1 

 Pimples Made Simple: Pimple Pus Removal Using a Hydrocolloid 
 Patch with Salicylic Acid 

 BEE/MAE 4530: Computer Aided Engineering: Applications to Biological Processes 
 Keywords: Salicylic Acid, Hydrocolloid, COMSOL, Pimple Patch, Skin Diffusivity 

 Team 1 
 © AJ Villaruel, Frank Fang, Kyra Husen, Nadya Lumy 

 May 6, 2025 



 2 

 Table of Contents 
 1.0  Executive  summary  ...............................................................................................................  3 
 2.0  Introduction  ............................................................................................................................  3 

 2.1  What  is  acne?  How  is  a  pimple  structured?  .......................................................................  3 
 2.2  What  is  a  pimple  patch?  What  is  a  hydrocolloid?  ..............................................................  4 
 2.3  What  is  salicylic  acid?  ........................................................................................................  4 
 2.4  Our  hypothesis  ...................................................................................................................  5 
 2.5  Cartoon  ..............................................................................................................................  5 

 3.0  Problem  Statement  and  Design  Objectives  ........................................................................  6 
 3.1  Problem  Statement  ............................................................................................................  6 
 3.2  Research/Design  Objectives  .............................................................................................  6 

 4.0  Methods  ..................................................................................................................................  7 
 4.1  Schematic  and  qualitative  description  of  the  physics  ........................................................  7 
 4.2  Assumptions  ......................................................................................................................  7 
 4.3  Governing  Equations,  Boundary,  and  Initial  Conditions  .....................................................  8 
 4.4  Input  parameters  ..............................................................................................................  11 
 4.5  Software  Implementation  .................................................................................................  12 

 5.0  Results  and  Discussions  ....................................................................................................  13 
 5.1  Mesh  convergence  ..........................................................................................................  13 
 5.2  Experimental  validation  ....................................................................................................  14 

 5.2.1  Pus  Mass  Uptake  ....................................................................................................  14 
 5.2.2  Capillary-Driven  Diffusion  of  Pus  into  Patch  ...........................................................  15 
 5.2.3  Concentration  of  Salicylic  Acid  ...............................................................................  16 

 5.3  Results  .............................................................................................................................  17 
 5.4  Sensitivity  analysis  ...........................................................................................................  20 

 6.0  Conclusions  and  Design  Recommendations  ...................................................................  22 
 6.1  Conclusions  .....................................................................................................................  22 
 6.2  Design  Recommendations  ...............................................................................................  23 
 References  ............................................................................................................................  24 



 3 

 1.0 Executive summary 

 This  study  aims  to  investigate  how  a  pimple  patch  with  salicylic  acid  impacts  the  epidermis  for  pimple 

 pus  extraction.  Pimple  patches  are  used  to  treat  acne  and  have  grown  popular  due  to  their  discreet  nature 

 and  effectiveness.  However,  the  mechanism  of  pus  removal  using  these  patches  has  yet  to  be  fully 

 understood.  We  seek  to  understand  the  relationship  between  salicylic  acid  and  pus  extraction  to  identify 

 possible  methods  to  optimize  pimple  patches  for  a  more  efficient  and  cost-effective  treatment.  In  our 

 model,  salicylic  acid  is  delivered  to  the  skin  via  direct  contact  with  the  pimple  patch,  resulting  in  a 

 concentration  gradient  that  allows  the  acid  to  penetrate  into  the  dermis.  As  salicylic  acid  diffuses  from  the 

 patch  into  the  skin,  pimple  pus  is  drawn  out  of  the  skin  and  into  the  patch  by  diffusion  driven  by  a 

 concentration  gradient  and  capillary  action.  This  allows  the  absorption  of  pus  into  the  patch  above  the 

 skin.  We  hypothesize  that  as  the  salicylic  acid  diffuses,  the  skin  around  the  pimple  softens  and  becomes 

 more  porous,  allowing  the  pus  to  diffuse  out  of  the  skin  more  easily  into  the  hydrocolloid  patch.  Using 

 COMSOL,  we  have  simulated  the  increase  of  pus  diffusivity  in  the  epidermis  as  salicylic  acid  from  the 

 hydrocolloid  patch  diffuses  into  the  skin  and  the  increase  of  pus  diffusivity  in  the  hydrocolloid  patch  as 

 pus  enters  the  patch.  Based  on  our  model,  we  have  found  that  this  particular  pimple  patch  has  room  for 

 improvement.  In  an  8-hour  simulation,  which  parallels  the  typical  duration  a  user  wears  a  pimple  patch, 

 only  a  minimal  amount  of  pus  mass  is  removed  from  the  skin.  This  demonstrates  that  pimple  patches  may 

 not  be  the  most  effective  means  of  pimple  removal.  However,  since  research  on  this  topic  is  not  readily 

 available  to  the  public,  we  anticipate  that  our  model  will  be  useful  as  a  starting  point  for  future  pimple 

 patch development. 

 2.0 Introduction 

 2.1 What is acne? How is a pimple structured? 

 Acne  is  a  common  inflammatory  skin  condition  that  occurs  when  hair  follicles  become  clogged  with  oil 

 (sebum),  dead  skin  cells,  and  bacteria,  resulting  in  papules  and  pustules,  which  are  small,  red,  tender 

 bumps  caused  by  inflammation  in  clogged  pores  (Bolognia  &  Jorizzo,  2002).  It  primarily  affects  areas  of 

 the  skin  with  a  high  concentration  of  sebaceous  glands,  such  as  the  face,  chest,  back,  and  shoulders 

 (National  Institute  of  Arthritis  and  Musculoskeletal  and  Skin  Diseases,  n.d.).  Pimple  patches  are  typically 

 applied on the face to remove acne papules and pustules. 



 4 

 Figure 1:  Hydrocolloid patches are pasted onto pimples  to protect them from bacteria and to absorb pus 

 from the pimple underneath the skin (reproduced from Amazon.com). 

 2.2 What is a pimple patch? What is a hydrocolloid? 

 Pimple  patches  are  essentially  hydrocolloids,  traditionally  used  in  wound  dressings  for  their  ability  to 

 absorb  excess  moisture  and  promote  healing  (Burey  et  al.,  2008).  Beyond  moisture  absorption, 

 hydrocolloids  also  form  a  protective  barrier  that  shields  the  affected  area  from  external  contaminants, 

 reducing  the  risk  of  bacterial  infection  (Burey  et  al.,  2008).  Additionally,  some  pimple  patches  are 

 formulated  with  active  ingredients  such  as  salicylic  acid,  tea  tree  oil,  or  niacinamide  to  enhance  their 

 acne-fighting properties. This investigation focuses on salicylic acid. 

