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

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 (D-CL). High-speed imaging is used to resolve the stick-slip dynamics of the CL with 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 A post-pinning energy {K + A}(p)/A(o) independent of viscosity, only depending on the rest angle alpha(p), equilibrium angle (alpha) over bar 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.

Automated summary

The study investigates the energetics of drop deposition in different wetting and contact angle conditions. The impacting event is decomposed into three different stages, with observation of contact line dissipation and successful resolution of the slip dynamics of the contact line through high-speed imaging.