Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

Phys. Rev. E 60, 1734 – Published 1 August 1999
R. Folch, J. Casademunt, A. Hernández-Machado, and L. Ramírez-Piscina


We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers, and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.


  • Received 24 February 1999
  • Published in the issue dated August 1999

© 1999 The American Physical Society

Authors & Affiliations

R. Folch, J. Casademunt, and A. Hernández-Machado

  • Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain

L. Ramírez-Piscina

  • Departament de Física Aplicada, Universitat Politècnica de Catalunya, Avinguda Dr. Marañón, 50, E-08028 Barcelona, Spain


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