 2.3 What is salicylic acid? 

 As  a  beta-hydroxy  acid,  it  effectively  penetrates  the  stratum  corneum,  promoting  the  shedding  of  dead 

 skin  cells  and  unclogging  pores  (Arif,  2015).  This  desmolytic  action  disrupts  cellular  junctions  without 

 damaging  intercellular  keratin  filaments,  making  it  particularly  beneficial  for  treating  acne  vulgaris  (Arif, 

 2015). 



 5 

 2.4 Our hypothesis 

 Our  hypothesis  is  that  salicylic  acid  increases  the  permeability  of  the  dermis,  which  allows  for  the  pus  to 

 get  absorbed  by  the  pimple  patch  following  capillary  diffusion.  By  analyzing  the  interactions  between 

 salicylic  acid,  pus,  and  the  dermis,  we  aim  to  determine  the  optimal  concentration  of  salicylic  acid  and  the 

 ideal  duration  of  application.  Ultimately,  our  goal  is  to  develop  a  framework  for  optimizing  and  designing 

 a more efficient pimple patch. 

 2.5 Cartoon 

 Figure 2:  Geometry and boundary conditions for our  pimple patch model, along with the dimensions of 

 the patch, pus pocke, and different skin layers. 



 6 

 3.0 Problem Statement and Design Objectives 

 3.1 Problem Statement 
 Current  pimple  patch  designs  rely  primarily  on  hydrocolloid  technology  to  extract  pus,  yet  their  overall 

 effectiveness  remains  limited  due  to  a  lack  of  quantitative  understanding  of  how  active  ingredients  like 

 salicylic  acid  enhance  the  treatment  process.  To  address  this  challenge,  we  propose  a  quantitative  model 

 using  COMSOL  Multiphysics®  to  simulate  the  interactions  between  salicylic  acid,  dermal  layers,  and  pus 

 diffusion.  The  model  will  evaluate  how  salicylic  acid  diffuses  through  the  epidermis  and  dermis  to 

 enhance  permeability,  followed  by  the  resulting  pus  removal  by  the  hydrocolloid  patch  through  a 

 concentration  gradient.  This  model  is  2D-axisymmetric  and  applies  a  fixed  concentration  boundary 

 condition  to  represent  pus  diffusing  out  of  the  pus  pocket.  No-flux  boundary  conditions  are  used  where 

 appropriate  to  realistically  simulate  pus  movement  into  the  patch  and  to  capture  the  downward  diffusion 

 of  salicylic  acid.  We  propose  a  function  that  relates  skin  diffusivity  to  the  concentrations  of  salicylic  acid 

 and  pus,  based  on  literature  suggesting  that  salicylic  acid  enhances  pus  diffusivity.  By  analyzing  the 

 relationship  between  salicylic  acid  concentration  and  pus  diffusion,  this  study  will  quantitatively 

 determine  how  much  pimple  pus  is  removed  using  a  hydrocolloid  patch.  By  analyzing  the  interactions 

 between  salicylic  acid,  pus,  and  the  dermis,  we  aim  to  determine  the  optimal  concentration  of  salicylic 

 acid  and  the  ideal  duration  of  application.  The  findings  will  directly  inform  the  development  of  more 

 efficient  pimple  patches,  offering  improved  pimple  pus  removal  for  users  and  reducing  production  costs 

 for manufacturers. 

 3.2 Research/Design Objectives 
 1.  Develop  a  2D  axisymmetric  model  using  COMSOL  of  salicylic  acid  from  a  hydrocolloid  pimple 

 patch and its effect on the removal of pimple pus via capillary diffusion into the patch. 

 2.  Determine  the  exact  contribution  of  salicylic  acid  to  the  permeability  of  the  dermis  and  thus,  the 

 diffusion of pus from a pimple into the pimple patch. 

 3.  Quantitatively  measure  and  optimize  the  total  mass  of  pus  extracted  by  a  hydrocolloid  patch  with 

 salicylic acid 



 7 

 4.0 Methods 

 4.1 Schematic and qualitative description of the physics 
 When  the  pimple  patch  is  applied  onto  the  skin,  salicylic  acid  from  the  pimple  patch  diffuses  down  into 

 the  skin  layers,  which  initially  have  zero  concentration  of  salicylic  acid.  Due  to  the  capillary  pressure 

 from  the  patch,  the  pus  inside  the  skin  undergoes  capillary  diffusion  upwards  into  the  patch,  thus  resulting 

 in  the  removal  of  pus  from  the  pimple.  As  salicylic  acid  concentration  increases  in  the  skin  layers,  the 

 porosity  of  the  skin  will  increase,  allowing  pus  to  diffuse  into  the  patch  at  a  faster  rate.  For  a  complete 

 visual schematic of the processes mentioned above, please refer to Figure 2. 

 4.2 Assumptions 
 We made assumptions to simplify the model while still ensuring that the core behavior of the pimple 
 patch was maintained. 

 Assumption  Why? 

 2-D Axisymmetric Geometry  By approximating the pus geometry as a capped 
 uniform sphere in the skin, this reduces the 
 computational complexity of our problem 
 formulation. 

 Negligible Bulk Flow in Skin  In the skin layer for our model, we assume there is no 
 convective movement of the pus or acid further into 
 the skin due to blood flow. This is a reasonable 
 approximation as there are no veins in the top layers 
 of the skin where our model takes place. 

 No External Evaporative or Absorption Loss  We assume that moisture loss due to skin evaporation 
 and external absorption does not significantly affect 
 the patch’s performance during the simulation. 

 No Immune Cell Response  The model assumes that immune cell activity, such as 
 inflammation and bacterial response, does not 
 significantly impact pus diffusion or salicylic acid 
 absorption. While immune cells play a crucial role in 
 acne progression, their dynamics occur over a longer 
 timescale than the duration of the simulation 

 Ignore pH Effects  The model does not account for variations in skin pH 
 or how salicylic acid might alter local pH conditions. 
 Although pH affects enzymatic activity and skin 



 8 

 barrier function, it is outside the scope of our model. 

