Stationary finger solutions in the Hele-Shaw cell

TL;DR

This paper numerically solves the nonlinear differential equation for the Hele-Shaw Saffman-Taylor problem, finding stationary finger solutions that match experimental patterns and widths based on physical parameters.

Contribution

It provides a numerical solution to the nonlinear equation for stationary fingers in the Hele-Shaw cell, aligning theoretical predictions with experimental data.

Findings

Stationary finger solutions fit measured patterns.

Calculated finger widths agree with experiments.

Numerical solutions match physical parameters.

Abstract

We solve numerically the nonlinear differential equation for the Hele-Shaw, Saffman-Taylor problem derived in the preceding work. Stationary solutions with no free phenomenological parameters are found to fit the measured patterns. The calculated finger half-widths as a function of the physical parameters of the cell, compare satisfactorily with experiment.