(608c) Analysis of Multicomponent Vesicles Under General Linear Flows

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 such as pearling, buckling, tank-treading, and tumbling. 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. This project deals with the analysis of linear flows around a multi-component vesicle. We consider a nearly spherical giant unilamellar vesicle (GUV) with two phospholipids (DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) and DPPC (dipalmitoyl phosphatidylcholine)) and cholesterol forming a ternary mixture on the surface of the vesicle. 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 Φ that represents the phospholipid composition as one marches along a tie line of the ternary phase diagram. We set up the problem by laying out the governing energy and momentum equations. We provide a detailed analysis of the characteristic time scales and length scales along with a summary of the dimensionless quantities governing the problem. We consider a perturbation analysis of a nearly spherical vesicle with the excess area as the perturbation variable. 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. This distribution is determined by a Cahn-Hilliard equation which involves convection and diffusion under the action of a double-well potential energy landscape. The membrane tension distribution is affected by the flow dynamics, which in-turn alters the shape and phase separation behavior of the multicomponent vesicles. We provide certain benchmarks to isolate the underlying phenomena and comment on the implications.