Coalescence and Breakup: Solutions Without Singularities

Abstract

The problem of the mathematical modelling of coalescence and breakup of liquid volumes surrounded by an inviscid gas is discussed. It is argued that these phenomena can be modelled without singularities inherent in existing theories. The key idea of the new approach to the problem is that the topological transition, being a particular case of an interface formation/disappearance process, involves a free-surface cusp either propagating away from the point of initial contact of two volumes, thus leading to their coalescence, or ‘severing’ a liquid thread connecting them, which results in a breakup. The interface becomes (or, in a reverse flow, ceases to be) smooth at a finite distance from the point where, in the standard approach, a singularity would have taken place. An earlier developed macroscopic theory of an interface formation is applied without any ad hoc changes.