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A phase-field model of two-phase Hele-Shaw flow

Published online by Cambridge University Press:  09 October 2014

Luis Cueto-Felgueroso  and
Ruben Juanes
Luis Cueto-Felgueroso*
Affiliation:
Department of Civil Engineering: Hydraulics, Energy and the Environment, Universidad Politécnica de Madrid, 28014 Madrid, Spain Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Ruben Juanes
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: luis.cueto@upm.es
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Abstract

We propose a continuum model of two-phase flow in a Hele-Shaw cell. The model describes the multiphase three-dimensional flow in the cell gap using gap-averaged quantities such as fluid saturation and Darcy flux. Viscous and capillary coupling between the fluids in the gap leads to a nonlinear fractional flow function. Capillarity and wetting phenomena are modelled within a phase-field framework, designing a heuristic free energy functional that induces phase segregation at equilibrium. We test the model through the simulation of bubbles and viscously unstable displacements (viscous fingering). We analyse the model’s rich behaviour as a function of capillary number, viscosity contrast and cell geometry. Including the effect of wetting films on the two-phase flow dynamics opens the door to exploring, with a simple two-dimensional model, the impact of wetting and flow rate on the performance of microfluidic devices and geological flows through fractures.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Hele-Shaw flows Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 522 - 552
Copyright
© 2014 Cambridge University Press 

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Cueto-Felgueroso supplementary movie

Numerical simulation of viscous fingering in a Hele-Shaw cell (corresponds to Figs. 13c and 14 in the manuscript)

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