 No Sebum Production  Sebum (natural oil) production is assumed to remain 
 negligible and does not dynamically influence pus 
 removal or salicylic acid absorption. While excess 
 sebum contributes to acne formation, its production 
 rate is relatively slow compared to the timeframe of 
 pimple patch application. 

 4.3 Governing Equations, Boundary, and Initial Conditions 
 We  derived  governing  equations  from  the  cylindrical  mass  transfer  equation.  These  equations  model 

 time-dependent  and  radial  diffusion  of  salicylic  acid  and  pus  within  a  radially  symmetric  cylinder.  D  A  and 

 D  p  are  the  diffusivities  of  acid  and  pus,  respectively.  C  A  and  C  p  are  the  concentrations  of  acid  and  pus, 

 respectively.  accounts  for  the  radial  diffusion  of  species.  accounts  for  the  vertical  1 
 𝑟 

∂
∂ 𝑟 ( 𝑟 

∂ 𝐶 
 𝐴     𝑜𝑟     𝑝 

∂ 𝑟 )    
∂ 2  𝐶 

 𝐴     𝑜𝑟     𝑝 

∂ 𝑧  2 

 diffusion  of  species.  Finally,  accounts  for  how  the  concentration  of  acid  and  pus  changes  over 
∂ 𝐶 

 𝐴     𝑜𝑟     𝑝 

∂ 𝑡 

 time.  In  the  skin  layers  included  in  our  model,  bulk  fluid  flow  is  negligible,  and  only  diffusion  is 

 significant.  Thus,  our  governing  equations  only  include  the  diffusion  and  transient  terms  while  excluding 

 the convection term. 

 Salicylic Acid:     𝐷 
 𝐴 

[  1 
 𝑟 

∂
∂ 𝑟 ( 𝑟 

∂ 𝐶 
 𝐴 

∂ 𝑟 )   +    
∂ 2  𝐶 

 𝐴 

∂ 𝑧  2 ]   =
∂ 𝐶 

 𝐴 

∂ 𝑡 
 (1) 

 Pus:  𝐷 
 𝑝 
[  1 

 𝑟 
∂

∂ 𝑟 ( 𝑟 
∂ 𝐶 

 𝑝 

∂ 𝑟 )   +    
∂ 2  𝐶 

 𝑝 

∂ 𝑧  2 ]   =
∂ 𝐶 

 𝑝 

∂ 𝑡     (2) 

 To  take  into  account  the  effects  of  capillary  diffusion  of  the  pus  into  the  patch,  we  modeled  the  capillary 

 diffusivity  of  the  pus  in  the  patch  using  the  following  equations  based  on  a  paper  by  Ashari  and  Vahedi 

 Tafreshi  (2009),  which  models  capillary  pressure  in  a  thin  fibrous  sheet.  The  values  of  the  capillary 

 diffusivity  D  p  are  then  obtained  by  plotting  D  p  across  varying  concentrations  of  pus  in  the  patch  based  on 

 equation  (6).  This  plot  can  be  seen  in  Figure  3  below.  To  fully  derive  equation  (6),  we  used  equation  (5) 

 based  on  a  study  by  Brooks  and  Corey  (1964),  where  K  is  the  total  permeability  and  K  i  is  the  intrinsic 

 permeability of the patch. 

 𝐷 
 𝑝 
   =    − 𝑑𝑃 

 𝑑  𝐶 
 𝑝 

 𝐾 ρ
 𝑝  (3) 



 9 

− 𝑑𝑃 
 𝑑  𝐶 

 𝑝 
   = − 1 

 𝑀 
 𝑝 
 𝐶 

 𝑝 

 𝑣𝑔 
 1 − 𝑏 

 2 

σ 𝑐𝑜𝑠 (θ)
σ

 𝑤 
 𝑐𝑜𝑠 (θ

 𝑤 
)

 𝑀 
 𝑝 
 𝐶 

 𝑝 

ϕρ
 𝑝 

( )
 𝑏 

 2 

 1 − 𝑏 
 2 

−  1 
⎡
⎢
⎢
⎢
⎣

⎤
⎥
⎥
⎥
⎦

 1 
 𝑏 

 2 
− 1 

 𝑀 
 𝑝 
 𝐶 

 𝑝 

ϕρ
 𝑝 

( )
 𝑏 

 2 

 1 − 𝑏 
 2 

    (4) 

 𝐾    =    
 𝑀 

 𝑝 
 𝐶 

 𝑝 

ϕρ
 𝑝 

( ) 3 

 𝐾 
 𝑖 
       (5) 

 𝐷 
 𝑝 
   =    

− 𝐾 
 𝑖 
ρ

 𝑝 

 𝑀 
 𝑝 
 𝐶 

 𝑝 

 𝑣𝑔 
 1 − 𝑏 

 2 

σ 𝑐𝑜𝑠 (θ)
σ

 𝑤 
 𝑐𝑜𝑠 (θ

 𝑤 
)

 𝑀 
 𝑝 
 𝐶 

 𝑝 

ϕρ
 𝑝 

( )
 𝑏 

 2 

 1 − 𝑏 
 2 

−  1 
⎡
⎢
⎢
⎢
⎣

⎤
⎥
⎥
⎥
⎦

 1 
 𝑏 

 2 
− 1 

 𝑀 
 𝑝 
 𝐶 

 𝑝 

ϕρ
 𝑝 

( )
 𝑏 

 2 

 1 − 𝑏 
 2  𝑀 

 𝑝 
 𝐶 

 𝑝 

ϕρ
 𝑝 

( ) 3 

       (6) 

 Figure 3:  Capillary diffusivity of pus as pus enters  the hydrocolloid patch. 

