Phase-separated lipid vesicles: continuum modeling, simulation, and validation

The paper presents a complete research cycle comprising continuum-based modeling, computational framework development, and validation setup to predict phase separation and surface hydrodynamics in lipid bilayer membranes. We starting with an overview of the key physical characteristics of lipid bilayers, including their composition, mechanical properties, and thermodynamics, and then discuss continuum models of multi-component bilayers. The most complex model is a Navier--Stokes--Cahn--Hilliard (NSCH) type system, describing the coupling of incompressible surface fluid dynamics with phase-field dynamics on arbitrarily curved geometries. It is discretized using trace finite element methods, which offer geometric flexibility and stability in representing surface PDEs. Numerical studies are conducted to examine physical features such as coarsening rates and interfacial dynamics. The computational results obtained from the NSCH model are compared against experimental data for membrane compositions with distinct phase behaviors, demonstrating that including both phase-field models and surface hydrodynamics is essential to accurately reproduce domain evolution observed in epi-fluorescence microscopy. Lastly, we extend the model to incorporate external forces that enable the simulation of vesicles containing cationic lipids, used to enhance membrane fusion.