Fluid Deformable Surfaces: Modeling, Numerics and Applications
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Over the past decades, various extensions have been proposed to couple the classical Helfrich energy with surface fluid dynamics, typically within the framework of inextensible viscous surfaces. Such models for fluid deformable surfaces account for membrane viscosity and consider surface Navier--Stokes equations, or their Stokes limit, coupled with bending properties. With this solid–fluid duality any shape change contributes to tangential flow and vice versa any tangential flow on a curved surface induces shape deformations. We consider various derivations of such models [1,2,3], and extensions towards two-phase surface flows [4,5], active surfaces [6,7] and surfaces with internal degrees of freedom [3,7,8]. Furthermore we describe the considered numerical method based on an Arbitrary Lagrangian Eulerian (ALE) surface finite element method (SFEM) and discuss applications for biological membranes and epithelial tissue.
