PeE' is plotted for the silver ink and PEO/water systems in Fig. 3.9. The 
ℇE value is observed to increase linearly with PeE'. As PeE' is inversely proportional to 
the conductivity of the solution, values for PEO/water system are at low PeE' 
dimensionless number compared to the silver ink system. However, one value for 
PEO/water system is at higher PeE' because of earlier onset position of the whipping 
motion. From Fig. 3.10, the plot for ℇE Vs PeE' shows the linear regression line and the 
simulation and experimental result give similar slope and intercept values. The 
empirical correlation obtained from the experiments and simulation is given in Eq. 
(3.10) & (3.11) respectively. The correlation can be used as a guideline to predict the 
stable jet length as the values of ℇE and PeE are known from the process conditions and 
printing solution properties.  
𝜀™,› Y = 1.0153𝑃𝑒Ÿ™ − 1.1494,																																																			(3.10) 
51 
 
 
𝜀™,y"% = 0.9241𝑃𝑒Ÿ™ − 0.9551,																																																			(3.11) 
10
Experiment	(Ag	ink)
8 Simulation	(Ag	ink)
Experiment	(PEO)
6 Simulation	(PEO)
4
2
0
0 2 4 6 8 10 12
PeE'  
Figure 3.9. ℇE Vs PeE' plot for silver ink and PEO/water solution 
10
9
Experiment y	=	1.0153x	- 1.1494
8
7 Simulation y	=	0.9241x	- 0.9551
6
5
4
3
2
1
0
0 2 4 6 8 10 12
PeE'
 
Figure 3.10. ℇE Vs PeE' linear regression plot for experimental and simulation results 
for silver ink and PEO/water solutions 
52 
 
ℇE ℇE
 
3.5 Conclusions 
The whipping instability in the electrohydrodynamic (EHD) jet system affects the jet 
trajectory and its control deposition for printing process. In the current study, three 
different model fluids are chosen for the study based on their viscoelasticity and 
electrical conductivity; i) polyisobutylene in polybutene (PIB/PB): high viscoelasticity 
and low conducting, ii) Silver ink: low viscoelasticity and high conducting, and iii) 
Polyethylene oxide in water (PEO/water): high conducting and high viscoelasticity. The 
radius thinning profile of the jet is compared between the three fluids from simulations 
and experiments. PIB/PB and silver ink jet showed Taylor cone behavior at the tip of 
the nozzle and PEO/water jet showed instantaneous thinning at the nozzle due to its high 
viscoelasticity. In addition, to study the effect of whipping instability for these three 
model fluids, the onset of the whipping motion is studied from bead-spring model 
(simulations) and high speed camera images of experiments at different applied voltage 
and spinning distance. PIB/PB solution did not show any whipping motion due to its 
low conductivity. However, the high conducting PEO/water solution had smaller jet 
length (i.e. earlier onset of whipping motion). With the choice of right process 
conditions and material properties of the printing solution the whipping instability can 
be controlled. Furthermore, the predictions from the simulations show a good match 
with the experiments, and it can be useful to predict the conditions for the printing 
solution to obtain an accurate pattern. 
 
  
53 
 
 
REFERENCES 
 
[1] Y. H. Chuang and W. J. Dong, Manufacturing Letters 2 96-99 (2014).  
	
[2] M. N. Awais, H. C. Kim, Y. H. Doh and K. H. Choi, Thin Solid Films 536 308-312 
(2013).  
	
[3] Park J. -U., Hardy M., Kang S. J., Barton K., Adair K., Mukhopadhyay D. K., Lee 
C. Y., Strano M. S., Alleyne A. G., Georgiadis J. G., Ferreira P. M. and Rogers J. A., 
Nature Materials, 6 782 (2007). 
 
[4] D. B. Chrisey, Science 289 879-881 (2000). 
 
[5] P. Ferraro, S. Coppola, S. Grilli, M. Paturzo, and V. Vespini, Nat. Nanotechnol. 5 
429 (2010). 
 
[6] P. Jaehong, P. Ji-Woon, N. Ali Mohamadi and H. J. Hwang, Appl. Phys. Lett. 109 
134104 (2016). 
 
[7] V. D. Nguyen and D. Byun, Appl. Phys. Lett. 94 173509 (2009). 
 
[8] R. G. Sweet, U.S. Patent 3596275 (1971). 
 
[9] Mishra S., Barton K. L., Alleyne A. G., Ferreira P. M. and Rogers J. A., J. 
Micromech. Microeng. 20 (2010) 095026. 
 
[10] E. L. Kyser and S. B. Sears, U.S. Patent 3946398 (1976).  
 
[11] G.I. Taylor, Proc. R. Soc. Lond. A 280 383–397 (1964). 
 
[12] G.I. Taylor, Proc. of the Royal Society of London A: Mathematical, Physical & 
Eng. Sci., 291, 145-158 (1965).  
 
[13] G.I. Taylor, Proceedings of the RoyalSociety of London A: Mathematical, Physical 
& Engineering Sciences 313 453-475 (1969). 
 
[14] C.P. Carroll, Y.L. Joo, Phys. Fluids 18 053102 (2006). 
 
[15] C. P. Carroll, Y. L. Joo, J. Non-Newtonian Fluid Mech. 153 130-148 (2008).  
 
[16] C. P. Carroll, Y. L. Joo, Phys. Fluids 21 103101-102110 (2009). 
 
54 
 
 
[17] C.P. Carroll, Y.L. Joo, Journal of Applied Physics 109 094315-094319 (2011). 
 
[18] M. J. Divvela, Y.L. Joo, J. Appl. Physics 121 134306 (2017). 
 
[19] M. J. Divvela, L. M. Shepherd, M. W. Frey and Y. L. Joo, 3D Printing and Additive 
Manufacturing 5 248-256 (2018). 
 
[20] M. J. Divvela, A.C. Ruo, Y. Zhmayev, Y.L. Joo, J. Non-Newtonian Fluid Mech., 
247 62–77 (2017).  
 
[21] M. J. Divvela, R. Zhang, Y. Zhmayev, S. Pinge, J. H. Lee, S. W. Kim and Y.L. 
Joo, Small (2019) (Manuscript submitted).  
 
[22] S. S. Bamji and A. T. Bulinski, IEEE Trans. Electr. Insul. 28 420 (1993). 
 
[23] W. B. Russel, D. A. Saville and W. R. Schowalter, Colloidal Dispersions, 
Cambridge University Press (1989).  
  
55 
 
 
CHAPTER 4 
CONTROLLED DEPOSITION AND MOTIONLESS PRINTING OF 3D 
PATTERNS USING MELT ELECTROSPINNING SYSTEM 
4.1 Introduction 
The field of 3D printing has gained attention and has become a viable industrial 
production technology because of several advantages like rapid prototyping, on-demand 
and customized manufacturing with complex shapes and geometry, repeatability and 
precision [1-3]. The three-dimensional object is built from a digital 3D or a computer 
aided design model by successively adding material layer by layer. Most of the 
commercially available 3D printers use polymer melt extrusion for the printing process 
[1-5]. The polymer resin is heated to its melting temperature in a reservoir and it is 
extruded out of a nozzle at a constant flow rate towards a collector or substrate. 
Additionally, the melt electrospinning process, wherein a voltage difference that is 
applied to the spinning gap can form thinner fibers (micron to submicron range) 
resulting in the formation of high resolution printing patterns.  
In the melt electrospinning process, the repulsion between the surface charges of 
the jet due to the electrical field can cause whipping instability because of which the jet 
travels in a helical path with increasing radial distance as it travels away from the nozzle 
[6, 7]. The whipping instability does not occur near the nozzle but at a point downstream 
of the jet, and the initial region near the nozzle without the instability is the stable jet 
region. For the melt electrospinning setup to be used for 3D printing application, it is 
essential to study the onset of the whipping instability to obtain controlled pattern 
56 
 
 
formation. In the conventional 3D printing technique, the printing pattern is formed 
from the mechanical motion of the nozzle or the collector which results in long print 
time, noise and accuracy of the pattern [1-5]. However, recently Larissa et al. [8] and 
Divvela et al. [7] studied a motionless printing approach in which the nozzle and 
collector are stationary, and the electric field steers the printing jet to form the necessary 
pattern. This switching of electric field can be attained by designing the collector with 
different conducting points and automating the voltage at these points to form the 
pattern. 
In this work, we study the onset of the whipping instability and motionless 3D 
printing approach using the melt electrospinning system from simulations and 
experiments. For the simulations, we use a discretized model in which the jet is assumed 
to be made of beads connected with springs [9-11]. This discretization approach reduces 
the computation time required for solving the equations of motion and can easily track 
the 3D trajectory of the jet under whipping motion. The predictions for the simulation 
are essential to obtain the necessary process conditions to control the onset of whipping 
instability. In addition, for 3D motionless printing, the switching time of the voltage at 
different conducting points on the collector can be predicted with the simulations and 
these values can be used as a baseline for the automation of printing the desired pattern. 
 
