Surfactant-driven motion and splitting of droplets on a substrate

Abstract

A theoretical and computational model is presented to predict the motion of a small sessile liquid droplet, lying on a solid substrate including surfactant effects. The model, as formulated, consists of coupled partial differential equations in space and time, and several auxilliary relationships. The validity of the long-wave, or ‘lubrication’ approximation is assumed. It is shown that there are circumstances where surfactant injection or production will cause the droplet to split into two daughter droplets. It is conjectured that the results are relevant to basic mechanisms involved in biological cell division (cytokinesis). It is also demonstrated that motion of a droplet, analogous to the motility of a cell, can be produced by surfactant addition. Computed examples are given here, in both two and three space dimensions. Approximate energy requirements are also calculated for these processes. These are found to be suitably small.