A Meshfree Method for Simulations of Dynamic Wetting

Abstract

In this paper we present a meshfree Lagrangian particle method for the simulation of dynamic wetting phenomena. The essence of dynamic wetting is that the contact angle between the interface of the immiscible fluids and the solid surface is a dynamic quantity. The dynamic contact angle is modeled as a boundary condition. The two-phase immiscible flow is described by the incompressible Navier-Stokes equations in combination with the continuous surface tension force model. The phases are distinguished by assigning colors to the particles, and the normal vector and curvature of the interface are computed from this color function. Chorin’s pressure projection method is used to solve the model equations in a meshfree framework. A two-phase Couette flow is considered, with a capillary bridge spanning the distance between the two walls. The details of the numerical methods can be found in Tiwari and Kuhnert (J Comput Appl Math 203:376–386, 2007), Tiwari et al. (Numerical simulation of wetting phenomena by a meshfree particle method. J Comput Appl Math 292:469–485, 2016. It is shown that the numerical results reproduce the employed empirical law for the dynamic contact angle.