Effects of temperature-dependent contact angle on the flow dynamics of an impinging droplet on a hot solid substrate

A temperature-dependent dynamic contact angle as a function of temperature-dependent surface tension and reference equilibrium contact angle is proposed for modeling of moving contact line flows, in particular, for computations of liquid droplet impingement on a hot solid substrate. The fluid flow in the liquid droplet is described by the time-dependent incompressible Navier-Stokes equations, whereas the heat transfer in the liquid droplet and in the solid substrate is described by the energy equation. The arbitrary Lagrangian-Eulerian (ALE) approach together with the finite element method is used to solve the governing equations in a time-dependent domain. Further, the Marangoni effects are incorporated into the model without evaluating the tangential derivatives of the temperature on the free surface. The effects of temperature-dependent contact angle on the flow dynamics of the droplet and on the heat transfer from the solid substrate into the liquid droplet are studied for different Reynolds numbers, Weber numbers, solid phase Peclet numbers, solid phase initial temperatures and reference equilibrium contact angles. Numerical studies show that the influence of the temperature-dependent contact angle is negligible in partially wetting droplets, whereas the effects on the wetting diameter and on the total heat transfer are 10.79% and 7.36% respectively in the considered highly wetting and non-wetting droplets.