A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.
CitationHernández-Machado, A. et al. Phase-field model of Hele-Shaw flows in the high-viscosity constrast regime. "Physical Review E". vol. 68, núm. 4, p. 046310
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