 
 
 
57 
 
 
4.2 Experimental Procedure 
The schematic of the experimental setup for the melt electrospinning study is shown 
in Fig. 4.1. The basic components are a micro-flow controller (PHD2000, Harvard 
Apparatus), a high-voltage supplier (ES30P, Gamma High Voltage Research, Inc.), and 
a collector. The collector is designed with different conducting points for the motionless 
printing application. The experiments were performed using a PLA resin obtained from 
Cargill-Dow and has a molecular weight around 186,000 and polydispersity of 1.76 with 
major L configuration. PLA resins are kept in a 5-ml syringe and heated for half an hour 
in the shielded heating unit at 200 ◦C. The micro-flow controller then fed the PLA melt 
through a nozzle with a flow rate from 0.01 to 0.1 ml/min. Temperature of the nozzle 
ranged from 185 to 255 ◦C, and the potential difference and distance between the nozzle 
and the collector were 5–25 kV and 0.1 m, respectively. The charged melt jet was spun 
either with or without the heated guiding chamber before being collected on an air-
cooled collector. To verify the suppression of the whipping motion of the PLA melt jet 
during electrospinning, a high-speed camera (MotionPro HS-3, Redlake) was utilized 
to record a close-up high speed (1000–5000 frames per second) movie of the PLA melt 
jet near the collector at various spinning temperatures. 
58 
 
 
 
 
Figure 4.1. Experimental setup for motionless printing with melt electrospinning  
 
4.3 Simulation Procedure 
The jet behavior in the melt electrospinning setup is simulated to study the 
whipping instability and obtain pattern formation with the system. The simulation of the 
system is performed by using a discretized model in which the jet is considered to be a 
series of beads with springs [9-11]. In this model, the equations of motion using 
Newton’s second law are applied to the beads (Eq. (4.1)).  
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒔𝒕,𝒊 + 𝑭𝒗,𝒊 + 𝑭𝒅,𝒊 + 𝑭𝒆,𝒊 + 𝑭𝒈,𝒊,																																			(4.1) 
Where,	𝒙𝒊 is position vector, 𝑚" is the mass of the bead, 𝑭𝒔𝒕,𝒊 is surface tension force, 
𝑭𝒗,𝒊 is viscoelastic force, 𝑭𝒅,𝒊 is drag force, 𝑭𝒆,𝒊 is electric force and 𝑭𝒈,𝒊 is gravitational 
force. The surface tension force, drag force, gravitational forces are similar to the 
previous electrospinning studies [7, 11].  
59 
 
 
The electric field force used in this model is different from the previous model used 
in electrospinning. Most of the electrospinning studies use uniform applied electric field 
V0/h, with V0 as the applied voltage difference and h as the spinning distance. However, 
in reality a highly divergent field is expected at the needle tip [12]. As the distance 
between the needle and the collector is lower in the current system, it is important to 
incorporate the effect of the diverging field. Therefore, the electric field equation as 
given in Eq. (4.2) is used to give a more realistic expression of the divergent field near 
the needle. This electric field result was compared with numerical results from boundary 
element simulations and it provides a good approximation to the electric field. 
2𝑉
𝐸Š(𝑧) = (𝑎 + 2𝑧 − 𝑧=/ℎ)ln	(1 + 4ℎ/𝑎 ),																																												(4.2) r r
Where, 𝐸Š is the electric field due to the voltage difference in the spinning gap,	𝑧 
is the axial distance from the needle, 𝑉 is the voltage applied to the needle, ℎ is the 
spinning gap, and 𝑎r is the radius of the needle. 
The electric force on a bead ‘i’ is given in Eq. (4.3). The electric field on the element 
i, has two terms: i) Electric field due to the applied voltage on the needle, and ii) 
Coulombic interaction with the rest of the beads j with charge 𝑞k at a distance 𝑥"k from 
bead ‘i’.  
1 	𝑞
𝑭𝒆,𝒊 = 𝑞"𝑬
k
𝒆,𝒊 = 𝑞" p𝐸Š(𝑧)𝒆𝒛 + 4𝜋𝜖 s𝑥 t 𝒙𝒊𝒋w,																												(4.3) r kv" "k
The equilibrium value of the surface charge on the jet is obtained by assuming the 
radial charge conduction is instantaneous (Eq. (4.4)). This assumption is the extreme 
60 
 
 
case of “leaky dielectric” model in which the electric charge migrates quickly to the jet 
surface for slightly conducting fluids [13]. In addition, the conductivity of the melt 
solution is very small which results in negligible conduction current and the convection 
current is equal to the total current.  
𝑞 = 2𝜋𝑎𝜀r|𝑬𝒆|,																																																															(4.4) 
The viscoelastic force acting on a bead ‘i’ from its neighboring elements is written as  
𝑭 = =𝒗,𝒊 = (𝜋𝑎F"𝜏F")𝒆𝒅𝒊 − (𝜋𝑎G"𝜏G")𝒆𝒖𝒊,																																										(4.5) 
Where, 𝜏 is the viscoelastic stress and 𝒆𝒅𝒊 and 𝒆𝒖𝒊 are the orientations of 
downstream and upstream elements respectively and 𝑎F" and 𝑎G" are the radius of 
downstream and upstream elements. The viscoelastic stress has two components: 
polymeric stress and Newtonian solvent stress. The polymeric stress is described by the 
non-isothermal form of Giesekus model [14].  
𝑑𝑙
𝜏 = 𝜏Y + 𝜏y = 𝜏Y + 𝜇y𝑓Š 𝑙𝑑𝑡 ,																																																						(4.6) 
𝑇n›R 𝑑𝜏Y 1 𝑑𝑇 𝜆 𝑇𝜏 + 𝜆𝑓 ¡ n›R =
𝑑𝑙
Y Š 𝑇 𝑑𝑡 − 𝜏Y 𝑇 D𝑑𝑡H¢ + 𝛼 𝜇 𝑇 𝜏Y = 𝜇Y𝑓Š 𝑙𝑑𝑡 ,																							(4.7) Y
𝜇(𝑇) ∆𝐻 1 1
𝑓Š = = exp¡𝑅 ª𝑇 − 𝑇 «¢,																																			(4.8) 𝜇†𝑇n›R‡ "© n›R
Where, 𝑇n›R is the reference temperature, 𝛼 is the mobility factor, ∆𝐻 is the 
activation energy of the flow, 𝑅"© is the ideal gas constant,	𝜆 is the polymer relaxation 
time at the reference temperature, and 𝑓Š represents the temperature dependence of the 
zero-shear-rate viscosity. The subscripts s and p indicate the contributions from the 
61 
 
 
solvent and the polymer, respectively. Likewise, 𝜇y and 𝜇Y represent the contributions 
of polymer and of solvent to the zero-shear-rate viscosity,	𝜇. 
𝜇 = 𝜇y + 𝜇Y,																																																																								(4.9) 
The temperature 𝑇 for each element is updated by considering the 1-D energy 
equation on a fluid element (Eq. (4.10)). The energy balance includes the viscous 
dissipation in the jet and heat transfer with the surrounding air.   
𝑑𝑇 𝜏 𝑑𝑙 2ℎ(𝑇 − 𝑇 )
𝜌𝐶 œ"nY 𝑑𝑡 = 2 𝑙𝑑𝑡 − 𝑎 ,																																																		(4.10) 
Where, 𝐶Y is the heat capacity per unit mass, ℎ is the heat transfer coefficient in 
the surrounding air, and 𝑇œ"n is the bulk cooling air temperature. The heat transfer 
coefficient can be estimated by generalizing the Kase-Matsuo’s empirical formula [15] 
(Eq. (4.11)). 
c c/±
2𝑎ℎ 2|𝑽W|𝑎 t 𝜌œ"n𝐶Y,œ"n𝜈
c/= 8|𝑽 | =
𝑁𝑢 = 𝑘 = 0.495ª « D
œ"n
𝜈 𝑘 H ¯1 + ª
𝒏
|𝑽 | « ° ,											(4.11) œ"n œ"n œ"n 𝒕
Where, 𝑽𝒕 and 𝑽𝒏 are the tangential and normal velocity of the jet relative to the 
external air velocity. 𝜌œ"n, 𝐶Y,œ"n, 𝑘œ"n and 𝜈œ"n are the density, heat capacity, thermal 
conductivity and kinematic viscosity of air, respectively. These properties, excluding 
𝐶Y,œ"n, are function of temperature and evaluated at air temperature (𝑇œ"n) (Eq. (4.12)-
(4.14)). 
352
𝜌œ"n = 𝑇 ,																																																																																		(4.12) œ"n
𝑘 = 1.879 × 10ž²𝑇r.³±±œ"n œ"n ,																																																																(4.13) 
62 
 
 
𝑇=.µ
𝜈 = 4.291 × 10ž´ œ"nœ"n 𝑇 + 120,																																																										(4.14) œ"n
For dry air, the correlations (in SI units) can be used to < 2% error compared to tabulated 
values in the range 300 K < 𝑇œ"n < 650 K.  
 
4.4 Results and discussion 
4.4.1 Jet behavior in melt electrospinning system 
The radius thinning profile at three different temperatures is plotted in Fig. 4.2. The 
melt electrospinning jet at higher nozzle temperature undergoes faster thinning and 
forms thinner jets. The nozzle temperature affects the rheological properties of the melt, 
the viscosity at higher temperature is lower and the viscous forces that inhibit the inertia 
of the jet.  
 
1.2
1 T = 255 C
T = 230 C
0.8 T = 215 C
0.6
0.4
0.2
0
0 2 4 6 8 10
Length of the jet  
Figure 4.2. Radius thinning profile of the jet at different nozzle temperatures 
63 
 
Radius of the jet
 
The temperature variation along the length of the jet is shown in the Fig. 4.3. The 
jet temperatures are different near the nozzle. However, the temperature discrepancy 
disappears downstream of the jet and reaches almost a steady value. This behavior is 
due to the heat transfer with the surrounding cool air, in the current case, the surrounding 
temperature is 20 oC. 
300
250 T = 255
T = 230
200 T = 215
150
100
50
0
0 20 40 60 80 100 120
Length of the jet  
Figure 4.3. Jet temperature profile at different nozzle temperatures 
 
The radius thinning profile of the jet at different air temperatures with all the other 
process conditions constant is shown in Fig. 4.4. The jet temperature increases with the 
ambient air temperature resulting in different rheological properties of the jet and 
forming thinner jets at higher ambient air temperature. However, from the Fig. 4.4, we 
can observe that the difference radius is not very evident, so a log-scale plot was used 
to distinguish the radius profiles for different ambient air temperature cases. The initial 
thinning behavior is almost same for all three different cases as the jet is in contact with 
the nozzle and the temperature of the nozzle influences the jet behavior more than the 
64 
 
Temperature (C)
 
ambient air. However, downstream of the jet, at higher air temperature (100 oC) the jet 
undergoes further thinning and forms thinner fibers and at lower air temperature (20 oC) 
the further thinning of the jet is not observed and results in the formation of thicker jets. 
1
Tair = 20 C
Tair = 80 C
Tair = 100 C
0.1
0.01
0 50 100 150
Length of the jet  
Figure 4.4 Radius thinning profile at different air temperatures 
 
