Hydrodynamics of Multicomponent Vesicles
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In this work, a numerical algorithm is presented to study the dynamics of a multicomponent vesicle in quiescent flow and in an external flow. The objective is to develop a predictive model that can be used to compare results with experimental studies, as well as attain a better understanding of the multicomponent vesicles in various physical situations such as in presence of external flow. A vesicle is a body of fluid enclosed within a lipid bilayer membrane. In a multicomponent lipid membrane, cholesterol combines with saturated lipids to form energetically stable domains surrounding unsaturated lipids on the surface of a vesicle. This multicomponent system is modeled using a two phase surface-Cahn-Hilliard equation using a combined level set/closest point method. Convergence is performed based on quantitative measure of lipid domain growth rate. Statistical studies are conducted to study Cahn-Hilliard and Cahn-Hilliard-Cook on smooth curved surfaces. Impact of the under lying geometry on the domains is also examined. The multicomponent vesicle has various energies of the system including bending, tension and phase field energy that now depends on lipid concentration. The variational energy approach is used to derive additional force expressions on the fluid field and the domains. This fully-coupled predictive model is tested in various conditions such as quiescent flow and shear flow and comparison with experimental studies is performed.