Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow

Abstract

Using an unstructured boundary integral method with curvature determination via Loop subdivision surfaces, we explore a region of moderate reduced volume vesicles in flow that includes prolate, biconcave, and stomatocyte shapes. We validate our Loop subdivision code against previously published spectral method simulations. In shear flow, we report dynamic phase diagrams at reduced volumes ranging from 0.65 to 0.95 and determine the critical viscosity ratio at which the vesicle moves away from tank treading. We examine biconcave shapes and find the elimination of the trembling regime and a tumbling that includes significant stretch in the vorticity direction, as well as a general reduction in shear and normal stresses versus a prolate shape. Finally, we re-examine over a wider range of reduced volume the shape instability originally reported by Zhao and Shaqfeh [“The shape stability of a lipid vesicle in a uniaxial extensional flow,” J. Fluid Mech. 719, 345–361 (2013)] of a vesicle placed in an extensional flow. At sufficiently low reduced volume and high capillary number, we find the steady elongated dumbbell shape is unstable to odd perturbations and the vesicle's dumbbell ends become unequal in size. We also find that the critical capillary number as a function of reduced volume is similar between uniaxial and planar extensional flow.