A numerical method for the simulation of viscoelastic fluid surfaces

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 longer scales. Hence, realistic simulations of cell shape dynamics require a model capturing entire to spectrum. However, currently there are no numerical methods simulate deforming viscoelastic surfaces. Thus models cortex, or other surfaces, usually based on assumptions simplifications limit their applicability. In this paper we develop first approach simulation To end, derive equivalent upper convected Maxwell using GENERIC formulation nonequilibrium thermodynamics. The distinguishes between shear dilatational dynamics. embedded fluid modelled by Navier-Stokes equation. Both systems solved Finite Elements. combined Arbitrary Lagrange-Eulerian (ALE) Method that conserves grid spacing during rotations translations surface. We verify implementation against analytic solutions find good agreement. demonstrate its potential experimentally observed tumbling tank-treading vesicles flow. also supply phase-diagram influence parameters behaviour vesicle Finally, explore cytokinesis as future application method simulating start spatially dependent function tension.