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Drop depositions are impacts where post impact the drop remains on the surface and its liquid/gas (LG) interface does not break apart. Our focus is on drop depositions in the capillary-ballistic regime. During drop impact, the falling drop’s pre-impact energy transforms into fast-time scale motion of the three-phase contact-line (CL). The CL then comes to rest and the LG interface oscillates, viscously dissipating remaining energy on a slow-time scale. The energetics of drop deposition are characterized by high Reynolds number and moderate Weber number. Experiments are performed by impacting water/glycol drops onto substrates with varying wettability and hysteresis. The impacting event can be decomposed into three regimes: i) pre-impact, ii) inertial spreading, and iii) post CL pinning, which are conveniently framed using the theory of Dussan and Davis (1986). First we focus on the inertial spreading regime. Here we use high-speed imaging to resolve the stick-slip dynamics of the CL. The only form of dissipation during this fast-time scale is CL dissipation. Loss of energy occurs during a slip leg, and this observation is used to derive a closed-form expression for the ‘post-pinning’ energy. This prediction is independent of viscosity, only depending on the rest angle, equilibrium angle and hysteresis. This prediction agrees well with experimental observation for a range of liquid viscosities. We find this prediction of the post-pinning energy can be used to evaluate contact-line dissipation during inertial spreading. Next we focus on the drop’s post-pinning dynamics. We show the LG interface vibrates with the frequencies and mode shapes predicted by Bostwick and Steen (2014), irrespective of the droplet’s ‘pre-impact’ energy. Decay rates for the resonant modes are determined experimentally from FFTs of the interface dynamics. We find that the ‘post-pinning’ energy is independent of the ‘pre-impact’ energy and can be broken into modal components. Next we consider oblique drop impacts as an inverse problem framed analogously to mathematician Mark Kac’s famous question ‘Can one hear the shape of a drum?’ (Kac, 1966). We find that knowledge of the drop’s post-pinning LG frequency spectrum allows one to determine the rest angle and drop volume using theory for sessile drop oscillations (Bostwick and Steen, 2014). We also find that the substrate’s inclination angle can be determined from the ‘post-pinning’ energy partitioning of the [1,1] and [2,0] vibrational modes. These results demonstrate that details of the impacting event can be known ex post facto without a priori knowledge of the experimental conditions. Last we discuss some future problems, including experiments to be performed on the International Space Station later this year. In microgravity capillary phenomenon occur with slower time scales and at larger length scales than their earth-based counterparts. Here we hope to expand our understanding of the fast moving CL by benefiting from this effective spatial/temporal magnification, alleviating earth based imaging restrictions.
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130 pages
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capillary flows; capillary waves; contact lines; drops
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Union Local
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Daniel, Susan
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Jenkins, Jim
Hanrath, Tobias
Steen, Paul H.
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Chemical Engineering
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Ph. D., Chemical Engineering
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Doctor of Philosophy
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Government Document
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Attribution 4.0 International
dissertation or thesis
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