Deformations of an active liquid droplet

TL;DR

This paper develops an analytical perturbation theory to describe how active forces deform liquid droplets, revealing that shape fluctuations significantly influence internal and external flow fields even with high surface tension.

Contribution

It introduces a novel analytical approach using vector spherical harmonics to compute droplet deformations under active driving forces.

Findings

Deformations are first order in inverse surface tension.

Flow fields are affected at zeroth order by shape fluctuations.

Shape fluctuations must be considered for accurate flow descriptions.

Abstract

A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse surface tension using an approach based on vector spherical harmonics. In lowest order, the deformation is of first order, yet it affects the flow fields inside and outside of the droplet in zeroth order. Hence a correct description of the flow has to allow for shape fluctuations, even in the limit of large surface tension.