Influence of Contact Line Velocity Implementation in Dynamic Contact Angle Models for Droplet Bouncing and Non-bouncing Dynamics on a Solid Substrate

In this work, we studied numerically the dynamic behaviour of droplet impact over two different wettability surfaces having equilibrium contact angles of 91° and 147° in hydrophilic and hydrophobic range, respectively. Numerical simulations are performed using an in-house code based on Dual Grid Level Set Method (DGLSM) (Gada and Sharma in Numerical Heat Transfer, Part B: Fundamentals 59:26–57, 2011) as an interface tracking method. We implemented Yokoi’s dynamic contact angle model in solver, in which the dynamic contact angle varies as the function of contact line velocity. We considered the computational domain as 2D cylindrical axisymmetric. An in-house code developed by (Gada, V. H. (2012). A novel level-set based CMFD methodology in 2D/3D Cartesian and cylindrical coordinates and its application for analysis of stratified flow and film boiling. IIT Bombay.) with modifications on contact line velocity is implemented, considering the dynamic contact angle as a boundary condition in the DGLSM (Yokoi et al. in Phys Fluids 21, 2009). Sudden jumps in thermo-physical properties across interface are smoothened by considering the interface to be diffused. It has been found that implementation of Second-Order Upwind (SOU) and First-Order Upwind (FOU) schemes to approximate contact line velocity show a good match of numerically obtained temporal variation of droplet diameter and droplet height, with published results for both the bouncing and non-bouncing droplets. But the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme gives a comparatively better result specifically for bouncing and errors for non-bouncing cases.