4.4.2 Onset of whipping motion 
The onset of the whipping motion in the melt electrospinning system is studied at 
different voltage and ambient air conditions. In general, the rapid chaotic motion of the 
jet due to whipping motion increases the extension of the jet and results in the formation 
of thinner jets. In the current study, as we are studying the melt electrospinning process 
for printing application the deposition of the jet cannot be controlled easily with 
whipping instability. Therefore, we are studying the onset of the whipping instability at 
different process conditions from experiments and simulations to predict the jet 
behavior and obtain the necessary conditions for printing process. 
65 
 
Radius of the jet
 
In Fig. 4.5(a) the jet trajectory in the XZ plane obtained from simulations is plotted. 
We can observe that an earlier onset of the instability is observed for high voltage (20 
kV) case compared to the 5 kV and 15 kV cases. The whipping instability is in 
conducting mode and the instability is caused from the electrical repulsion between the 
surface charges of the jet. The magnitude of the surface charges is proportional to the 
electric field acting on the jet (Eq. (4.2)). Therefore, earlier onset of the instability is 
observed at higher voltage. In addition, the amplitude of the whipping instability, which 
is the radial distance of the jet from the axis increases with the applied voltage.  
We can observe from Fig. 4.5(b) that with increase in the ambient air temperature, the 
onset of the whipping is earlier, and the whipping motion is more vigorous at higher 
temperature. The rapid cooling with the external air can suppress the whipping motion 
in the melt electrospinning setup. 
a)                                                             b) 
0 0
-0.1 -0.05 0 0.05 0.1 -0.4 -0.2 0 0.2 0.4
-50 -50
20 kV
-100 15 kV -100 Tair=25
5 kV
-150 -150 Tair=80
-200 -200
-250 -250
X X  
Figure 4.5. Jet trajectory in the XZ plane for cases: a) different voltages b) different 
air temperatures 
66 
 
Z
Z
 
The high speed camera images of the melt electrospinning of PLA is shown in Fig. 
4.6. The images are obtained for different voltage differences in the spinning gap and 
air temperatures by Zhou et al. [16]. From these experimental results, agreeing with the 
simulations, earlier onset and rigorous whipping motion are observed with increase in 
applied voltage and air temperature.  
 
 
 
 
 
 
 
67 
 
 
 
 
Figure 4.6. High speed camera images of jet trajectory to observe whipping motion 
near collector at air temperature a) 25 oC, and b) 80 oC [16] 
68 
 
 
The simulation and experimental results are compared in Fig. 4.7, the onset position of 
the whipping from the nozzle is plotted with respect to voltage and temperature. From 
Fig. 4.7(a), as the applied voltage increased from 5 kV to 20 kV, the onset position of 
the whipping motion reduced by ~25%. Whereas, with increase in the air temperature 
from 25 to 80 oC, the onset position reduced by ~45% from simulations and experiments 
(Fig. 4.7(b)).  
 
Figure 4.7. Onset of whipping motion position comparison between simulations and 
experiments at a) different voltages b) different air temperatures 
 
The onset position of the whipping motion is analyzed for the melt electrospinning 
system using dimensionless parameters using the time scales of the of the main driving 
processes of the system. The dimensionless parameters considered in the system are 
electrostatic force parameter (ℇE) and electric field Peclet number (PeE). The definitions 
of these dimensionless parameters are mentioned in Eqs. (4.15) & (4.16).  
69 
 
 
𝜀 𝐸=
𝜀 =  r
𝑡
= ›)›A™ = 𝑡 ,																																																											(4.15) 𝜌𝑣r "Z›nW"œ
2𝜀 𝑣 𝑡
𝑃𝑒 =  r™ 𝐾𝜆 =
›)›AžAhZF
𝑡 ,																																																					(4.16)  AhZŠ
 
In the Fig. 3.9, a modified PeE is used taking into account the convection of the 
instability along the axis of the jet. The modified 𝑃𝑒™ is given in Eq. (4.17). 
Ÿ 𝑟𝑃𝑒™ = 𝑃𝑒™ ×
r
ℎ ,																																																																			(4.17) 
The ℇE Vs PeE' is plotted for the melt electrospinning system in Fig. 3.9. The ℇE 
value is observed to increase linearly with PeE'. However, one value for PEO/water 
system is at higher PeE' because of earlier onset position of the whipping motion. From 
Fig. 3.10, the plot for ℇE Vs PeE' shows the linear regression line and the simulation and 
experimental result give similar slope and intercept values.  
0.25
0.2 y	=	18841x	- 0.5896
0.15
y	=	23994x	- 0.7196
0.1
Experiment
0.05 Simulation
0
0.00002 0.000025 0.00003 0.000035 0.00004 0.000045 0.00005
PeE  
Figure 4.8. ℇE	Vs PeE' for melt electrospinning system 
70 
 
ℇE
 
The effect of temperature is studied by modifying the electrostatic force parameter 
(ℇE') by including the effect of viscous forces. The modified equation for ℇE is given in 
Eq. (4.18). With increase in air temperature, the viscosity decreases increasing ℇE value 
(Fig. 4.9). In addition, the slope of the plot at 80 oC is lower compared to the slope at 25 
oC. At lower temperature, the jet solidifies early so the onset position is does not vary 
much with the change in the electric field. Therefore, the slope of the plots for 25 oC is 
higher and at 80 oC there is large variation in the onset position with electric field. 
Ÿ 𝜀
=
𝜀 = 
𝐸r𝑟r 𝑡›)›A 𝑡"Z›nW"œ 𝑡"Z›nW"œ
™ 𝑣 𝜂 = 𝑡 × 𝑡 = 𝜀™ × ,																								(4.18) r r "Z›nW"œ Š"yA 𝑡Š"yA
 
2.5
Experiment
2
Simulation
1.5
60-90	oC
1
0.5 25-60	oC
0
0 0.0001 0.0002 0.0003
PeE'  
Figure 4.9. ℇE'	Vs PeE' for melt electrospinning system to study the effect of air 
temperature 
 
 
71 
 
ℇE '
 
4.4.3 Motionless printing with melt electrospinning system 
The motionless printing approach is studied using the melt electrospinning system. 
This printing method was first attempted in an immersion electrospinning setup by 
Shepherd et al. [8] and Divvela et al. [7]. In their work, the electrospinning system is 
placed in a liquid medium and the whipping motion is controlled by the drag forces and 
dielectric effect of the spinning media on the jet. However, a proper contact of the 
material on the substrate is not achieved and because of which 3D structures are difficult 
to form with the immersion electrospinning system. To address this issue, we studied 
the modeling of the motionless printing method with melt electrospinning as the print 
can have contact and most of the current commercial printing approaches [1-3] use melt 
spinning. Therefore, the current commercially available 3D printers can be easily 
modified for motionless printing by using a different collector and applying voltage 
difference in the spinning with an external voltage source.  
In the motionless printing approach, the nozzle and the collector are stationary, and 
the printing jet changes its direction to forma desired pattern by changing the electric 
field. The collector is designed with several conducting points at which the collector has 
conducting material and is connected to voltage source. The conducting point on the 
collector is switched ON where we want the printing jet to land on the substrate and the 
voltage at this point is switched OFF, and then the next point is switched ON and the 
printing jet travels to this new point. In this way, the printing jet’s direction is steered 
towards the position it needs to land on the collector or the printing substrate for the 
pattern formation by changing the electric field.    
72 
 
 
In the current melt electrospinning study, the 3D print formation of a square pattern 
of size 1x1 cm is studied using the simulation. The voltage difference used is 10 kV and 
the distance between the nozzle and the collector is 5 cm. The square pattern from the 
simulations is obtained for different switching times of the electric fields between the 
conducting points and different resolutions of the conducting points (orange square 
points in the plots in Fig. 4.10) on the collector (Fig. 4.10). The switching time is 
optimized to obtain an accurate pattern, and later the number of conducting points are 
increased from 4 to 8 resulting in the improvement of the square pattern. 
This pattern formation will be attempted by experiments by automating the 
switching of the electric fields for the pattern formation. Each conducting point on the 
collector will be connected to an optocoupler which will send the voltage signal to these 
conducting points. The optocouplers are controlled with a microcontroller that is coded 
accordingly to automate voltage switching ON and OFF at different conducting points. 
The optocoupler communicates with the microcontroller using light as a signal so the 
high voltage that is used in electrospinning will not pass and destroy the microcontroller. 
73 
 
 
 
Figure 4.10. Simulation of motionless printing of 3D square pattern at different 
switching times and resolution 
74 
 
 
4.5 Conclusion 
Melt extrusion and melt electrospinning processes are used commercially for 3D 
printing application. Melt electrospinning process can be used to form high resolution 
patterns as it forms micro/nano sized fibers. However, the presence of electric field 
causes whipping instability of the jet which leads to uncontrolled deposition. This 
affects the printing process and therefore, in this work, we first studied the onset of the 
whipping instability from simulations and experiments. We used a bead-spring model 
to predict the position from the nozzle at which the onset of the whipping motion will 
occur. We also analyzed the onset of the whipping with respect to the time scales of 
electrical force and inertial force. Later, we used the simulation to obtain 3D printing 
structure for a square pattern using the motionless printing approach. In the motionless 
printing approach, the electric field direction is used to steer the direction of the printing 
jet to form the pattern and using the simulation the switching of the electric field to 
obtain an optimized pattern. The motionless printing can be attempted with the use of 
optocouplers that are controlled by a microcontroller to switch the electric field 
direction.    
 
  
75 
 
 
REFERENCES 
 
[1] C. W. Hull, US Patents US4575330A, 1986. 
 
[2] T. D. Ngo, A. Kashani, G. Imbalzano, K. T. Q. Nguyen, D. Hui, Composites Part 
B, 143, 172-196, 2018. 
 
[3] B. N. Turner, R. Strong, S. A. Gold, Rapid Prototyping Journal, 20, 192-204, 
2014. 
 
