Dynamics of nearly spherical, multicomponent vesicles in simple shear flow

In biology, 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. Often, these cells are surrounded by fluids whose flows influence their shape and stability. This project deals with the analysis of shear flow around a multi-component vesicle. We consider a nearly spherical giant unilamellar vesicle (GUV) made up of a ternary mixture of a saturated phospholipid, an unsaturated phospholipid, and cholesterol. The bending energy of the vesicle is governed by the Helfrich model and the mixing energy is governed by a Landau-Ginzburg model with an order parameter that represents the phospholipid composition as one marches along a tie line of the ternary phase diagram. We use spherical harmonics basis sets to come up with reduced order equations that solve the Stokes equations inside and outside the vesicle as well as the phospholipid distribution on the membrane surface, in the limit of small deformations (small excess area). We observe a wide range of regimes including tank treading, phase treading, swinging, and tumbling depending on the characteristic dimensionless numbers governing the line tension, average bending stiffness, and flow variables. This talk discusses what gives rise to the behaviors seen.