 For  the  capillary  diffusivity  of  pus  in  the  skin,  we  based  our  equation  on  a  study  which  establishes  the 

 capillary  diffusivity  of  oil  in  a  porous  medium,  specifically  a  potato  (Halder  et.  al,  2007).  Since  the  skin  is 



 10 

 also  a  porous  medium  and  pus  has  similar  properties  to  oil,  we  decided  to  use  equation  (7)  given  by  the 

 paper  for  the  capillary  diffusivity  of  pus  in  the  epidermis  skin  layer.  Furthermore,  we  found  that  salicylic 

 acid  helps  in  removing  dead  skin  cells,  thus  opening  up  the  pores  of  the  skin  and  increasing  the  porosity 

 of  the  skin  layers  (Arif,  2015).  This  helps  in  allowing  the  pus  to  diffuse  more  easily  out  of  the  skin  into 

 the  patch  (Randjelović  et  al.,  2015).  This  eventually  leads  to  an  increase  in  the  diffusivity  of  pus  out  of  the 

 skin  into  the  patch.  To  take  this  effect  into  account,  we  assumed  that  the  concentration  of  acid  C  A  directly 

 affects the capillary diffusivity of pus in the skin, giving us equation (7) below. 

 (7)  𝐷 
 𝑠 

=  𝐷 
 0 
   ·    ( 𝐶 

 𝐴 
)   ·  𝑒 

(− 2 . 8 + 2 . 0 (
 𝑀 

 𝑝 
 𝐶 

 𝑝 
      

( ⍴ 
 𝑠𝑘𝑖𝑛 

   )( 1 −ϕ
 𝑒 
) ))

 Figure 4:  Capillary diffusivity of pus in the skin  which depends on two variables, the concentration of 

 pus and the concentration of salicylic acid in the skin. 

 Our  model  involves  a  combination  of  no-flux  boundary  conditions  and  constant-concentration  boundary 

 conditions. Complete details of these boundary conditions can be found in Figure 2. 

 At  the  start  of  the  simulation,  salicylic  acid  will  only  be  found  in  the  patch,  with  an  initial  concentration 

 of  480.09  mol/m  3  .  As  for  the  pus,  it  will  initially  only  be  found  in  the  pocket  of  pus,  as  shown  in  the 

 schematic  previously.  Based  on  the  density  of  facial  pus,  the  concentration  of  pus  in  this  pocket  will 



 11 

 initially  be  3537.54  mol/m  3  (Butcher  &  Coonin,  1949).  There  is  no  pus  in  the  patch  or  any  of  the  other 

 regions  of  the  skin  at  the  start  of  the  simulation.  To  model  the  diffusion  of  pus  from  the  bottom  of  the 

 epidermis  layer  of  the  skin  into  the  patch,  we  used  this  pus  concentration  to  set  a  concentration  boundary 

 condition  for  the  pus  at  the  bottom  of  the  epidermis.  We  set  the  concentration  at  the  bottom  of  the 

 epidermis  to  be  3537.54  mol/m  3  as  seen  in  Fig.  2.  For  clarity,  we  have  tabulated  the  initial  and  boundary 

 conditions below. 

 Initial Conditions 

 C  A, patch  (t = 0) = 480.09 mol/m  3 

 C  A, skin  (t = 0) = 0 mol/m  3 

 C  p, patch  (t = 0) = 0 mol/m  3 

 C  p, skin  (t = 0) = 0 mol/m  3 

 Boundary Conditions 

 C  p, skin  (z = bottom of epidermis) = 3537.54 mol/m  3 

 No-flux at all edges for both salicylic acid and pus 

 4.4 Input parameters 

 Parameters  Symbol  Values  Units  Source 

 Geometry: 
 -  Thickness of epidermis layer 
 -  Thickness of dermis layer 
 -  Thickness of subcutaneous fat 

 layer 
 -  Height of pus pocket 
 -  Width of pus pocket 
 -  Diameter of patch 
 -  Volume of patch 
 -  Volume of pimple 

 0.0461 
 1.37 
 1.20 

 0.50 
 1.00 
 8.00 
 0.0150796 
 0.0638833 

 mm 
 mm 
 mm 

 mm 
 mm 
 mm 
 cm  3 

 mm  3 

 Pimple Properties: 
 -  Pus concentration or density 

 at the bottom of the dermis 

 -  Initial mass of pus 
 -  Mass of pimple pus 
 -  Molar mass of pus 

 ⍴  p 

 M  p 

 3537.54 

 0.05749498 
 254.41 

 mol/m  3 

 g 
 g/mol 

 (Butcher & 
 Coonin, 1949) 

 (National Center 
 for Biotechnology 
 Information, 2025) 



 12 

 Skin Properties: 
 -  Epidermis porosity 
 -  Diffusivity of salicylic acid in 

 the skin and patch 
 -  Density of skin 

 -  Capillary diffusivity of pus in 
 the skin 

 -  Maximum concentration of 
 salicylic acid that enters 
 epidermis according to model 

 ɸ  e 
 D  A 

 ⍴  skin 

 D  s 

 0.17 
 2.45  ·  10  -9 

 1.1 

 See equation (7) 

 4.3159 

 cm  2  /s 

 g/cm  3 

 (Liu et al., 2018) 
 (Dasgupta et al., 
 2008) 

 (National Institute 
 of Standards and 
 Technology 
 [NIST], n.d.) 

 Patch Properties: 
 -  Initial mass of salicylic acid in 

 patch 
 -  Initial concentration of 

 salicylic acid in the patch 
 -  Initial diffusivity of pus in 

 patch 
 -  Capillary diffusivity of pus in 

 patch as pus enters the patch 
 -  Porosity of patch 
 -  Van-Genuchten coefficient 
 -  Intrinsic permeability 

 -  Van-Genuchten power 
 -  Surface tension of oil and 

 patch in model 
 -  Reference surface tension 

 -  Contact angle of oil and patch 
 in model 

 -  Reference contact angle 

 D  0 
 D  p 

 ɸ 
 vg 
 K  i 

 b  2 
 σ 

 σ  w 

 θ 

 θ  w 

 1 

 480.09 

 2  ·  10  -8 

 See Figure 3 

 0.78 
 1008 
 1.343  ·  10  -14 

 3.612 
 0.0277 

 0.072 

 27 

 80 

 mg 

 mol/m  3 

 cm  2  /s 

 M  2 

 N/m 

 N/m 

 ° 

 ° 

 (Starface, n.d.) 

