# Stokesian jellyfish: Viscous locomotion of bilayer vesicles 

Arthur A. Evans $^{1}$, ∗ Saverio E. Spagnolie $^{2}$, and Eric Lauga2 † 

1 Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla CA 92093-0354 and 

2 Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla CA 92093-0411. 

(Dated: October 24, 2018) 

## Abstract 

Motivated by recent advances in vesicle engineering, we consider theoretically the locomotion of shape- changing bilayer vesicles at low Reynolds number. By modulating their volume and membrane composition, the vesicles can be made to change shape quasi-statically in thermal equilibrium. When the control param- eters are tuned appropriately to yield periodic shape changes which are not time-reversible, the result is a net swimming motion over one cycle of shape deformation. For two classical vesicle models (spontaneous curvature and bilayer coupling), we determine numerically the sequence of vesicle shapes through an en- thalpy minimization, as well as the fluid-body interactions by solving a boundary integral formulation of the Stokes equations. For both models, net locomotion can be obtained either by continuously modulating fore- aft asymmetric vesicle shapes, or by crossing a continuous shape-transition region and alternating between fore-aft asymmetric and fore-aft symmetric shapes. The obtained hydrodynamic efficiencies are similar to that of other low Reynolds number biological swimmers, and suggest that shape-changing vesicles might provide an alternative to flagella-based synthetic microswimmers. 

PACS numbers: 47.63.-b, 47.15.G-, 87.16.D-, 87.19.ru 

