Axisymmetric rim instability of water droplet impact on a super-hydrophobic surface

Abstract

Fingering of an inviscid liquid droplet upon impact on a super-hydrophobic surface is revisited. Generation of coronal fingers is investigated here using a transverse rim instability analysis based on the toroidal curvature of rim, instead of the linear front assumption in the classical Rayleigh-Plateau (R-P) model. The governing equations are formulated from the first principles and solved numerically. For a droplet with a known volume and impact velocity, the model predicts the number of spires upon impact, k. Here k is found to be the largest wave number with a positive growth rate on the droplet rim and is shown to be in the order of (Weber)3/5. The theoretical model is consistent with our water droplet experiments for 60 < We < 160, superseding the R-P prediction.