A lattice Boltzmann method for immiscible two-phase Stokes flow with a local collision operator

Abstract

We propose a lattice Boltzmann model for immiscible two-phase Stokes flow with a local collision operator. The model is based on two different lattice Boltzmann automata, one for the flow field and one for an indicator function for the two different phases. The model is described in detail and verified by the following test-cases: a static bubble for the surface tension, a closed capillary tube for the contact angle and two phase flow in a concentric annulus for the viscosity ratio. In the appendix an asymptotic analysis for the derivation of the two-phase Stokes equation is given.