 (Viljoen et al., 
 2015) 

 (Bustos et. al, 
 2010) 
 (Becker 2008) 
 (Spielman and 
 Goren, 1968) 
 (Becker 2008) 
 (Mozes et. al, 
 2017) 

 (Ashari and Vahedi 
 Tafreshi, 2009) 
 (Mozes et. al, 
 2017) 

 (Ashari and Vahedi 
 Tafreshi, 2009) 

 4.5 Software Implementation 

 We  implemented  our  2D  axisymmetric  model  in  COMSOL  using  the  “Transport  of  Diluted  Species” 

 physics  module  for  both  the  diffusion  of  salicylic  acid  from  the  patch  into  the  skin  layers  and  for  the 



 13 

 capillary  diffusion  of  pus  into  the  patch.  We  then  computed  solutions  using  a  time-dependent  solver,  along 

 with a constant time step of 0.005, initial time step of 0.001 and the BDF time stepping method. 

 5.0 Results and Discussions 

 5.1 Mesh convergence 

 To conduct mesh convergence, we plotted the final mass of pus that has been absorbed by the patch using 

 different mesh choices by increasing the number of domain elements in the mesh. This allows us to check 

 that the results from our model approximately converge across different meshes of increasing refinement. 

 Figure 5:  Mesh convergence analysis. 

 In  Figure  5  above,  we  can  see  that  by  increasing  the  number  of  mesh  elements  used,  the  mass  profile  of 

 pus  converges  after  around  118,000  elements  are  used.  This  suggests  that  we  can  eliminate  the  possibility 



 14 

 of  discretization  error  due  to  meshing  by  using  mesh  densities  higher  than  approximately  118,000 

 triangular elements. 

 5.2 Experimental validation 

 5.2.1 Pus Mass Uptake 

 To  validate  the  modeled  mass  uptake  of  pus  over  time,  we  compared  our  simulation  results  to 

 experimental  data  from  Bertrand  (1995),  who  studied  the  absorption  of  water  and  lubricating  oils  into 

 porous  nylon  over  several  hours.  While  literature  on  capillary-driven  diffusion  of  fluids,  particularly  oils, 

 into  porous  media  is  limited,  this  study  provides  a  useful  benchmark  for  assessing  the  physical  plausibility 

 of  our  model.  At  each  timestep,  we  calculated  the  total  mass  of  pus  absorbed  in  the  patch  domain  and 

 normalized  it  by  the  final  mass  at  the  end  of  the  simulation.  This  yielded  a  percent  uptake  curve  over 

 time,  which  we  compared  against  Bertrand’s  experimental  water  uptake  curve.  The  resulting  plot  allows 

 for  direct  comparison  of  the  characteristic  absorption  behavior,  independent  of  fluid  properties  or  patch 

 material. 

 Figure 6:  Normalized pus mass uptake from the model compared to water uptake from 

 Bertrand et al. (1995). 



 15 

 While  Bertrand’s  curve  shows  a  steep  initial  rise  followed  by  early  saturation,  our  model  exhibits  a 

 slower,  near-linear  increase  in  pus  mass  uptake  over  time.  These  results  are  not  perfectly  comparable,  but 

 this  aids  in  validating  our  model  because  pus  has  a  higher  viscosity  than  water.  As  a  result,  we  would 

 expect the uptake of pus to exhibit slower behavior than water, which is depicted in Figure 6. 

 5.2.2 Capillary-Driven Diffusion of Pus into Patch 

 To  further  validate  the  observed  behavior  of  capillary-driven  pus  diffusion  into  the  patch,  we  compared 

 our  model  with  Beuther  et  al.  (2010),  who  used  X-ray  imaging  to  characterize  how  fluids  wick  into  towel 

 and  tissue  materials.  They  observed  a  square-root  relationship  between  fluid  mass  absorbed  and  time, 

 indicative  of  the  Lucas-Washburn  Model,  which  describes  how  capillary  forces  drive  liquid  flow  into  a 

 porous  medium,  predicting  that  the  total  mass  of  liquid  absorbed  grows  proportionally  with  the  square 

 root  of  time  (Lucas  1918;  Washburn  1921).  Observing  this  relationship  in  towel  absorption  experiments 

 supports  the  idea  that  pimple  patches  likely  follow  similar  capillary-driven  dynamics  for  pus  uptake  into 

 the  patch.  The  following  data  were  extracted  from  Beuther  et  al.’s  (2010)  Figure  2  and  present  radial 

 absorbance data for a 1-ply towel, analogous to our 2D axisymmetric geometry. 

 Figure 7:  Liquid mass absorbed over time for a 1-ply  towel, showing differences based on which side of 

 the towel faces upward during fluid uptake (Buether et al., 2010). 



 16 

 An  R²  test  (used  to  quantify  how  well  data  fit  a  given  trend)  was  conducted  on  data  from  our  model  to 

 confirm the validity of the √time dependence in our model, as shown in Figure 8 below. 

 Figure 8:  Total pus mass in patch (left), and corresponding  R  2  test against √time (left). 

 Based  on  these  results,  we  find  that  our  model  predicts  a  square-root  uptake  trend,  consistent  with  the 

 experimental  data  from  Buether  et  al.  (2010)  and  the  Lucas-Washburn  Model.  Mass  uptake  shows  a 

 strong  linear  relationship  with  the  square  root  of  time  (R²  =  0.9714),  consistent  with  capillary-driven 

 absorption  behavior.  This  agreement  reinforces  the  validity  of  our  model’s  assumption  that  pus  uptake  is 

 governed by capillary diffusion dynamics, similar to other porous absorption systems. 

 5.2.3 Concentration of Salicylic Acid 

 For  validating  the  concentration  of  salicylic  acid  over  time,  we  consider  the  case  of  simple  diffusion 

 without  capillary-driven  forces.  We  compared  our  results  to  experimental  data  from  Métayer  et  al.  (1999), 

 who  measured  water  diffusion  through  polyester  films.  The  cumulative  uptake  data  from  their  Figure  5 

 displays  a  sigmoidal  uptake  curve  over  a  comparable  time  scale,  reflecting  the  diffusion-dominated 

 transport  behavior  relevant  to  our  system.  Although  their  results  represent  cumulative  mass  rather  than 

 point  concentration,  both  curves  exhibit  the  characteristic  shape  expected  for  diffusion-driven  uptake  in 

 porous media. 



 17 

 Figure 9:  Normalized salicylic acid concentration  from the model compared to cumulative water uptake 

 data from Métayer et al. (1999). 

 The sigmoidal shape of both curves reflects a gradual transition from low to high concentrations, which is 

 characteristic of diffusion-controlled processes in porous media. While the reference curve rises more 

 steeply due to convective enhancement, the agreement in shape supports that our model captures the 

 essential physics of simple diffusion of salicylic acid (delayed onset and progressive saturation). The 

 behavior is also consistent with the analytic solution for diffusion in a semi-infinite domain. 

