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Drop impact on solids: contact-angle hysteresis filters impact energy into modal vibrations

Published online by Cambridge University Press:  21 July 2021

Vanessa R. Kern Open the ORCID record for Vanessa R. Kern [Opens in a new window] ,
Joshua B. Bostwick Open the ORCID record for Joshua B. Bostwick [Opens in a new window]  and
Paul H. Steen Open the ORCID record for Paul H. Steen [Opens in a new window]
Vanessa R. Kern*
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY14850, USA
Joshua B. Bostwick
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
Paul H. Steen
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY14850, USA
*
†Email address for correspondence: vrk24@cornell.edu
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Abstract

The energetics of drop deposition are considered in the capillary-ballistic regime characterized by high Reynolds number and moderate Weber number. Experiments are performed impacting water/glycol drops onto substrates with varying wettability and contact-angle hysteresis. The impacting event is decomposed into three regimes: (i) pre-impact, (ii) inertial spreading and (iii) post contact-line (CL) pinning, conveniently framed using the theory of Dussan & Davis (J. Fluid Mech., vol. 173, 1986, pp. 115–130). During fast-time-scale inertial spreading, the only form of dissipation is CL dissipation ($\mathcal {D}_{CL}$). High-speed imaging is used to resolve the stick-slip dynamics of the CL with $\mathcal {D}_{CL}$ measured directly from experiment using the $\Delta \alpha$-$R$ cyclic diagram of Xia & Steen (J. Fluid Mech., vol. 841, 2018, pp. 767–783), representing the contact-angle deviation against the CL radius. Energy loss occurs on slip legs, and this observation is used to derive a closed-form expression for the kinetic K and interfacial $\mathcal{A}$ post-pinning energy $\{K+\mathcal {A}\}_p/\mathcal {A}_o$ independent of viscosity, only depending on the rest angle $\alpha _p$, equilibrium angle $\bar {\alpha }$ and hysteresis $\Delta \alpha$, which agrees well with experimental observation over a large range of parameters, and can be used to evaluate contact-line dissipation during inertial spreading. The post-pinning energy is found to be independent of the pre-impact energy, and it is broken into modal components with corresponding energy partitioning approximately constant for low-hysteresis surfaces with fixed pinning angle $\alpha _p$. During slow-time-scale post-pinning, the liquid/gas ($lg$) interface is found to vibrate with the frequencies and mode shapes predicted by Bostwick & Steen (J. Fluid Mech., vol. 760, 2014, pp. 5–38), irrespective of the pre-impact energy. Resonant mode decay rates are determined experimentally from fast Fourier transforms of the interface dynamics.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Capillary waves Interfacial Flows (free surface): Contact lines
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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