Contact angle dynamics in droplets impacting on flat surfaces with different wetting characteristics

Abstract

An experimental study is presented on contact angle dynamics during spreading/recoiling of mm-sized water droplets impacting orthogonally on various surfaces with $\hbox{\it We}\,{=}\,O(0.1)-O(10)$, $Ca\,{=}\,O(0.001)-O(0.01)$, $\hbox{\it Re}\,{=}\,O(100)-O(1000)$, $Oh\,{=}\,O(0.001)$ and $Bo\,{=}\,O(0.1)$. In this impact regime, inertial, viscous and capillary phenomena act in unison to influence contact angle dynamics. The wetting properties of the target surfaces range from wettable to non-wettable. The experiments feature accelerating and decelerating wetting lines, capillary surface waves in the early impact stages, contact angle hysteresis, and droplet rebound under non-wetting conditions. The objective of the work is to provide insight into the dynamic behaviour of the apparent (macroscopic) contact angle $\theta$ and its dependence on contact line velocity $V_{\hbox{\scriptsize{\it CL}}}$ at various degrees of surface wetting. By correlating the temporal behaviours of $\theta$ and $V_{\hbox{\scriptsize{\it CL}}}$, the angle vs. speed relationship is established for each case examined. The results reveal that surface wettability has a critical influence on dynamic contact angle behaviour. The hydrodynamic wetting theory of Cox (J. Fluid Mech. vol. 357, 1998, p. 249) and the molecular-kinetic theory of wetting by Blake & Haynes (J. Colloid Interface Sci.) vol. 30, 1969, p. 421) are implemented to extract values of the corresponding microscopic wetting parameters required to match the experimentally observed $\theta$vs. $V_{\hbox{\scriptsize{\it CL}}}$ data. Application of hydrodynamic theory indicates that in the slow stage of forced spreading the slip length and the microscopic contact angle should be contact line velocity dependent. The hydrodynamic theory performs well during kinematic (fast) spreading, in which solid/liquid interactions are weak. Application of the molecular kinetic theory yields physically reasonable molecular wetting parameters, which, however, vary with impact conditions. The results indicate that even for a single liquid there is no universal expression to relate contact angle with contact line speed. Finally, analysis of the spreading dynamics on the non-wettable surfaces shows that it conforms to the Cassie-Baxter regime (only partial liquid/solid contact is maintained). The present results offer guidance for numerical or analytical studies, which require careful attention to the implementation of boundary conditions at the moving contact line, including the need to specify the dependence of contact angle on contact line speed.