Singularity dynamics in a Hele-Shaw flow with surface tension

Abstract

The singularity dynamics of two immiscible fluids in a Hele-Shaw cell is studied using two numerical methods. Evidence is given for the existence of -4/3 singularities in this flow. Their trajectories are accurately approximated by the solutions of a system of ordinary differential equations for the position of couples of zeros and poles. This model also describes secondary tip-splitting instabilities and remains valid for values of the surface tension and time intervals where previous perturbative calculations do not apply.