Simulation of two-phase flow with varying surface tension.

Abstract

This thesis is a study on the effects of varying surface tension along an interface separating two fluids. Varying surface tension leads to tangential forces along the interface. This is often called the Marangoni effect. These forces are discussed in detail, and two test cases are considered to analyse the Marangoni effect, and to verify the present implementation. The first test studies steady-state two-phase flow where the fluids are separated with plane interfaces and the flow is driven by a linear surface-tension gradient. The second case is an analysis of the initial forces on a two-dimensional droplet due to a linear surface-tension gradient. The tests indicate that the present implementation is capable of simulating two-phase flow with a given surface-tension gradient. The underlying model is a two-phase flow model for Newtonian fluids with constant viscosity and density. The two-phase model is based on the Navier-Stokes equations coupled with a singular surface force, which together with the difference in fluid properties induces discontinuities across the interface. The Navier-Stokes equations are solved using a projection method, and a combination of the level-set method for capturing the interface and the ghost-fluid method (GFM) for handling the interface discontinuities. The thesis also discusses the effect of surfactants on an interface. The presence of surfactants reduces the local surface tension, and a non-uniform surfactant distribution results in varying surface tension and the Marangoni effect. A surfactant model is reviewed, where an equation of state couples the surface tension to the surfactant concentration and a transport equation is used to solve the surfactant mass-conservation.