[4] B. L. Farrugia BL, T. D. Brown, Z. Upton, et al., Biofabrication 5, 025001, 2013.  
 
[5] T. D. Brown, F. Edin, N. Detta, et al., Mater Sci Eng, 45, 698–708, 2014. 
 
[6] D. H. Reneker, A. L. Yarin, H. Fong, et al., J Appl Phys, 87, 4531–4547, 2000. 
 
 
[7] M. J. Divvela, L. M. Shepherd, M. W. Frey and Y. L. Joo, 3D Printing and Additive 
Manufacturing 2018, 5, 248-256. 
 
[8] L. M. Shephard, M. W. Frey, Y. L. Joo, Macromol Mater Eng., 302, 1700148, 
2017. 
 
[9] C.P. Carroll, Y.L. Joo, Journal of Applied Physics 109, 094315-094319, 2011. 
[10] M. J. Divvela, A.C. Ruo, Y. Zhmayev, Y.L. Joo, J. Non-Newtonian Fluid Mech., 
247, 62–77, 2017.  
[11] M. J. Divvela, Y.L. Joo, J. Appl. Physics, 121, 134306, 2017. 
[12] S. S. Bamji and A. T. Bulinski, IEEE Trans. Electr. Insul., 28, 420, 1993. 
[13] E. Zhmayev, H. Zhou, Y. L. Joo, J. Non-Newtonian Fluid Mech., 153, 95–108, 
2008. 
 
[14] Y.L. Joo, J. Sun, M.D. Smith, R.C. Armstrong, R.A. Brown, R.A. Ross, J. Non-
Newt. Fluid Mech., 102, 37–70, 2002. 
 
[15] T. Matsuo, S. Kase, J. Appl. Polym. Sci., 20, 367–376, 1976. 
 
[16] H. Zhou, T.B. Green, Y.L. Joo, Polymer, 47, 7497–7505, 2006. 
 
 
76 
 
 
CHAPTER 5 
CONTROL OF FORMATION OF VISCOELASTIC DROPLETS AND 
DISTRIBUTION OF NANO-INCLUSIONS IN FUNCTIONAL DEPOSITION FOR 
LITHIUM-SULFUR BATTERIES 
5.1 Introduction 
Electrospray process is used to produce electrically charged droplets of size in 
micron and submicron range. This process is used in diverse applications like 
production of thin and uniform coating, nanodroplet and nanostructure production, 
biomedical engineering, energy storage and mass spectrometry[1-10]. In this process, the 
electrospraying liquid is pumped out of a needle through a syringe and an electric field 
is applied between the needle and the collecting plate. When the liquid is released out 
of the needle the electric field causes the charges to separate inside the liquid meniscus 
and it takes the shape of a cone at the needle, which is called as Taylor cone[11]. When 
Taylor cone becomes unstable, depending on the process conditions either jets or 
droplets are ejected from the cone[11-14]. The axisymmetric instability on the jet results 
in modulations in the radius of the jet. There have been several classical works on this 
mode of instability by Plateau and Rayleigh[15] who studied the onset of the instability 
on a free-falling stream.  
In the spray process for viscoelastic jets, the jet extends due to viscoelastic forces 
and the axisymmetric instability acts on the jet before the break-up. Whereas, in non-
viscoelastic liquids, the atomization of the meniscus at the nozzle is responsible for the 
formation of droplets. In the electrospray process, the electric field force is responsible 
for the growth of the instability and the jet breaks into droplets[16-18]. In the air spray 
77 
 
 
process, the external air flow is applied axially to the jet and the air drag accelerates the 
growth of the axisymmetric instability. In the current work, we look at spray phenomena 
for the following cases: i) electrospray (only electric field), ii) air spray (only airflow) 
and iii) air controlled electrospray (airflow and electric field).  
There are several theoretical studies on the shape of Taylor cone and electrically 
driven viscoelastic polymer jets[16-24] but there is less theoretical work on the jet breakup 
and droplet dynamics in the electrospray process. Among the studies on electrically 
driven droplets, there have been separate theoretical studies on: i) capillary jet break up 
under electric field force[25-26], and ii) dynamics of the droplets formed under electric 
field[27-28]. However, there is no theoretical model combining these two phenomena, as 
both together are responsible for the electrospray process.  Therefore, this work focuses 
on the breakup of the jet into droplets due to the increase in the growth of the 
axisymmetric instability, and the dynamics of the droplets as they reach the collecting 
plate. Combining these two phenomena is difficult with a Eulerian approach as there is 
a discontinuity in the equations of motion as we shift from jet regime to droplet regime. 
Therefore, in this work, we use a Lagrangian discretized model as it is suitable to model 
both the jet breakup and droplet dynamics[18, 24, 29-30].  
In the discretized model, we consider the liquid jet to be made up of a series of 
beads attached together with springs. Newton’s second law of motion is applied to 
conserve the momentum. This model has been used in our previous works on centrifugal 
spinning, and axisymmetric and bending instability study in the electrospinning 
process[18, 24, 29-30]. We extend our previous axisymmetric instability[18] work to study 
the break-up of the jet, which is responsible for the formation of droplets during the 
78 
 
 
electrospray process. In addition, we incorporate equations of motion for the formed 
droplets to study their dynamics. In this model, we also model the spray process due to 
external air flow by incorporating the air drag effects for air spray and air controlled 
electrospray cases.  We also conducted experiments for 5 wt% polyvinyl alcohol in 
water. The air spray, electrospray, and air controlled electrospray processes are 
visualized with a high-speed camera. The average radius of the droplets obtained from 
experiments is compared with simulation results. The surface roughness and efficiency 
of the coating of PVA/H20 solution on the collector are obtained to study the effect of 
air flowrate on air controlled electrospray of the solution. We further investigated the 
effect of additional deformation on the deposition homogeneity and the dispersion of 
carbon NPs (Carbon Black) in resulting coatings, as it plays a crucial role in energy-
storage applications. In addition, we also studied the air controlled electrospray of the 
solution of graphene oxide dispersion in water to understand the behavior of nano-
inclusions in the spray process. Finally, we used the air controlled electrospray process 
to fabricate cathodes with microporous structures for lithium sulfur batteries. With the 
application of the air controlled electrospray technique, it is possible to control the 
morphology of cathode by changing spray parameters and obtain a uniform coating with 
high sulfur loading. Also, higher sulfur utilization can be achieved through improved 
electron transfer from low polarization and fast redox reaction kinetics. 
 
 
 
 
79 
 
 
5.2 Electrospray experiment 
5.2.1 Experimental fluids 
The spraying solution is 5 wt% of polyvinyl alcohol (PVA) (Mw=25,000 g/mol) in 
deionized water. The 88% mole hydrolyzed polyvinyl alcohol was purchased from 
Polysciences, Inc. The material properties of the spinning solution (PVA & water 
solution) are presented in Table 5.1. The viscosity and relaxation times are obtained 
from a TA Instruments AR2000 Rheometer with a 20 mm cone steel plate geometry.  
 
Table 5.1. Material properties of 5 wt% of PVA & H2O solution 
Material properties of 5 wt% PVA in H2O 
Density (kg/m3) 964.5 
Viscosity (Pa s) 0.026 
Relaxation time (s) 0.16 
Surface tension 0.00538 
 
The dispersion study of the coating is performed with electrospray and AC 
electrospray of 3 wt% PVA/H2O solution with 15 vol.% Carbon Black. Carbon Black 
(CB) was provided by TIMCAL Graphite & Carbon Super P® Conductive. The 
graphene oxide solution (2 wt% in water) was obtained from Dongjin Semichem. This 
graphene oxide solution was further diluted to 3 wt% solution in water. 
For the preparation of spraying solution for lithium sulfur cathodes, carbon/sulfur 
composite was first prepared by grinding 0.336 g sulfur and 0.084 g Ketjen Black 
80 
 
 
(AkzoNobel) together and heating at 155oC in a for 12 hours to ensure sulfur 
impregnation. Then the composite was mixed with 0.06 g PAA (Mw =450,000 g/mol, 
Sigma Aldrich) and 2 g of 6 wt% graphene water solution (ACS Nano). Finally, the 
mixture was dispersed in 2:8 weight ratio of isopropanol and water to form 6 wt% 
solution. 
 
5.2.2 Experimental setup 
The experimental setup for the electrospraying is illustrated in Figure 5.1. The 
PVA/H2O solution is pumped out of a 16-gauge needle at a flowrate of 0.01 ml/min by 
using a programmable PHS Ultra syringe pump (Harvard Apparatus). The voltage 
difference in the spinning gap is obtained with a Gamma High Voltage Research 
voltmeter. The experiments are conducted for 7.5, 12.5 and 15 kV voltage differences 
and the spinning distance is at ~ 16 cm. The spinning behavior of the polymer fiber is 
visualized using a high-speed camera (RedLake MotionPro HS-3 with Nikon MICRO 
NIKORR 60mm 1:2:8 lens). The images are taken at 1000 frames per second. Finally, 
the images are digitized using MotionStudio x64 software and are analyzed using 
ImageJ. 
 
81 
 
 
 
Figure 5.1 Schematic of a) Electrospray b) Air spray c) Air controlled (AC) 
electrospray 
 
The coating of 3% PVA/H2O solution containing 15 vol.% Carbon Black is 
prepared and sprayed via electrospraying and AC electrospraying. The flow rates for 
electrospraying and AC electrospraying are 0.005 and 0.06 ml min-1 respectively, and 
the electric field is kept constant at 100 kV m-1 for both processes. Graphene oxide 
dispersion in water is sprayed using AC electrospray process at 0.1 ml/min flow rate 
and voltage difference at 25 kV with spinning distance at 25 cm. Coating morphology 
and topology are characterized using scanning electron microscopy (Tescan Mira3 
FESEM).  
Lithium sulfur cathode solution is sprayed onto a carbon coated aluminum foil 
using a coaxial needle (12-gauge inside, 16 gauge outside). The flow rate and distance 
82 
 
 
are kept at 0.05 ml min-1 and 10 cm respectively. The voltage and air pressure are 
changed to have electrodes sprayed at no electric field (0 kV/ 25 psi), no air (25 kV/ 0 
psi) and both the electric field and air (25 kV/ 25 psi). Sample cathodes are used in 2032 
coin cell with lithium disk as the anode. Cycling performances are tested with a battery 
analyzing station (BTS8-MA, MTI) at 0.2 C in a voltage window of 1.8 – 2.8 V. 
 