 𝐶 ( 𝑥 ,  𝑡 ) =  𝐶 
 0 
   ·  𝑒𝑟𝑓 (  𝑥 

 2√  𝐷𝑡 )  (8) 

 This applies here because the acid penetrates only a small distance relative to the much larger domain of 

 the skin, resulting in a sigmoidal concentration profile over time. 

 5.3 Results 
 Since  pimple  patches  are  usually  recommended  to  be  used  throughout  an  8-hour  work  day,  we  decided  to 

 simulate  our  model  over  a  period  of  8  hours.  The  next  two  figures  illustrate  the  diffusion  of  salicylic  acid 

 into the skin. 



 18 

 Figure  10  shows  the  initial  concentration  of  salicylic  acid  throughout  the  patch  and  skin  layers.  Figure  11 

 then  shows  the  diffusion  of  salicylic  acid  after  a  total  of  8  hours.  The  salicylic  acid  has  diffused  into  the 

 epidermis,  but  not  as  much  into  the  dermis  layer.  This  is  still  acceptable,  because  our  primary  interest  is  in 

 the  epidermis  layer,  as  this  is  where  most  of  the  pus  is  diffusing  out  from.  Overall,  salicylic  acid  in  the 

 patch decreased as the acid entered the skin layers over the course of 8 hours as expected. 

 Figure 10:  Initial concentration of salicylic acid  throughout the hydrocolloid patch and skin layers. 

 Figure 11:  Concentration of salicylic acid throughout  the patch and skin layers after 8 hours of usage. 

 Figures  12  and  13  below  illustrate  the  capillary  diffusion  of  pus  from  the  epidermis  layer  into  the 

 hydrocolloid  patch.  Figure  12  shows  the  initial  concentration  of  pus,  while  Figure  13  shows  the  resulting 



 19 

 concentration  of  pus  after  capillary  diffusion  into  the  patch  throughout  8  hours.  From  these  figures,  we 

 can  see  that  pus  is  gradually  diffusing  into  the  patch  from  the  skin,  showing  that  our  patch  is  indeed 

 functioning as expected. 

 Figure 12:  Initial concentration of pus throughout  the hydrocolloid patch and epidermis layer. 

 Figure 13:  Concentration of pus throughout the patch  and epidermis layer after 8 hours of usage. 



 20 

 5.4 Sensitivity analysis 
 For  our  sensitivity  analysis,  we  decided  to  test  the  sensitivity  of  our  model  to  four  parameters  that  we 

 believe  will  have  the  greatest  influence  on  the  simulation  results.  In  particular,  the  four  parameters  chosen 

 include  the  initial  diffusivity  of  pus  in  the  patch,  the  diffusivity  of  salicylic  acid  through  the  skin  layers, 

 the  initial  concentration  of  salicylic  acid  present  in  the  patch,  and  the  density  of  the  skin.  To  test  the  effect 

 of  varying  these  four  parameters,  we  measured  the  mass  of  pus  absorbed  by  the  patch  over  a  period  of  8 

 hours for each time we changed a parameter. 

 We  first  chose  to  vary  the  initial  diffusivity  of  pus  in  the  patch,  as  this  parameter  largely  influences  the 

 rate  at  which  pus  gets  absorbed  into  the  patch  from  the  skin.  Overall,  with  lower  pus  diffusivity  in  the 

 patch,  we  would  expect  to  see  a  lower  amount  of  pus  removed  from  the  skin  by  the  patch.  On  the  other 

 hand,  with  higher  pus  diffusivity,  we  would  expect  to  see  a  higher  amount  of  pus  present  in  the  patch  at 

 the end. This indicates a high rate of pus removal from the skin. 

 We  then  chose  to  vary  the  diffusivity  of  salicylic  acid,  as  this  parameter  has  a  great  influence  on  the  rate  at 

 which  salicylic  acid  enters  the  skin  layers  from  the  patch.  We  have  established  that  salicylic  acid  helps  in 

 removing  dead  skin  cells,  thus  opening  up  the  pores  of  the  skin  (Arif,  2015).  This  contributes  to 

 increasing  the  rate  of  pus  removal  into  the  patch  from  the  skin.  Thus,  if  there  is  a  higher  rate  of  salicylic 

 acid  diffusion  into  the  skin,  then  the  mass  of  pus  absorbed  into  the  patch  should  increase  at  a  faster  rate, 

 too.  Consequently,  if  the  diffusivity  of  salicylic  acid  is  decreased,  we  expect  to  observe  a  slower  rate  of 

 absorption of pus into the pimple patch. 

 Furthermore,  we  also  chose  to  vary  the  concentration  of  salicylic  acid  that  is  initially  present  in  the  pimple 

 patch  before  usage  for  similar  reasons.  With  more  starting  salicylic  acid  provided,  we  expect  that  there 

 will  be  more  salicylic  acid  entering  the  skin  over  time.  Hence,  we  correspondingly  expect  to  see  a  higher 

 mass  of  pus  absorbed  into  the  patch  after  a  period  of  8  hours.  Similarly,  if  we  decrease  the  initial 

 concentration  of  salicylic  acid  in  the  patch,  we  expect  to  see  a  lower  mass  of  pus  in  the  patch  after  8  hours 

 of usage. 

 The  last  parameter  we  chose  to  vary  is  the  density  of  the  skin.  We  know  that  different  people  have 

 different  skin  types.  Some  individuals  may  have  a  denser  and  tougher  skin  complexion  than  others,  and 

 vice  versa.  This  variation  in  skin  density  will  affect  how  easily  pus  is  removed  from  the  skin  into  the 

 patch.  With  higher  skin  density,  it  will  be  more  difficult  for  the  pus  to  diffuse  out  of  the  skin,  resulting  in  a 

 lower  mass  of  pus  in  the  patch  at  the  end  of  the  simulation.  On  the  other  hand,  with  lower  skin  density,  it 



 21 

 will  be  easier  for  the  pus  to  diffuse  out  of  the  skin,  leading  to  a  higher  mass  of  pus  in  the  patch  after  a 

 period of 8 hours. 

