Hydrodynamics of an inertial active droplet

Abstract

Extensive studies have focused on the self-propulsion of a droplet in a viscous environment driven by the Marangoni effect in the absence of inertial effects. In order to capture the influence of inertia on the self-propulsion of a droplet, we use the singular perturbation solution for small but finite Reynolds number flow past a spherical droplet with inhomogeneous surface tension. We calculate the swimming speed and the corresponding flow fields generated by the droplet in an axisymmetric unbounded medium at. The present results reveal how the choice of the stress parameter, which is the ratio of the first two modes of the induced stress field, distinguishes between the different swimming styles, and determines the role of inertia on the swimming speed, energy expenditure and swimming efficiency of the droplet. Inertia enhances the swimming speed and the associated swimming efficiency of the droplet by abating the energy expenditure. It is striking to observe how a droplet swimmer with