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

Mobilities of a drop and an encapsulated squirmer

We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position [Formula: see text]. The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of [Formula: see text], relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer.

Controlled locomotion of a droplet propelled by an encapsulated squirmer

We work out the propulsion of a viscous drop which is driven by two mechanisms: the active velocity of an encapsulated squirmer and an externally applied force acting on the squirmer. Of particular interest is the existence of a stable comoving state of drop and squirmer, allowing for controlled manipulation of the viscous drop by external forcing. The velocities of droplet and squirmer, as well as the conditions for a stable comoving state are worked out analytically for the axisymmetric configuration with a general displacement of the squirmer from the center of the droplet.