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Bacterial motility is strongly influenced by confinement. Here, we derive an asymptotic solution for the flow about a microswimmer enclosed in a weakly deformable Hele-Shaw drop—a drop sandwiched between two solid planes. For a microswimmer modelled as a dipole, we explore the swimmer’s trajectory, the evolution of the droplet interface and the drop velocity. The results show that at steady state, the dipole induces droplet translation with a velocity independent of the dipole location and in the same direction as the dipole orientation. The trajectory of the swimming dipole is significantly affected by droplet deformability. This article is part of the theme issue ‘Biological fluid dynamics: emerging directions’. 

The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to a non-trivial shape dynamics and droplet displacement. To understand this behaviour, we derive an asymptotic solution for the fluid flow about a deformable droplet containing an active particle, modelled as a Stokes-flow singularity, in the case of small shape distortions. We develop a general solution for any Stokes singularity and apply it to compute the flows and resulting droplet velocity due to common singularity representations of active particles, such as Stokeslets, rotlets and stresslets. The results show that offsetting of the active particle from the centre of the drop breaks symmetry and excites a large number of generally non-axisymmetric shape modes as well as particle and droplet motion. In the case of a swimming stresslet singularity, a run-and-tumble locomotion results in superdiffusive droplet displacement. The effect of interfacial properties is also investigated. Surfactants adsorbed at the droplet interface counteract the internal flow and arrest the droplet motion for all Stokes singularities except the Stokeslet. Our results highlight strategies to steer the flows of active particles and create autonomously navigating containers.