Circulation-induced shape deformations of drops and bubbles: Exact two-dimensional models

In this paper simple two-dimensional mathematical models for understanding the fluid dynamical problem of how circulation affects the free surface shapes of inviscid drops and bubbles with surface tension are presented. This theoretical paradigm is of interest in many areas of science including large-scale transport processes in chemical engineering. Exact solutions for the finite-amplitude steady-state equilibria of the mathematical models are found. Equilibrium states are shown to exist right up to steady capillary pinch-off in the case of a bubble, the bubbles just before pinch-off having large perimeter-to-area ratios.