On a Diffuse Interface Model for Two-Phase Flows of Viscous, Incompressible Fluids with General Densities
by
Helmut Abels
Max Planck Institute for Mathematics in the Sciences, Leipzig

In this presentation we discuss a "diffuse interface model" for the flow of two viscous incompressible Newtonian fluids in a bounded domain with general (non-matched) densities. Such models were introduced to describe the flow when singularities in the interface, which separates the fluids, (droplet formation/coalescence) occur. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, for which we discuss the existence of weak solutions globally in time as well as short-time existence of strong solutions. In the general case that the two fluids have different the pressure occurs in the equation for the chemical potential and the (mean) velocity field is no longer divergence free. This leads to extra difficulties in the construction of weak solutions as well as to a completely different linear system for the construction of locally strong solutions.

Date received: June 27, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavg-93.