A theoretical study on the dynamics of a compound vesicle in linear shear flow

Abstract: The dynamics of a nucleate cell in shear flow is of great relevance in cancer cells and circulatory tumor cells where they dominate the dynamics of blood. Buoyed by the success of Giant Unilamellar vesicles in explaining the dynamics of anucleate cells such as Red Blood cells, compound vesicles have been suggested as a simple model for nucleate cells. In this work, a theoretical model is presented to study the deformation and dynamics of a compound vesicle in linear shear flow using small deformation theory and spherical harmonics with higher order approximation to the membrane forces. The results indicate that size of the inner vesicle does not affect the tank-treading dynamics of the outer vesicle. The inner vesicle admits a greater inclination angle than the outer vesicle. However, the transition to trembling-swinging and tumbling is significantly affected. The inner and outer vesicle exhibit identical dynamics in most of the modified viscosity-shear rate parameter space. At moderate size of the inner vesicle, a swinging mode is observed for the inner vesicle while the outer vesicle exhibits tumbling. The inner vesicle also exhibits modification of the TU mode to IUS-Intermediate Tumbling Swinging mode. Moreover, synchronization of the two vesicles at higher inner vesicle size and a capillary number sensitive motion at small inner vesicle size is observed in the tumbling regime. These results are in accordance with the few experimental observations reported by Levant and Steinberg2014. A reduction in the inclination angle is observed with an increase in size of the inner vesicle when the inner vesicle is a solid inclusion. Additionally a very elaborate phase diagram is presented in the modified viscosity-shear rate parameter space, which could be tested in future experiments or numerical simulations