MATHICSE Technical Report : A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities

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.


Year:
2017-01
Publisher:
Écublens, MATHICSE
Keywords:
Note:
MATHICSE Technical Report Nr. 01.2017
Laboratories:




 Record created 2019-06-25, last modified 2019-07-05

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