Dynamics of 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 phase separation and coarsening dynamics. In this talk, we consider the motion of a nearly spherical, giant unilamellar vesicle (GUV) in shear flow, where the lipid membrane is 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. We use spherical harmonics basis sets to come up with reduced order equations that solve the fluid flow (Stokes equations) in the limit of small deformations (small excess area), as well as the nonlinear Cahn-Hilliard equations for phospholipid distribution on the membrane surface. We observe a wide range of dynamical regimes for shape and concentration, including tank treading, phase treading, swinging, and tumbling depending on the characteristic dimensionless numbers governing the line tension, average bending stiffness, and shear rate. This talk discusses what gives rise to the observed shape and phase separation behaviors.