(415g) Dynamics of a Multicomponent Vesicle in Shear Flow

In biology, cells undergo deformations under the action of flow caused by the fluid surrounding them. These flows lead to shape changes and instabilities that have been explored in detail for single component vesicles. However, cell membranes are often multi-component in nature, made up of multiple phospholipids and cholesterol mixtures that give rise to interesting thermodynamics and fluid mechanics. Our work analyses shear flow around a multi-component vesicle using a small-deformation theory based on vector and scalar spherical harmonics. We set up the problem by laying out the governing momentum equations and the traction balance arising from the phase separation and bending. These equations are solved along with a Cahn-Hilliard equation that governs the coarsening dynamics of the phospholipid-cholesterol mixture. We provide a detailed analysis of the vesicle dynamics in-plane and out-of-plane (e.g., tumbling, breathing, tank-treading, and swinging/phase-treading) in two regimes -- when flow is faster than coarsening dynamics (Peclet number Pe>>1) and when the two time scales are comparable (Pe ~ O(1)) -- and provide a discussion on when these behaviors occur. We conclude the study by comparing our results with a relevant experimental system.