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

Abstract

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. Graphical abstract

Optimal swimmers can be pullers, pushers or neutral depending on the shape

“…2018; Sprenger et al. 2020). The stresslet further determines the intensity of fluid stirring in suspensions of swimmers (Lin, Thiffeault & Childress 2011).…”

Rayleigh–Plateau instability of anisotropic interfaces. Part 1. An analytical and numerical study of fluid interfaces

“…The solution method starts from the Stokes equation and is again based on the previous B.1. Here, the interface viscosity results in an additional force acting from the interface onto the fluid (Scriven 1960;Narsimhan et al 2015;Sprenger et al 2020). The component normal to the interface is given by…”

Mobilities of a drop and an encapsulated squirmer

“…Most theoretical studies of composite systems have focussed on simple internal active devices. The simplest ones are point forces [13,14], which can be combined to model pullers and pushers. Alternatively the active device has been taken as a squirmer [15] whose slip velocity generates a flow inside the droplet and thereby can propel it [16,17].…”