Hydrodynamics of a vesicle enclosing an active particle suspension*

A viscous drop enclosing active particles (such as bacteria, active colloids, or synthetic microswimmers) can propel through its hydrodynamic interactions with the encaged swimmers. A vesicle, often modeled as a self-enclosing inextensible elastic membrane, can encage microswimmers and gain propulsion only in a much more specific way, a stark contrast to a viscous drop. In this work, we examine the hydrodynamics of a vesicle enclosing an active particle suspension using both theoretical analysis and numerical simulations based on an integral formulation, where we show the conditions for the vesicle propulsion in terms of the type of singularity of the microswimmers. Using boundary integral simulations, we show that the formation of a tube from a microswimmer pushing the vesicle membrane is insufficient for vesicle propulsion.