Phase-field modeling of multicomponent vesicles in viscoelastic fluid

TL;DR

This work develops a CSF-based phase-field framework to study multicomponent vesicles in viscoelastic fluids with inertia, coupling Navier–Stokes–Oldroyd–B dynamics to membrane phase-field evolution and surface Cahn–Hilliard diffusion. The model is solved monolithically with stabilized methods (RBVMS, SUPG) and isogeometric analysis, enabling accurate area/volume conservation and high spatial fidelity. Key findings show that viscoelastic damping stabilizes swinging and tumbling motions in shear flow, lengthening phase-treading periods and, at sufficient $\mathcal{W}i$, driving transitions to tank-treading; in Poiseuille flow, viscoelastic effects are milder and mainly enhance alignment with the flow. The framework provides a unified, high-accuracy tool to explore how membrane composition, bending rigidity, and viscoelastic stresses interact to shape vesicle dynamics, with potential extensions to 3D and broader rheologies.

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-$α$ 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.

Figures (28)

• Figure 1: The multicomponent vesicle, filled with Newtonian fluid, is suspended in an Oldroyd-B fluid within the computational domain.
• Figure 2: Initialization of homogeneous vesicle in shear flow.
• Figure 3: Homogeneous vesicles in N/N shear flow. Evolution of the inclination angle over time for two cases: matched Newtonian viscosity ($\alpha_{\mu_n} = 1$) and high viscosity contrast ($\alpha_{\mu_n} = 19$).
• Figure 4: Unmatched homogeneous vesicle in shear flow. Evolution of the inclination angle over time for three cases: N/N fluid, N/O fluid, and the N/O case reported in SEOL20191009, Fig. 16.
• Figure 5: Negative inclination angle tank-treading motion at stationary state: $t = 15$.