The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics

Abstract

We consider the impact of surface hydrodynamics on the interplay between membrane curvature and lipid composition in coarsening processes on model systems for biomembranes. This includes the influence on scaling laws and equilibrium configurations, which are investigated by computational studies of a surface two-phase flow problem with additional phase-dependent bending terms. These additional terms geometrically favor specific configurations. We find that the effect of hydrodynamics strongly depends on the composition. In situations where the composition allows a realization of a geometrically favored configuration, hydrodynamics enhances the evolution toward this configuration. We restrict our model and numerics to stationary surfaces of varying curvature and validate the numerical approach with various benchmark problems and convergence studies.

A surface finite element method for the Navier–Stokes equations on evolving surfaces

“…The results as before $$e_{\operatorname{div}_{\!\bm{P}}\! }$$ are similar to the results of [2, 3, 18, 37], and according to [25] third‐order convergence of $$e_N$$ is optimal by using the surface normal ν in the penalization term.…”

“…In Figure 2, a convergence study is done which confirms third-order convergence with respect to both errors. The results as before 𝑒 div 𝑷 are similar to the results of [2,3,18,37], and according to [25] third-order convergence of 𝑒 𝑁 is optimal by using the surface normal 𝝂 in the penalization term.…”