(151d) Linear Stability of the Thin Film Between Two Approaching Drops during Coalescence

In most simulations of the coalescence process, the rupture of the thin film between two drops is assumed to be axisymmetric. We examine the possibility of a non-axisymmetric rupture by carrying out a three dimensional linear stability analysis of the thin film region. The stability calculation is interfaced with the full axisymmetric simulation of two drops approaching in an external flow in order to obtain the correct base state film shape at each time interval. We show that the thin film first becomes unstable to a non-axisymmetric disturbance under all conditions studied here. We compare the critical thickness from the stability calculations with the full drop axisymmetric calculations. The drainage time for coalescence obtained from the stability calculations shows a good agreement with the experimental observations. The calculations show that the curvature of the base-state film shape has a pronounced effect on it's stability to perturbations. We also provide scaling arguments for the critical thickness based on a non-axisymmetric rupture of the thin film.