Dynamic contact angles in CFD simulations

Abstract

The accurate modelling of contact angle properties plays an important role in the simulation of free-surface micro flows. Taking capillary filling as an example, we first discuss the analytical solutions of a corresponding 1D description in certain limits and then derive an approximate analytical expression for the general case with constant contact angle. In case of a dynamic contact angle and contact line friction, the model is beyond an analytical treatment. We show that computational fluid dynamics (CFD) results exhibit a pronounced mesh dependence which is partly inherent to the modelling approach since the (non-integrable) viscous stress divergence at the three-phase contact line is commonly neglected in standard CFD simulations (see e.g. Hessel V, Hardt S, Löwe H. Chemical micro process engineering: fundamentals, modelling and reactions. Weinheim: Wiley-VCH; 2004). Moreover, the numerical description of contact angles suffers from artificial diffusion for the type of volume-of-fluid method used. Introduction of a macroscopic slip range in combination with a localised body force close to the contact line turns out to remedy both problems. Considering capillary filling as an example, we show that accurate, mesh independent solutions of fluid dynamic problems involving contact angle dynamics are obtained already on coarse meshes.