2021/04/24 by Eloy de Kinkelder, E M de Kinkelder, Leonard M.C. Sagis +2 · 21 citations
Biochemistry, Genetics and Molecular Biology · Chemical Engineering · Mathematics · Medicine · Physics and Astronomy · #Blood properties and coagulation #Cellular Mechanics and Interactions #Classical mechanics #Flow (mathematics) #Geometry #Mathematical analysis #Mathematics #Mechanics #Numerical analysis #Physics #Rheology #Rheology and Fluid Dynamics Studies #Shear flow #Surface (topology) #Thermodynamics #Viscoelasticity #Viscous liquid #physics.flu-dyn
paper · pdf · open access · doi:10.1016/j.jcp.2021.110413
published in Journal of Computational Physics 440, 110413 (Elsevier BV)
arxiv created 2021/04/24 · openalex publication_date 2021/05/15 · arxiv updated 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Viscoelastic surface rheology plays an important role in multiphase systems. A typical example is the actin cortex which surrounds most animal cells. It shows elastic properties for short time scales and behaves viscous for longer time scales. Hence, realistic simulations of cell shape dynamics require a model capturing the entire elastic to viscous spectrum. However, currently there are no numerical methods to simulate deforming viscoelastic surfaces. Thus models for the cell cortex, or other viscoelastic surfaces, are usually based on assumptions or simplifications which limit their applicability. In this paper we develop a first numerical approach for simulation of deforming viscoelastic surfaces. To this end, we derive the surface equivalent of the upper convected Maxwell model using the GENERIC formulation of nonequilibrium thermodynamics. The model distinguishes between shear dynamics and dilatational surface dynamics. The viscoelastic surface is embedded in a viscous fluid modelled by the Navier-Stokes equation. Both systems are solved using Finite Elements. The fluid and surface are combined using an Arbitrary Lagrange-Eulerian (ALE) Method that conserves the surface grid spacing during rotations and translations of the surface. We verify this numerical implementation against analytic solutions and find good agreement. To demonstrate its potential we simulate the experimentally observed tumbling and tank-treading of vesicles in shear flow. We also supply a phase-diagram to demonstrate the influence of the viscoelastic parameters on the behaviour of a vesicle in shear flow. Finally, we explore cytokinesis as a future application of the numerical method by simulating the start of cytokinesis using a spatially dependent function for the surface tension.