A phase-field model of Hele-Shaw flows in the high viscosity contrast regime
A. Hernandez-Machado, A. M. Lacasta, E. Mayoral, E. Corvera Poire
Abstract
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 the width of which goes to one half of the channel width as the velocity increases.