Derivation and simulation of a two-phase fluid deformable surface model

2023/05/24 by Elena Bachini, Bachini, Elena, Veit Krause +5 · 6 citations
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Aquatic and Environmental Studies #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Micro and Nano Robotics #Numerical Analysis (math.NA) #Surface Modification and Superhydrophobicity

paper · pdf · doi:10.48550/arxiv.2305.15147

openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the Lagrange-D'Alembert principle considering various dissipation mechanisms. The highly nonlinear model is solved numerically to explore the tight interplay between surface evolution, surface phase composition, surface curvature and surface hydrodynamics. It is demonstrated that hydrodynamics can enhance bulging and furrow formation, which both can further develop to pinch-offs. The numerical approach builds on a Taylor-Hood element for the surface Navier-Stokes part, a semi-implicit approach for the Cahn-Hilliard part, higher order surface parametrizations, appropriate approximations of the geometric quantities, and mesh redistribution. We demonstrate convergence properties that are known to be optimal for simplified sub-problems.

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