 Figure 14:  Sensitivity analysis by varying the diffusivity  of pus, the diffusivity of acid, the initial 

 concentration of acid in the patch, and the density of skin. 

 We  began  modeling  the  patch  with  an  initial  pus  diffusivity  of  2  ·  10  -8  m  2  /s.  We  decreased  it  by  10%  to 

 1.8  ·  10  -8  m  2  /s  and  increased  it  by  10%  to  2.2  ·  10  -8  m  2  /s.  We  found  a  percentage  change  of  mass  absorbed 

 of  -0.2632%  when  we  decreased  the  initial  pus  diffusivity  and  an  increase  of  0.4644%  when  we  increased 

 the initial pus diffusivity. 

 The  initial  diffusivity  of  acid  in  salicylic  acid  through  skin  layers  was  2.45  ·  10  -9  cm  2  /s.  We  decreased  it 

 by  10%  to  2.2  ·  10  -9  cm  2  /s  and  increased  it  by  10%  to  2.7  ·  10  -9  cm  2  /s.  Both  decreasing  and  increasing 

 this  parameter  resulted  in  significant  variation  with  a  percentage  change  of  -0.4954%  and  0.2079%, 

 respectively. 

 For  the  initial  concentration  of  acid  in  the  patch,  we  found  a  bit  more  variation.  The  initial  concentration 

 of  acid  in  the  patch  began  as  480.09  mol/m  3  .  We  decreased  it  by  10%  to  432.081  mol/m  3  and  increased  it 

 by  10%  to  528.099  mol/m  3  .  This  led  to  a  percentage  change  of  -0.1150%  for  decreased  initial 

 concentration and 0.6524% for increased initial concentration. 



 22 

 Finally,  we  varied  the  skin  density.  The  established  skin  density  was  1.1  g/cm  3  .  We  decreased  it  by  10%  to 

 0.99  g/cm  3  and  increased  it  by  10%  to  1.21  g/cm  3  .  This  led  to  a  percentage  change  of  0.3185%  for 

 decreased skin density and -0.2963% for increased skin density. 

 The  information  that  we  gained  from  the  sensitivity  analysis  is  that  increasing  the  initial  concentration  of 

 acid  in  the  patch  leads  to  significantly  more  pus  absorption  into  the  patch.  Therefore,  a  manufacturer  may 

 want  to  increase  the  concentration  of  acid  that  they  insert  into  the  hydrocolloid  to  ensure  maximum  pus 

 removal.  We  also  see  that  the  density  of  skin  impacts  how  much  pus  is  removed,  which  can  guide 

 manufacturing  by  adjusting  the  pimple  patch  for  individuals  with  varying  skin  densities.  Perhaps,  the 

 manufacturer  would  want  to  increase  the  initial  concentration  of  salicylic  acid  in  the  patch  for  individuals 

 with  dense  skin.  For  the  diffusivity  of  the  salicylic  acid  and  pus,  these  are  fundamentally  material 

 properties  that  would  be  difficult  for  a  manufacturer  to  vary.  However,  the  sensitivity  analysis  of  these 

 values  emphasizes  the  importance  of  choosing  the  correct  diffusivity  values  for  the  pus  and  acid  to  ensure 

 that the absorption of the pus in the patch is accurate. 

 6.0 Conclusions and Design Recommendations 

 6.1 Conclusions 
 Overall,  our  model  has  allowed  us  to  observe  the  relationship  between  salicylic  acid  diffusion  and  pus 

 uptake  into  a  pimple  patch.  Through  our  simulation,  we  observed  that  salicylic  acid  diffuses  into  the 

 epidermis  skin  layer  while  a  minimal  amount  of  pus  was  absorbed  by  the  patch.  There  are  several 

 limitations  and  large  assumptions  in  our  model,  such  as  how  we  used  equations  for  oil  diffusivity  in 

 potatoes  for  the  pus  diffusivity.  Nevertheless,  our  model  is  a  relatively  good  illustration  of  how  salicylic 

 acid  diffusivity,  along  with  other  factors  such  as  initial  concentration  of  salicylic  acid  and  skin  density, 

 affects  pus  uptake  into  the  pimple  patch.  Furthermore,  the  results  of  our  model  have  been  validated 

 against published literature online on closely related physical scenarios. 

 In  order  to  further  improve  this  model,  we  would  need  to  conduct  experiments  with  actual  pimple  patches 

 for  primary  data  collection.  This  would  enable  us  to  validate  our  model  using  more  accurate  experimental 

 data  on  how  a  pimple  patch  absorbs  pus  through  capillary  action.  Furthermore,  we  would  need  to  better 

 take  into  consideration  other  factors  that  were  considered  negligible  in  this  report,  such  as  skin  types, 



 23 

 surrounding  humidity,  and  surrounding  temperature.  With  that  said,  this  model  is  a  good  precursor  for  the 

 development of a pimple patch, especially for reducing time, resources and experimentation. 

 6.2 Design Recommendations 
 From  a  business  analytics  or  sales  perspective,  we  would  like  to  minimize  the  costs  of  producing  the 

 pimple  patch  while  maintaining  its  effectiveness.  This  means  taking  our  sensitivity  analysis  into  account, 

 particularly  the  initial  concentration  of  salicylic  acid  in  the  patch  as  this  would  contribute  to  input  costs. 

 For  instance,  to  minimize  costs  and  the  chances  of  acid  overapplication  on  the  skin,  skincare  companies 

 can  use  less  salicylic  acid  without  compromising  pus  removal  significantly.  They  can  then  recommend  a 

 longer  time  of  usage  instead  to  compensate  for  this  change.  Furthermore,  we  also  suggest  creating  two 

 different  versions  of  the  same  pimple  patch,  one  with  a  slightly  higher  initial  concentration  of  salicylic 

 acid  for  individuals  with  denser  skin.  In  theory,  this  would  enable  a  streamlined  production  process  while 

 enhancing patch efficacy for users with varying skin types. 



