SINGULARITY DYNAMICS IN A HELE-SHAW FLOW WITH SURFACE-TENSION

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