5.3 Discretized model 
The electrospinning system is modeled using the bead-spring model; the jet is 
assumed to be a series of beads attached to each other with springs. The modeling 
approach is similar to the model used previously in the electrospinning and centrifugal 
spinning systems[18, 24, 29-30]. The polymer jet that is ejected out of the nozzle is subject 
to axisymmetric instabilities. This instability further leads to breaking of the jet into 
droplets. The modeling procedure used in this work follows from our previous work on 
axisymmetric instability[18].  
When Eulerian frame of reference is used, it is difficult to have one coordinate 
system as we shift the frame of reference from the continuous flow of the jet to discrete 
droplets. However, in the Lagrangian model used in the current study, we can 
incorporate the equations of motion for both, the continuous polymer jet and the 
droplets. The beads for the jet are connected with viscoelastic springs and when the jet 
breaks up and forms droplets, and each droplet is considered as one bead. This model is 
for predicting the spray process close to the needle so we do not consider the fission of 
the droplets. Until now all the studies were separately on either the capillary jet breakup 
83 
 
 
or droplet dynamics but this model incorporates both these phenomena in the 
electrospray process[25-28].  
For the jet, the equations of motion for a bead ‘i’ of mass 𝑚", length 𝑙", and radius 
𝑟" are obtained by applying Newton’s second law (Equation (1)). The position vector 𝒙𝒊 
is obtained from the forces acting on the bead ‘i’, which are surface tension 𝑭𝒔𝒕,𝒊, 
viscoelastic force 𝑭𝒗,𝒊, drag force 𝑭𝒅,𝒊, electric force 𝑭𝒆,𝒊 and gravitational force 𝑭𝒈,𝒊. 
The effects of solvent evaporation are not significant and are not considered in the model 
as we are studying the jet behavior close to the nozzle.  
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒔𝒕,𝒊 + 𝑭𝒗,𝒊 + 𝑭𝒅,𝒊 + 𝑭𝒆,𝒊 + 𝑭𝒈,𝒊,																																						(5.1) 
The surface tension force and viscoelastic force are obtained from the work by 
Divvela et al. [18, 24]. The surface tension force has two components: i) capillary force ii) 
bending force due to the local curvature of the jet. The viscoelastic force is due to the 
stress from the solvent and polymer; the solvent is a Newtonian fluid, and the polymer 
stress is obtained from the Giesekus model. The drag force due to the coaxial air flow 
is obtained by considering the average of the drag effects on the upstream and the 
downstream elements. The drag force has two components: i) friction drag due to shear 
stress on the surface of the jet and ii) pressure drag due to pressure difference in the 
radial direction of the jet[30]. 
The electric force on a bead ‘i’ is given from Equation (2). The electric field on the 
element i has two terms: i) voltage gradient with applied voltage difference 𝑉h and 
spinning length h, and ii) Coulombic interaction with the rest of the beads j with charge 
84 
 
 
𝑞k at a distance 𝑥"k from bead ‘i’. The surface charges are conserved by considering the 
convection and conduction currents[18]. 
𝑉 1 𝑞
𝑭𝒆,𝒊 = 𝑞"𝑬𝒆,𝒊 = 𝑞" p
h k
ℎ 𝒆𝒛 + 4𝜋𝜖 s𝑥 t 𝒙𝒊𝒋w,																																			(5.2) r kv" "k
The bead at the nozzle is disturbed with a normal mode of perturbation with 
amplitude 𝛿 and frequency 𝜔r. In the context of axisymmetric instability, our approach 
is similar to that used in the capillary jet breakup study[25-26]. In this study, small 
fluctuations are applied to the jet boundary condition at the nozzle. The applied 
perturbation is given in Equation (3), where 𝑎y is the stable jet radius.  
𝑎 = 𝑎 ¹ Wy + 𝛿𝑒 º ,																																																														(5.3) 
The simulation is run for different frequencies and amplitudes of the perturbations 
as given in Equation (3). This perturbation is applied when the bead is introduced at the 
nozzle exit and we obtain the jet variables by solving Equation (1). This solution will 
have information on the stable jet and the perturbed variables combined. We calculate 
the growth rate  𝜔n of the instability from Equation (4) by measuring the temporal 
evolution of the perturbation radius, 𝑎»(𝑡). Finally, we consider the amplitude 𝛿 and 
frequency  𝜔r for which we obtain the maximum growth rate.  
𝑙𝑛†𝑎»(𝑡)‡ = 𝜔n𝑡 + 𝑙𝑛†𝑎»(0)‡,																																											(5.4) 
The amplitude of the instability increases with time and when this amplitude is 
equal to the radius of the jet, the jet breaks and forms spherical droplets. Therefore, the 
jet breakup occurs when 𝑎»(𝑡) = 𝑅(𝑡), where 𝑅(𝑡) is the radius of the jet. The mass, 
85 
 
 
charge, and velocity of the new droplets formed are obtained from conservation of mass 
(Equation (5.5)), charge (Equation (5.6)) and momentum (Equation (5.7)) equations 
respectively. In Equations (5.5 – 5.7), the subscript ‘j’ denotes the indices of all the 
beads that are in the broken part of the jet. 
𝑚" =s𝑚k ,																																																																																																															(5.5) 
k
𝑞" = s𝑞k ,																																																																																																																	(5.6) 
k
𝑚"𝑣" = s𝑚k𝑣k ,																																																																																																						(5.7) 
k
The equations of motion for these droplets are also obtained from Newton’s second 
law of motion. The forces acting on the beads are aerodynamic drag force (𝑭𝒅,𝒊), electric 
field force (𝑭𝒆,𝒊) and gravitational force (𝑭𝒈,𝒊). The viscoelastic and surface tension 
forces are not included in the Equation (5.8) as we assume that the droplets are rigid 
spheres. 
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒅,𝒊 + 𝑭𝒆,𝒊 + 𝑭𝒈,𝒊,																																																																	(5.8) 
The air drag force on the droplets is given considering flow on a sphere. For bead 
‘i’ of radius 𝑟𝑖 the drag force is given in Equation (5.9). Where 𝑽𝒓𝒆,𝒊 is the relative 
velocity of the air with respect to the droplet i. 
𝐶 =
𝑭 = 
𝜋𝑟"
𝒅,𝒊 2 𝜌œ"n𝑽𝒓𝒆,𝒊U𝑽𝒓𝒆,𝒊U,																																																																	(5.9) 
86 
 
 
The drag coefficient 𝐶𝐷 (Equation (5.10)) is obtained from the shear stress acting 
on the surface of the sphere[31]. The shear stress is calculated from at the velocity profile 
of the surrounding air on a tiny boundary layer around the surface of the sphere. 
24 =
𝐶 = 𝑅𝑒 †1 + 0.1104¿𝑅𝑒œ"n‡ ,																																																						(5.10) œ"n
The above equation is valid for 𝑅𝑒œ"n < 5000. Where, 𝑅𝑒œ"n = 𝜌œ"nU𝑽𝒓𝒆,𝒊U𝑑"/𝜇œ"n with 
𝜌œ"n as the density of the air, 𝜇œ"n as the viscosity of the air and 𝑑" is the diameter of the 
droplet. 
The electric force acting on the droplets is similar to Equation (5.2), however, the 
Coulombic interactions between the droplets and the surface charges of the jet are also 
responsible for the total electric field force.  
 
5.4 Results and Discussion 
In this section, we studied the spraying process of PVA/H2O solution and the effect 
of air flow and voltage is observed. As we used a viscoelastic polymer solution in the 
experiments, the jet extends due to viscoelastic stress under driving force and then 
breaks into droplets. The spray process is different for fluids which are not viscoelastic. 
For non-viscoelastic fluids, the droplets are formed at the nozzle itself due to the 
atomization of the meniscus (Taylor cone). 
 In Section 5.4.1-5.4.2, the radius of the droplets and the size distribution is obtained 
for three cases: i) Electrospray ii) Air spray and iii) Air controlled (AC) electrospray. 
The radius of the droplets obtained from simulations for these three cases is compared 
87 
 
 
with the experimental results. However, the simulation results provide an average radius 
of the droplets, but the size distributions of the droplets are not obtained. Later, in 
Section 5.4.3 the effect of air flow on the surface morphology and the yield of the AC 
electrospray is studied. The surface morphology formed from the AC electrospray of 
the solution of graphene oxide dispersion in water, a non-viscoelastic fluid is studied. 
Finally, in Section 5.4.4, the three spray processes are applied to coat cathodes for 
Lithium Sulfur batteries and the electrochemical performance of these batteries is 
studied. 
 
