A novel approach to surface tension modelling with the Finite Volume Particle Method

Surface tension plays a key role in many applications such as spraying, diffusion in porous media, birds drinking, etc. But simulation of surface tension is challenging because it involves a moving interface, topology changes, and triple lines where the dynamic contact angle is generally unknown. Surface tension is a macroscopic force resulting from microscopic interactions. Based on recent developments of the Finite Volume Particle Method, we propose a surface tension formulation directly derived from the macroscopic force for a single-phase configuration. Each particle represents a physical volume of fluid, and the free-surface is the union of the free-surfaces for each particle. Motion of these particles will cause a deformation of the free-surface and change its energy. Through analytical computation of these changes, the surface tension force is modelled by a particle-particle interaction that does not involve parameters other than a constant surface tension γ and the equilibrium contact angle at the triple line, θe. After a formal derivation of the force, we use it in various drop applications to validate its behaviour, both qualitatively and quantitatively. We also show that empirical dynamic contact angle models can advantageously be replaced by a physically meaningful surface roughness model. In this case, the roughness parameter has to be empirically evaluated.