Volume 51, Number 6, November-December 2017
|Page(s)||2319 - 2366|
|Published online||12 December 2017|
Finite element approximation for the dynamics of fluidic two-phase biomembranes
1 Department of Mathematics, Imperial College, London, SW7 2AZ, U.K.
2 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany.
Received: 16 November 2016
Revised: 17 May 2017
Accepted: 14 August 2017
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn–Hilliard model on an evolving hypersurface coupled to Navier–Stokes equations on the surface and in the surrounding medium to model these phenomena. The evolution is driven by a curvature energy, modelling the elasticity of the membrane, and by a Cahn–Hilliard type energy, modelling line energy effects. A stable semidiscrete finite element approximation is introduced and, with the help of a fully discrete method, several phenomena occurring for two-phase membranes are computed.
Mathematics Subject Classification: 35Q35 / 65M12 / 65M60 / 76D05 / 76D27 / 76M10 / 76Z99 / 92C05
Key words: Fluidic membranes / incompressible two-phase Navier–Stokes flow / parametric finite elements / Helfrich energy / spontaneous curvature / local surface area conservation / line energy / surface phase field model / surface Cahn–Hilliard equation / Marangoni-type effects
© EDP Sciences, SMAI 2017
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