Deformations of an active liquid droplet

Abstract

A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity or active tractions on its interface. Starting from Stokes equations, we show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse of the surface tension γ, by using an approach based on vector spherical harmonics. We consider squirmer models and general active tractions, such as inhomogeneous surface tensions, which may result from the Marangoni effects. In the lowest order, the deformation is of order ε∝1/γ, yet it affects the flow fields inside and outside of the droplet in order to ε0. Hence, a correct description of the flow has to allow for shape fluctuations, —even in the limit of large surface tension. We compute stationary shapes and relaxation times and compare our results to an approach, which discards all effects of deformations on surface tensions. This approach leads to the same propulsion velocity but to significantly different flow fields.