A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities

Code:
04/2017
Title:
A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities
Date:
Thursday 19th January 2017
Author(s):
Dede', L; Garcke, H.; Lam K.F.
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Abstract:
Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn-Hilliard-Navier-Stokes model introduced by Abels, Garcke and Grun (Math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity, we derive a diffuse interface model in a Hele-Shaw geometry, which in the case of non-matched densities, simplifies an earlier model of Lee, Lowengrub and Goodman (Phys. Fluids 2002). We recover the classical Hele-Shaw model as a sharp interface limit of the diffuse interface model. Furthermore, we show the existence of weak solutions and present several numerical computations including situations with rising bubbles and fingering instabilities.