Phase-field modeling of multicomponent vesicles in viscoelastic fluid

TL;DR

This paper develops a comprehensive phase-field model to simulate the complex hydrodynamics of multicomponent vesicles in viscoelastic fluids, incorporating advanced numerical methods for stability and accuracy.

Contribution

It introduces a coupled multi-field PDE model with innovative numerical schemes and isogeometric analysis for simulating vesicle dynamics in viscoelastic fluids.

Findings

Membrane composition significantly affects vesicle behavior.

Viscoelasticity alters vesicle deformation and flow patterns.

The model provides stable and accurate simulations of complex vesicle-fluid interactions.

Abstract

Multicomponent vesicles suspended in viscoelastic fluids are crucial for understanding a variety of physiological processes. In this work, we develop a continuum surface force (CSF) phase-field model to investigate the hydrodynamics of inextensible multicomponent vesicles in viscoelastic fluid flows with inertial forces. Our model couples a fluid field comprising both Newtonian and Oldroyd-B fluids, a surface concentration field representing the multicomponent distribution on the vesicle membrane, and a phase-field variable governing the membrane evolution. The viscoelasticity effect of extra stress is well incorporated into the full Navier-Stokes equations in the fluid field. The surface concentration field is determined by Cahn-Hilliard equations, while the membrane evolution is governed by a nonlinear advection-diffusion equation. The membrane is coupled to the surrounding fluid through the continuum surface force (CSF) framework. To ensure stable numerical solutions of the highly nonlinear multi-field model, we employ a residual-based variational multiscale (RBVMS) method for the Navier-Stokes equations, a Streamline-Upwind Petrov-Galerkin (SUPG) method for the Oldroyd-B equations, and a standard Galerkin finite element framework for the remaining equations. The system of PDEs is solved using an implicit, monolithic scheme based on the generalized-$\alpha$ time integration method. To enhance spatial accuracy, we employ isogeometric analysis (IGA). We present a series of two-dimensional numerical examples in shear and Poiseuille flows to elucidate the influence of membrane composition and fluid viscoelasticity on the hydrodynamics of multicomponent vesicles.