Numerical Simulation of Incompressible Two–Phase Flows with a Boussinesq–Scriven Interface Stress Tensor

We consider the numerical simulation of a three-dimensional two-phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier-Stokes model and the Boussinesq-Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011] a model problem with a spherical droplet in a Stokes Poiseuille flow with a Boussinesq-Scriven law for the surface viscosity has been analyzed. In that paper relations for the droplet migration velocity are derived. We relate the results obtained with our numerical solver for the two-phase Navier-Stokes model to these theoretical relations.