5.4.1 Electrospray and Air spray 
The experimental conditions used in this section are mentioned in Section 5.2.1. 
The electrospray process is studied at 3 different applied voltage differences. The 
electric field causes extension of the jet from Taylor cone and axisymmetric instability 
acts on the extended jet. There are two modes of axisymmetric instabilities; the capillary 
mode and conducting mode[16-17]. In the capillary mode of the instability, the instability 
grows due to high and low pressure regions caused due to the modulations in the radius 
of the jet[16]. The low pressure region has larger radius compared to the high pressure 
region as capillary pressure is inversely proportional to the radius of the jet. As the liquid 
travels from high pressure to low pressure, the region with larger radius keeps growing 
and the region with a lower radius keeps shrinking and finally causes the jet to break-
up. Whereas in the conducting mode, the modulations on the jet surface lead to 
modulations on the surface charges of the jet. The Coulombic interactions between these 
surface charges increase the instability and lead to the jet break-up. In highly conducting 
88 
 
 
polymers, the conducting mode plays a dominant role in the instability growth rate. With 
an increase in the electric field, both the capillary pressure and the surface charges of 
the jet increase due to the formation of thin jets because of jet extension[17]. As the 
capillary pressure and surface charges are responsible for the jet break-up phenomena, 
the increase in the electric field leads to an increase in the growth rate of the instability. 
Therefore, at higher voltages the droplet formation is more rapid, resulting in the 
formation of a large number of droplets. Also, the formation of thin jets at high voltage 
leads to smaller size droplets. 
In the electrospray process, the jet length is short and the break up occurs near the 
Taylor cone region. Also, from Figure 5.2a, the size of the droplets is more consistent 
as observed from the standard deviation in the droplet size distribution. However, only 
a fewer number of droplets are formed with the electrospray process. From Figure 5.2a, 
we can observe that the radius of the droplets obtained from experiments is comparable 
to the simulation result.  
The experimental result in air spray case is obtained without applying any voltage 
difference between the nozzle and the collector. The solution is ejected out of the nozzle 
at flowrate 0.01 ml/min and the air flow is applied coaxially to the jet. The drag force is 
mainly responsible for the extension of the jet. In this case, as there is no electric field, 
there is only the capillary mode of the instability and the drag force further accelerates 
the instability growth rate. The effect of air flow on the droplet size distribution is 
studied for 3 different air flow rates. From Figure 5.2b, we can observe that the size of 
the droplets decreases with the increase in air flow due to the formation of thin jets at 
high air flow rates. Also, the number of droplets increases with air flow as the instability 
89 
 
 
growth rate also increases with the air flow rates. We also observed that compared to 
the electrospray process the number of droplets is much higher and the spraying process 
is more chaotic and rapid for the air spray case. In addition, the droplets formed are not 
of uniform size with the air spray case as seen from the standard deviation plot in Figure 
5.2b. From the experimental result for 50 m/s air flow rate, we observe that there are 
multiple jets formed at the nozzle. However, in the simulations, we assume that only a 
single jet is ejected out of the nozzle.  
 
 
 
 
 
 
 
90 
 
 
 
 
Figure 5.2. a) Effect of voltage on average droplet radius for electrospray process b) 
Effect of air velocity on average droplet radius for air spray process 
 
91 
 
 
5.4.2 Air controlled  (AC) electrospray 
This AC electrospray process is the combination of the electrospray (Section 5.4.1) 
and air spray (Section 5.4.1) processes. The droplet size is more uniform in the AC 
electrospray process compared to the air spray case due to the application of electric 
field (Figures 5.3 and 5.4). The number of droplets increases with air flow as observed 
in the air spray case. Therefore, we can observe that the electric field is responsible for 
the uniformity of the droplets and the air flow is responsible for the formation of a large 
number of droplets. Also, the mean radius reduces as the air flow increases and the size 
of the droplets reduce by 65% under the effect of air flow compared to the no air flow 
case. We also observe that at a higher air flow rate, at 15 m/s, the Taylor cone deforms 
and ejects multiple jets. 
 
 
Figure 5.3. Air controlled electrospray at air flow a) 0 m/s b) 7.5 m/s c) 15 m/s 
 
 
 
92 
 
 
 
Figure 5.4. Effect of air flow on average droplet radius for air controlled electrospray 
process 
 
5.4.3 Controlling coating topology, morphology and nanoparticle dispersion via AC 
electrospraying 
The surface roughness of PVA/H2O spray is measured through Atomic Force 
Microscopy (Figure 5.5a-c) for AC electrospray process at 5 different air flow rates. 
From Figure 5.5d, for lower range (0 – 15 m/s) of air flow rates, with an increase in air 
flow, there is a decrease in surface roughness. However, at a higher air flow rate, at 60 
m/s, the surface roughness is increased. The initial decrease in surface roughness is due 
to the decrease in the size of the droplets sprayed on the substrate as observed in AC 
electrospray case (Section 5.4.2). However, at 60 m/s the spray is dry by the time it hits 
the surface of the collector, and because of which the droplets make a rough coating on 
the substrate. 
93 
 
 
 
Figure 5.5. AFM images of AC electrospray surface of PVA/H2O at air flow a) 0 m/s 
b) 15 m/s c) 60 m/s and d) Effect of air flow on surface roughness of the coating 
 
The coating efficiency of the spray is also measured for the AC electrospray process 
at 5 different air flow rates (Figure 5.6). The coating efficiency is calculated from the 
ratio of the weight of the coating on the substrate and weight of the polymer in the 
spinning solution as given in Equation (5.11). The coating efficiency increases for air 
flow rates of 0 – 15 m/s due to larger deposition, as the air flow carries the droplets 
axially towards the substrate. However, at higher air flow rates the coating efficiency is 
reduced because of loss in the spray material as the direction of the spray is very non-
axisymmetric and chaotic. 
94 
 
 
	𝑤𝑒𝑖𝑔ℎ𝑡	𝑜𝑓	𝑡ℎ𝑒	𝑠𝑝𝑟𝑎𝑦	𝑐𝑜𝑎𝑡𝑖𝑛𝑔
𝐶𝑜𝑎𝑡𝑖𝑛𝑔	𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦	(%) = 𝑤𝑒𝑖𝑔ℎ𝑡	𝑜𝑓	𝑡ℎ𝑒	𝑝𝑜𝑙𝑦𝑚𝑒𝑟 	× 	100%,													(5.11) 
 
Figure 5.6. Effect of air flow on coating efficiency of the AC electrospray of PVA/H2O 
 
Carbon black is added to the PVA solution to investigate the macro-, micro-, and 
nano-scale morphologies of the PVA-CB coating deposited via AC electrospraying 
process at different air flows (Figure 5.7). It is evident from the SEM images (Figure 
5.7) that there is a significant deviation in the size distribution of droplets that are 
sprayed via conventional electrospray (Figure 5.7a), ranging from 300 𝜇m (macro-scale) 
to 50 nm (nanoscale). The solvent evaporation is not precisely controlled in 
conventional electrospray, which results in deposition of solid polymer particles on the 
surface, creating rough topology. It can be observed in Figure 5.7b-d, that with the 
application of the air flow in AC electrospray, the morphology and topology have 
significantly improved at all magnifications, due to precise control over atomization and 
a significant decrease in the droplet dimensions. It is important to mention, that the 
95 
 
 
number of solid polymer particles on coating surfaces significantly decreased with the 
increase of the air flow (Figure 5.7c & d). The polymer droplets are effectively directed 
towards the substrate by the air flow, therefore, the final solvent evaporation takes place 
on the surface upon deposition. Extremely high assisting flows result in premature 
solidification of the droplet, due to forced convection, increasing the number of solid 
particles on the surface of the coating (Figure 5.7d). Therefore, AC electrospray can be 
effectively utilized to precisely control topology and morphology even at the nano scale. 
This is particularly useful for the development of superhydrophobic coatings, where the 
control of the surface roughness plays a crucial role and determines wetting angles[1–3]. 
 
 
96 
 
 
 
Figure 5.7. SEM images of macro/micro/nano-topology of 3% PVA solution with CB 
(15 vol% to PVA) coatings deposited via a) 0 m/s, b) 30 m/s, c) 55 m/s and d) 70 m/s 
sheath layer air flow AC electrospray. 
The AC electrospray of PVA-CB can obtain an electrically conductive coating due 
to the high electrical conductivity of the carbon powder. However, carbon black cannot 
be sprayed directly and needs to be sprayed with PVA which acts as a binder to stick to 
the substrate. In addition, Graphene oxide is electrically conductive and can form 
uniform coatings using AC electrospray process without the use of PVA (or any binder). 
Graphene oxide dispersion in water can directly be used to coat copper (Cu) substrate 
using the AC electrospray process. This solution is non-polymeric, unlike PVA/H2O 
97 
 
 
solution that is used in the experiments discussed in Sections 5.4.1-5.4.3. The graphene 
oxide sheets undergo folding under external forces and therefore, the morphology of the 
spray surface can give an insight into the droplet formation. When there is no air flow, 
the spray is very non-uniform and forms discrete particles from the SEM image (Figure 
5.8). However, with the application of air flow rate, the spray forms a film on the 
substrate. In addition, with an increase in the air flow rate, the spray has fewer wrinkles 
and a smoother morphology is observed (Figure 5.8). Furthermore, from the SEM image 
of the cross-section of the sprayed material, there are no layers formed for no air flow 
condition. However, layers can be observed when the air flow rate is applied on the 
spray and the layers are more densely packed for 100 m/s air flow case. This shows that 
the high air flow rate increases the rate of solvent evaporation of the spray yielding a 
dry layer of the coating on the substrate before another layer is coated. The layered 
structure of graphene oxide has been used to fabricate conductive and mechanically 
stable electrodes in batteries. The multi-layered structure can provide structural integrity 
and can accommodate large volume changes during the lithiation or delithiation process.  
 
