Dynamics of a spherical droplet driven by active slip and stress

Abstract

We study low Reynolds number locomotion of a spherical viscous droplet, in an unbounded arbitrary Stokes flow, under the combined influence of an inhomogeneous surfactant (diffusiophoresis) and non-isothermal temperature (Marangoni effect) fields. The self-generated gradient of the surfactant concentration and the influence of the external temperature field are respectively mapped as a slip velocity and stress discontinuity across the surface of the droplet. The drag force exerted on the droplet is computed in the form of Faxen’s laws. As a particular case, droplet migrating in a Poiseuille flow has been discussed. Depending on the directions of the induced slip and stress fields, with respect to the Poiseuille flow, the intermediate competitive behavior is highlighted by analyzing the migration velocity, power dissipation and the swimming pattern of the droplet. We have observed that the external stress inverts both the direction of migration velocity as well as the nature of swimming, i.e., turns a pusher into a puller and vice versa, induced by the active slip of the swimmer. Correspondingly, a set of critical points for the velocity reversal and the swimming pattern transition are obtained. Interestingly, the swimmer dissipates minimum power during the transitions. Finally, the present model can draw a striking analogy with the behavior of the microorganisms in an active stress environment, where the intrinsic slip velocity of the microorganisms and the external stress effects are self-reliant and expected to influence the swimming strategies significantly. The obtained analytical results corroborate with the existing literature in suitable limits, which show the accuracy and validity of the solutions.