 24 

 References 

 Amazon.com: Zatktk Pimple Patches (6 sizes 138 patches), acne patches for large zit breakouts, 
 hydrocolloid bandages for face, Chin, nose, forehead, body, back, neck & chest, oval 
 hydrocolloid acne patches : Beauty & Personal Care. (n.d.). 
 https://www.amazon.com/Breakouts-Hydrocolloid-Bandages-Forehead-Salicylic/dp/B0B 
 JVHGZ1W 

 Arif, T. (2015). Salicylic acid as a peeling agent: A comprehensive review.  Clinical, Cosmetic 
 and Investigational Dermatology, 8  , 455–461. https://doi.org/10.2147/CCID.S84765 

 Ashari, A., & Vahedi Tafreshi, H. (2009). General capillary pressure and relative permeability 
 expressions for through-plane fluid transport in thin fibrous sheets.  Colloids and Surfaces 
 A: Physicochemical and Engineering Aspects, 346  (1–3),  114–122. 
 https://doi.org/10.1016/j.colsurfa.2009.06.001 

 Becker, J., Schulz, V., & Wiegmann, A. (2008). Numerical determination of two-phase material 
 parameters of a gas diffusion layer using tomography images. Journal of Fuel Cell 
 Science and Technology, 5(2), 021006. https://doi.org/10.1115/1.2821600 

 Bertrand, P. A. (1995). Absorption of water and lubricating oils into porous nylon (NASA 
 Contractor Report No. NASA-CR-197344). NASA. 
 https://ntrs.nasa.gov/citations/19950015966 

 Bolognia, J. L., & Jorizzo, J. L. (2002). Pustular skin disorders.  American Journal of Clinical 
 Dermatology, 3  (6), 389–400. https://doi.org/10.2165/00128071-200203060-00003 

 Brooks, R. H., & Corey, A. T. (1964). Hydraulic properties of porous media (Hydrology Paper 
 No. 3). Colorado State University. https://doi.org/10.13031/2013.40684 

 Burey, P., Bhandari, B. R., Howes, T., & Gidley, M. J. (2008). Hydrocolloid gel particles: 
 Formation, characterization, and application.  Critical  Reviews in Food Science and 
 Nutrition, 48  (5), 361–377. https://doi.org/10.1080/10408390701347801 

 Bustos, J, Herrera, R, González, U, Martínez, A, & Catalán, A. (2010). Effect of Inmersion 
 Desinfection with 0.5% Sodium Hypochlorite and 2% Glutaraldehyde on Alginate and 
 Silicone: Microbiology and SEM Study.  International  journal of odontostomatology  , 
 4(2), 169-177. https://dx.doi.org/10.4067/S0718-381X2010000200011 

 Butcher, E. O., & Coonin, A. (1949). The physical properties of human sebum.  Journal of 
 Investigative Dermatology  , 12(4), 249–254. https://doi.org/10.1038/jid.1949.37 



 25 

 Dasgupta, R., Banthia, A., & Tibarewala, D. N. (2008). Study of diffusion characteristics of 
 salicylic acid through cellulose acetate membrane and extracted mouse skin by 
 iontophoresis.  Trends in Biomaterials and Artificial  Organs  , 21(2). 
 https://www.researchgate.net/publication/240638755_Study_of_Diffusion_Characteristic 
 s_of_Salicylic_Acid_through_Cellulose_Acetate_Membrane_and_Extracted_Mouse_Ski 
 n_by_Iontophoresis 

 Halder, A., Dhall, A., & Datta, A. K. (2007). An improved, easily implementable, porous 
 media-based model for deep-fat frying: Part I: Model development and input parameters. 
 Food and Bioproducts Processing  , 85(3), 209–219. https://doi.org/10.1205/fbp07033 

 Liu, P., Zhu, J.-Y., Tang, B., & Hu, Z.-C. (2018). Three-dimensional digital reconstruction of 
 skin epidermis and dermis. Journal of Microscopy, 270(2), 170–175. 
 https://doi.org/10.1111/jmi.12671 

 Lucas, R. (1918).  Ueber das Zeitgesetz des kapillaren  Aufstiegs von Flüssigkeiten  . 
 Kolloid-Zeitschrift, 23(1), 15–22. https://doi.org/10.1007/BF01461107 

 Métayer, M., Copinet, A., Coma, V., & Bayard, R. (1999). Diffusion of water through various 
 polymer films: Application to food packaging. International Journal of Pharmaceutics, 
 184(2), 189–198. https://doi.org/10.1016/S0142-9418(98)00052-X 

 Mozes, R., Cooper, P. K., Atkin, R., & Li, H. (2017). Ionic Liquids as Grease Base Liquids. 
 Lubricants, 5(3), 31. https://doi.org/10.3390/lubricants5030031 

 National Center for Biotechnology Information (2025). PubChem Compound Summary for CID 
 5312419, Sapienic acid. Retrieved April 28, 2025 from 
 https://pubchem.ncbi.nlm.nih.gov/compound/Sapienic-acid. 

 National Institute of Arthritis and Musculoskeletal and Skin Diseases. (n.d.). Acne.  U.S. 
 Department of Health and Human Services.  Retrieved  February 14, 2025, from 
 https://www.niams.nih.gov/health-topics/acne 

 National Institute of Standards and Technology (NIST). (n.d.). X-ray mass attenuation 
 coefficients – Water. NIST Physics Laboratory. Retrieved March 24, 2025, from 
 https://physics.nist.gov/cgi-bin/Star/compos.pl?matno=250 

 Randjelović, P., Veljković, S., Stojiljković, N., Sokolović, D., Ilić, I., Laketić, D., Randjelović, 
 D., & Randjelović, N. (2015). The beneficial biological properties of salicylic acid.  Acta 
 Facultatis Medicae Naissensis, 32  (4), 259–265. https://doi.org/10.1515/afmnai-2015-002 



 26 

 Spielman, L., & Goren, S. L. (1968). Improving resolution in Coulter counting by hydrodynamic 
 focusing. Journal of Colloid and Interface Science, 26(2), 175-182. 
 https://doi.org/10.1016/0021-9797(68)90310-X 

 Starface. (n.d.).  Salicylic acid hydro-stars  . Starface. 
 https://starface.world/products/salicylic-acid-hydro-stars 

 Viljoen, J. M., Cowley, A., du Preez, J., Gerber, M., & du Plessis, J. (2015). Penetration 
 enhancing effects of selected natural oils utilized in topical dosage forms. Drug 
 Development and Industrial Pharmacy, 41(12), 2045–2054. 
 https://doi.org/10.3109/03639045.2015.1047847 

 Washburn, E. W. (1921).  The dynamics of capillary  flow  . Physical Review, 17(3), 273–283. 
 https://doi.org/10.1103/PhysRev.17.273