 
 
98 
 
 
 
Figure 5.8. Surface morphology and cross-section of air controlled electrospray of 
GO at air flow a) 0 m/s b) 50 m/s c) 100 m/s 
 
5.4.4 Lithium Sulfur battery performance with air controlled electrospray coated 
electrodes 
Li-S batteries are a promising candidate for the next generation of energy storage 
due to its high theoretical capacity and low cost[40-41]. However, it needs to overcome 
challenges like the highly insulating nature of sulfur and volume expansion in the 
battery during discharging. Thus, effective reaction site, conductive pathway, and 
mechanical stability are necessary to increase the utilization of sulfur. Therefore, in this 
section, a uniform coated cathode is fabricated using AC electrospray process to 
improve the capacity and retention of Li-S batteries. 
99 
 
 
Figure 5.9 presents the SEM images for the slurry coating, air spray, electrospray, 
and air controlled electrospray.  For slurry coated electrode (Figure 5.9a), the surface 
image shows a dense layer with several cracks due to discrete grain boundaries formed 
during the drying process. The size of the cracks is observed to increase with the sulfur 
loading and electrode thickness[42]. In the spray techniques (Figure 5.9b-d), the 
morphology highly depends on the parameters like flow rate, distance, electric field, 
and convective air flow. In Figure 5.9b, the electrospray surface shows a dense surface 
consisting of inconsistent dark and light color regions.  However, air spray electrodes 
show a more uniform coating as shown in Figure 5.9c. Furthermore, by combining both, 
a more porous surface is obtained by air controlled electrospray. The voids and rough 
surfaces are beneficial as they can accommodate the sulfur expansion and also can 
enhance the electrolyte uptake[43].  
100 
 
 
 
Figure 5.9. SEM images of cathodes via a) slurry coating, b) electrospray, c) air spray 
and d) air controlled electrospray 
 
The electrochemical performance of the lithium sulfur battery is measured with 
four different coated electrodes: i) Slurry coating, ii) Electrospray – Only electric field, 
iii) Air spray – Only air, and iv) Air controlled electrospray – Both air and electric field. 
In Figure 5.10a, the discharge capacity of the electrode coated with air controlled 
electrospray is higher than the only air and only electric field cases. The higher number 
of porous micro-size structures formed with both air and electric field provides well-
101 
 
 
developed pathways to facilitate redox electron transfer and reduce interfacial 
resistance. It allows a higher conversion rate of lithium polysulfide to favorable 
chemical compounds for charge storage. Compared to slurry coating electrodes, 
elimination of cracks largely increases the mechanical stability, which further results in 
improved capacity retention. 
The rate capability of cells at different C-rates is presented in Figure 5.10b. As 
expected, the results followed a similar trend as cyclability. The difference in discharge 
capacities between the sprayed and slurry coating cells is even more evident at high 
current densities because the redox reaction kinetics are more significant at high current 
densities. At a C-rate of 2 C, the air controlled electrospray cell still maintained 49.9 % 
of its initial capacity, while the retention of slurry coating cathode is only 7.2 %. A 
discharge capacity of 756.8 mAh g-1 is recovered after returning to 0.1 C for air 
controlled electrospray. 
 
 
 
 
102 
 
 
 
 
Figure 5.10. a) Discharge capacity at 0.5C, and b) Rate capability of lithium sulfur 
battery cathode fabricated with air controlled electrospray, air spray and electrospray 
  
103 
 
 
5.5 Conclusions 
The spray behavior of a viscoelastic polymer solution (PVA/H2O) for air spray, 
electrospray, and air controlled electrospray cases are studied with simulations and 
experiments. A discretized model with the bead-spring approach is used for the 
simulations. The droplet formation from the jet break-up due to axisymmetric instability 
growth is studied from the model. The average radius of the droplets from simulations 
is compared with the experiments. The experimental observations are obtained from 
flow visualization with a high-speed camera and the droplet size distributions for the 
three spray cases are measured. The electric field is responsible for increasing the 
uniformity in the droplet size and the air flow rate is responsible for forming a large 
number of droplets. However, the size of the droplets reduced with the increase in both, 
the applied electric field and air flow rate. The surface roughness of the AC electrospray 
material measured from AFM is observed to decrease for lower range (0-15 m/s) of the 
applied air flow rate but the surface roughness increased at a high air flow rate (60 m/s). 
Furthermore, for PVA system, we observe a significant improvement in the spatial 
distribution of Carbon Black active nano-inclusions in the coatings with an increase in 
the applied air flow. The air controlled electrospray of graphene oxide/water system 
formed a smoother spray with packed distinct layers at a high air flow rate (100 m/s). 
The AC electrospray process is used to fabricate uniformly coated Li-S cathodes. The 
air controlled electrospray coated electrodes demonstrated improved capacity, retention 
and rate capability. The well-developed structure is efficient not only in providing 
conductive pathways for sulfur utilization but also for trapping polysulfides.  
 
104 
 
 
ACKNOWLEDGMENTS 
This work made use of the Cornell Center for Materials Research Shared Facilities 
which are supported through the NSF MRSEC program (DMR-1719875). 
 
  
105 
 
 
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108 
 
 
CHAPTER 6 
JET SPRAYING BEHAVIOR AND COATING DEPOSITION OF VISCOELASTIC 
LIQUID IN ROTARY BELL SPRAY PROCESS 
6.1 Introduction 
The automobile coating industry is highly automated, and the spray-painting 
technique used for high quality finishing of the automobiles is rotary bell spraying [1-
7]. In this process, there is a bell-shaped cup and the spraying solution is released from 
inside the bell. The bell rotates at high speed and the solution is released as jets from 
the grooves at the edges of the cup. The jets atomize and form droplets due the rotational 
velocity of the bell. Additionally, air is applied to the outer surface of the bell, this is 
called shaping-air as the air controls the droplet trajectory. The air further enhances the 
atomization process and forms smaller and large number of droplets. Furthermore, the 
electric field is also usually applied between the bell and the substrate to improve paint 
transfer efficiency and spray pattern consistency [3-4]. In automotive industry, the bell 
is attached to a robotic arm that is programmed to coat the surface automatically [3]. 
In the coatings industry, when the paint is formulated, the coating formulation is 
optimized by spray testing at different rheological properties on the car panels. This 
process leads to depletion of resources and time, and this can be avoided with a 
prediction tool for the rotary bell spray process that can provide a baseline for the paint 
formulation. Therefore, in this work, the simulation of the rotary bell spray process is 
developed using a discretized model [8-10] to study the behavior of the atomized 
droplets and compared with the experimental results. The experimental results are 
109 
 
 
obtained from the high-speed images and the images are analyzed with an in-house 
software created from MATLAB to analyze the images to obtain the diameters of the 
jet ejected from the bell. Also, the droplet sizes are obtained from an equipment called 
spray spy that sends a laser light and obtain the droplet size information from the laser 
light scattering data. 
In the current work, the simulation of the rotary bell spray system with the 
discretized model is an extension of our previous work in centrifugal spinning process 
[9]. In the discretized model, the jet is assumed to be made up beads with springs and 
the equations of motion is solved by applying Newton’s second law on the beads. This 
model saves computation time compared to the slender jet models used in the centrifugal 
spinning systems. Therefore, we can use this model in the rotary bell spray system as 
the model can easily accommodate the simulation of multiple jets that are ejected out of 
the bell. To simulate the atomization process in the system, we applied an approach 
similar to the model that was used in our previous work on electrospray process [10]. 
The jet is introduced with an axisymmetric instability and the compression stress is 
measured along the jet and the position when the compression stress is large the jet 
breaks into droplets. With the discretized model we first studied the droplet trajectories 
and size distributions at different process conditions. Later, we studied the deposition 
profile of the coating with the discretized model and calculated the brush size (radial 
coverage of the deposited coating) and brush thickness (coating thickness). 
 
 
 
110 
 
 
6.2 Experimental procedure 
The schematic of the rotary bell spray experimental setup and experimental image 
is shown in Fig. 6.1. In the experimental setup, the bell is attached to a high speed motor 
and rotates around its axis. The spraying solution is passed from the inside of the bell at 
constant flow rate and because of high rotational speed the solution forms a thin layer 
on the inner surface. The solution then ejects out as a continuous jet from the grooves 
present at the edges of the bell. The air is applied to the outer surface of the bell to 
control the deposition of the spray. The whole setup is attached to a robotic arm which 
provides movement to the setup to cover larger area with the coating. This setup is 
commercially used by the automotive industries to paint the exteriors of the cars. 
 
 
 
 
 
 
 
 
 
 
 
 
 
111 
 
 
          Top view 
   a )        
 
 
 Ω 
 
 
 
 
 Front view Bell 
 
 
 
 er 
 
 
 
 
                                b) 
 
Figure 6.1. a) Schematic of the rotary bell spray setup b) Experimental image of the 
rotary bell spray setup 
 
6.3 Simulation procedure 
In the model used in this current study, the jet is assumed to be a series of discrete 
beads attached to springs. The springs are massless and viscoelastic, whereas the beads 
have mass and the equations of motion are solved for the beads. This discretized model 
has been previously used in centrifugal spinning and electrospinning work [9, 10]. We 
112 
 
Shaping air 
g air 
Shap
in
 
used the model to study the centrifugal spinning process and obtained predictions on the 
jet trajectory and radius thinning profile. In this work, we have extended the discretized 
model for multiple jets along with the study of break-up of the jet into droplets.  
The spraying solution comes out of the rotating bell from its grooves as multiple 
jets. The axisymmetric instability on the ejected jets cause perturbations on the jet 
surface. This instability grows leading to break-up of the jet into droplets. In this model, 
we assume there is no collision between the multiple jets. Also, once the droplets are 
formed, we assume that they do not further break-up into smaller droplets. We consider 
each droplet as a bead and the equations of motion are also applied to the beads to obtain 
their trajectory.  
The spraying solution when released inside the bell flows along the inner surface 
of the bell forming a thin film due to the rotational speed of the bell as mentioned in 
Section 6.2. The velocity and the height of the thin film is given in Eqs. (6.1)-(6.2). The 
initial velocity and radius of the beads is given from the thin film approximation of the 
spraying solution before it is ejected out of the bell from the grooves [11].  
𝜌Ω=𝑅 𝑠𝑖𝑛𝜃ℎ=
𝑢 = Ǜ)) R")R") 3𝜇 ,																																																								(6.1) 
ℎt
3𝑄𝜇
R") = = = ,																																																										(6.2) 2𝜌Ω 𝑅Ǜ))𝑠𝑖𝑛𝜃
Where, 𝑢R") is the velocity of the filament, ℎR") is the height of the filament, Ω is the 
rotational speed of the bell, 𝑅Ǜ)) is the radius of the bell, 𝜃 is the angle of the bell, 𝑄 
is the flowrate of the spraying solution, 𝜇 is the viscosity, and 𝜌 is the density.  
113 
 
