Coalescence and break-up of nearly inviscid conical droplets

Abstract

AbstractIn the presence of electric fields, pairs of liquid drops can be rapidly drawn together such that, at contact, the deformed interface resembles a double-cone. Following contact, these drop pairs are observed to either coalesce or recoil. Experimental and theoretical results suggest that the transition between coalescence and recoil is due to the conical drop topology rather than charge effects. However, even with this assumption, existing models disagree on how the transition develops, leading to different predictions of the critical cone angle and bridge morphology. Here we use high-resolution numerical simulations to highlight the impact of the initial double-cone angle on drop coalescence and reconcile the differences in the previous models. The results demonstrate a self-similar behaviour at intermediate scales for both coalescence and recoil that is independent of the other length scales in the problem. We calculate a critical polar angle of ${\it\theta}_{c}=1.14$ rad ($65.3^{\circ }$), or a complementary angle of ${\it\beta}=90^{\circ }-{\it\theta}_{c}=25^{\circ }$. This calculated critical angle for morphological transition is in agreement with previous experimental observations of ${\it\beta}\approx 27\pm 2^{\circ }$.