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Activity-induced propulsion of a vesicle

Modern biomedical applications such as targeted drug delivery require a delivery system capable of enhanced transport beyond that of passive Brownian diffusion. In this work an osmotic mechanism for the propulsion of a vesicle immersed in a viscous fluid is proposed. By maintaining a steady-state solute gradient inside the vesicle, a seepage flow of the solvent (e.g., water) across the semipermeable membrane is generated which in turn propels the vesicle. We develop a theoretical model for this vesicle-solute system in which the seepage flow is described by a Darcy flow. Using the reciprocal theorem for Stokes flow it is shown that the seepage velocity at the exterior surface of the vesicle generates a thrust force which is balanced by the hydrodynamic drag such that there is no net force on the vesicle. We characterize the motility of the vesicle in relation to the concentration distribution of the solute confined inside the vesicle. Any osmotic solute is able to propel the vesicle so long as a concentration gradient is present. In the present work, we propose active Brownian particles (ABPs) as a solute. To maintain a symmetry-breaking concentration gradient, we consider ABPs with spatially varying swim speed and ABPs with constant properties but under the influence of an orienting field. In particular, it is shown that at high activity the vesicle velocity is $\boldsymbol{U}\sim [K_\perp /(η_e\ell_m) ]\int Π_0^\mathrm{swim} \boldsymbol{n} dΩ$, where $Π_0^\mathrm{swim}$ is the swim pressure just outside the thin accumulation boundary layer on the interior vesicle surface, $\boldsymbol{n}$ is the unit normal vector of the vesicle boundary, $K_\perp$ is the membrane permeability, $η_e$ is the viscosity of the solvent, and $\ell_m$ is the membrane thickness.