 
The equations of motion for the beads on the jet is obtained from Newton’s second law 
as written in Eq. (6.3). The different forces acting on the beads are centrifugal force, 
viscoelastic force, surface tension force, gravitational force and aerodynamic drag force 
[9]. 
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒔𝒕,𝒊 + 𝑭𝒗,𝒊 + 𝑭𝒅,𝒊 + 𝑭𝒈,𝒊,																																																					(6.3) 
The forces acting on the jet are obtained from the work by Divvela et al. [9, 10]. 
The surface tension force has two components: i) capillary force ii) bending force due 
to local curvature of the fiber. The viscoelastic force is due to the stress from the solvent 
and polymer; the solvent is a Newtonian fluid, and the polymer stress is obtained from 
the FENE-P model with a finite maximum extension of the jet [9]. 
The shaping air is applied tangential to the bell outer surface as discussed in Section 
6.2. The air profile depends on the swirl number as given in Eq. 6.4. The radial profile 
shows a Gaussian distribution, however, for high swirl numbers it gives a bimodal 
distribution. Whereas, the axial profile increases with distance and reaches a maximum 
and then decreases [2]. The drag force on any bead due to the air flow is the average of 
the drag on the upstream and downstream elements. The drag force has two components: 
i) friction drag, and ii) pressure drag. 
𝑆 = =ËÌÍÎÏÏ ,																																																																										(6.4)	   
ÐÑ&Ò
Where, Ω is the rotational speed of the bell, 𝑅Ǜ)) is the radius of the bell and 𝑈œ"n 
is the velocity of the air. 
114 
 
 
The axisymmetric instability is applied by perturbing the bead at the nozzle with a 
normal mode distribution [10]. The perturbation is applied to the radius of the bead with 
amplitude 𝛿 and frequency 𝜔h.  
𝑎 = 𝑎 + 𝛿𝑒¹ºWy ,																																																																							(6.5) 
The break-up of the jet is determined by measuring the compressive stress acting 
on the jet. When the measured compression stress at any bead is large, which is 
determined from the average and standard deviation of the compression stress, the jet 
breaks at that bead and forms droplets. The sizes and velocity of the droplets formed are 
obtained from mass and momentum conservation respectively. 
The equation of motion for these droplets is given in Eq. (6.6) from Newton’s 
second law of motion. The forces acting on the beads are aerodynamic drag force, 
gravitational force. The surface tension and viscoelastic forces do not affect the droplet 
motion. The aerodynamic drag force on the droplets is similar to the equation in the 
electrospray work [12]. 
𝑑=𝒙
𝑚 𝒊" 𝑑𝑡= = 𝑭𝒅,𝒊 + 𝑭𝒈,𝒊,																																																																		(6.6) 
 
6.4 Results and Discussion 
The diameter of the acrylate jets as they are ejected out of the rotating bell is 
compared from both the simulations and experiments. The images obtained from the 
high speed camera are analyzed in MATLAB to measure the average diameter of the 
filaments. The rotational speed of the bell is 15000 rpm. We can observe that with 
115 
 
 
increase in flowrate the diameter of the jets increases, due to increase in accumulation 
of mass at higher flowrates.  
0.3
0.25
0.2
0.15
0.1
0.05 Simulation
Experiment
0
0 50 100 150 200 250 300
Flowrate	(ml/min)  
0.3
0.25
0.2
0.15
0.1
Simulation
0.05 Experiment
0
0 10000 20000 30000 40000
Rotational	speed	(rpm)
 
Figure 6.2. Comparing initial diameter of jets from simulation and experiments at 
different a) flowrates b) rotational speed 
The high speed images from the experiments of the rotary bell spraying process are 
obtained at different flowrates and rotational speeds. The edge of the bell with multiple 
jets ejecting out of the grooves on the bell is visualized in Fig. 6.3. The air flow rate is 
116 
 
Filament	diameter	(mm) Filament	diameter	(mm)
 
kept constant at 425 L/min for the three images. The jet lengths are longer at lower 
rotational speed (15000 rpm) compared to 30000 rpm and 45000 rpm. In addition, more 
number of droplets are formed and the spray behavior is more chaotic at high rotational 
speed (30000 rpm and 45000 rpm).  
a)                                       b)                                           c) 
       
Figure 6.3. High speed camera images of rotary bell spray process at a) 15000 rpm 
and 50 ml/min b) 30000 rpm and 250 ml/min c) 45000 rpm and 250 ml/min 
The droplet trajectories of the spray are plotted in Fig. 6.4 for 8 jets ejected out of 
the bell. The bell used in the experiments has 420 grooves through which the jets are 
ejected, however, in the simulations we considered 8 jets to save computation time and 
have a clear representation of the trajectories in the plot. In Fig 6.4(a), the front view of 
the spray is plotted and in Fig. 6.4(b) the top view of the spray is plotted. We can observe 
from the plots that the droplets follow a helical motion and continue to move in 
rotational motion with increase in the radius of the rotational trajectory as it moves 
117 
 
 
downstream. The color bar on the plots in Fig. 6.4 (a) & (b) shows the velocity of the 
droplets in m/s. The velocity values are negative as the droplets are travelling in the 
negative Z-direction. We can observe from the Fig. 6.4(a) that as the droplets travel 
downstream away from the bell the velocity increases and then decreases.   
We can observe that with increase in the rotational speed, the number of droplets 
increases due to increase in atomization at higher rotational speed. Also, smaller size 
droplets are formed at higher rotational speed as observed in Fig. 6.4(c) as the rotational 
speed leads to the formation of thinner jets due to increase in the extensional forces. In 
addition, the standard deviation of the droplet sizes reduces with increase in the 
rotational speed. The radial coverage of the droplets increases with rotational speed, as 
the centrifugal force pushes the droplets away from the rotating bell. 
We also studied the effect of flowrate on the droplet trajectories and droplet 
diameters. The simulation results are obtained for rotational speed at 20000 rpm and 
compared for two different flowrates 150 ml/min and 250 ml/min. The size of the 
droplets increased with the applied flowrate. The average diameter of the droplets at 
150 ml/min is 40.4 microns and at 250 ml/min the diameter is 42.2 microns. In addition, 
the droplets at 250 ml/min are travelling at a higher velocity compared to 150 ml/min 
case. This is because, the initial inertia on the droplets is higher for the 250 ml/min 
flowrate case compared to the 150 ml/min case. However, from the Fig. 6.5, there is no 
difference in the radial coverage of the droplets in both the flowrate cases. 
118 
 
 
 
 
Figure 6.4. The droplet trajectories and droplet diameter for a) 150 ml/min and 15000 
rpm and b) 150 ml/min and 25000 rpm 
119 
 
 
 
Figure 6.5. The droplet trajectories and droplet diameter for a) 150 ml/min and 20000 
rpm and b) 250 ml/min and 20000 rpm 
 
120 
 
 
The deposition of the coating on the collector from rotary bell spraying from the 
simulations is also studied in this paper. In reality, the collector is at a distance of 10 cm 
from the bell, however, in the simulations the collection profile is obtained at 1 cm to 
save computational time. The coating deposited on the collector is called brush, and the 
brush size and thickness are obtained at different process conditions. The maximum 
brush size, which is the radius of the maximum coverage of the coating is shown in Figs. 
6.6(a) & (c) and the brush thickness, which is the thickness of the coating, is shown in 
Figs. 6.6(b).  
From Figs. 6.6 & 6.7 we can see that at lower rotational speed (15000 rpm) the 
maximum thickness of the deposited coating is larger than compared to the case at 
higher rotational speed (25000 rpm). This is because at lower rotational speed the size 
of the droplets is larger and results in the formation of thicker coating. However, there 
is more uniform coverage of the coating for 25000 rpm compared to 15000 rpm. In 
addition, the maximum brush size for 25000 rpm is 14.81 cm which is slightly higher 
than compared to the 15000 rpm case for which the brush size is 14.5 cm.  
 
 
 
 
 
 
 
 
121 
 
 
 
 
Figure 6.6. a) Brush size b) Brush thickness c) Deposited coating profile at 150 
ml/min and 15000 rpm  
122 
 
 
 
Figure 6.7. a) Brush size b) Brush thickness c) Deposited coating profile at 150 
ml/min and 25000 rpm  
The coverage of the coating for 250 ml/min is more compared to 150 ml/min as 
observed from Fig. 6.8(b) & 6.9(b), the maximum brush size for the 150 ml/min and 
20000 rpm case is 14.31 cm and for 150 ml/min and 20000 rpm case is 15.02 cm. The 
maximum brush thickness at 150 ml/min flowrate is higher (0.6 mm) compared to 250 
ml/min (0.41 mm) as at 150 ml/min is more concentrated in one region only. However, 
the coating is more uniform for 250 ml/min flowrate as observed from Fig. 6.9(c).                                                     
123 
 
 
 
Figure 6.8. a) Brush size b) Brush thickness c) Deposited coating profile at 150 
ml/min and 20000 rpm  
124 
 
 
 
Figure 6.9. a) Brush size b) Brush thickness c) Deposited coating profile at 250 
ml/min and 20000 rpm  
The modeling of rotary bell spraying is usually performed using CFD software [4-
7], which take a lot of computational time to study the process for multiple jets. With 
the discretized model, we not only simulated the multi jet behavior and droplet size 
distribution, but we also studied coating deposition profile. This is a first study that 
simulated the jet behavior in the rotary bell spraying system at different process 
conditions. The predictions from the simulation can be used to obtain the necessary 
125 
 
 
process conditions to obtain the desired coating profile, which would save time and 
resources during the testing and formulation of the paint while coating. 
 
6.5 Conclusions 
Rotary bell spray system is used commercially for the coating of automobiles. The 
study on the coating behavior based on the rheology of the paint and process conditions 
involves huge resources by the coating industries. Predicting the behavior of the coating 
with simulations can provide a starting point in formulating the composition of the 
paints. We studied the behavior of acrylate which has its rheological properties similar 
to the formulation of clear coat, which is the top layer of the automobile coating. The 
droplet trajectories and size distribution were studied for different rotational speed and 
flowrate conditions. In addition, we studied the coating deposition also for different 
process conditions. With increase in rotational speed and flowrate the coating is more 
uniform and covered a larger area of the substrate. 
  
ACKNOWLEDGMENTS 
The authors would like to thank BASF Coatings GmbH, Münster, Germany for funding 
this work. 
 
  
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