Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

TL;DR

This paper provides an analytical model for the movement of microswimmers inside drops, showing how surfactants influence their dynamics, with implications for controlling active matter and drug delivery.

Contribution

It introduces an analytical framework for microswimmer behavior in confined drops with surfactants, incorporating hydrodynamic interactions and interfacial stresses.

Findings

Surfactants significantly reorient microswimmers within drops.

Exact solutions for flow singularities are derived.

Insights for controlling active matter in confined environments.

Abstract

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.