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

TL;DR

This paper presents a phase-field simulation method for modeling two-fluid Hele-Shaw flows with arbitrary viscosity contrast, demonstrating its effectiveness in various flow regimes and validating against analytical and numerical benchmarks.

Contribution

The paper introduces a phase-field approach for Hele-Shaw flows with arbitrary viscosity contrast, providing a versatile and validated numerical tool.

Findings

Accurate simulation of Saffman-Taylor fingers across viscosity contrasts

Quantitative agreement with analytical predictions

Convergence analysis to sharp interface limit

Abstract

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.