Publication

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

2017
Working Papers

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 Gr un (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.

Official source

https://infoscience.epfl.ch/entities/publication/3ac04119-a4c3-4c82-b21b-9a654350247c

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2017
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3ac04119-a4c3-4c82-b21b-9a654350247c

About this result

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In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

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