TY - JOUR

T1 - Hydrodynamics of multicomponent vesicles

T2 - A phase-field approach

AU - Wen, Zuowei

AU - Valizadeh, Navid

AU - Rabczuk, Timon

AU - Zhuang, Xiaoying

N1 - Publisher Copyright: © 2024

PY - 2024/10/1

Y1 - 2024/10/1

N2 - In this paper, we introduce a thermodynamically-consistent phase-field model to investigate the hydrodynamics of inextensible multicomponent vesicles in various fluid flows with inertial forces. Our model couples the fluid field, surface concentration field representing chemical species on the membrane, and vesicle dynamics, while enforcing global area and volume constraints through a Lagrange multiplier method. Specifically, we employ full Navier–Stokes equations for the fluid field, the Cahn–Hilliard equations for the species concentration on the membrane, a nonlinear advection–diffusion equation to describe the evolution of the vesicle membrane, and an additional equation to enforce local inextensibility. We utilize a residual-based variational multiscale method for the Navier–Stokes equations and a standard Galerkin finite element framework for the remaining equations. The PDEs are solved using an implicit, monolithic scheme based on the generalized-α time integration method. We extend previous models for homogeneous vesicles (Aland et al., 2014; Valizadeh and Rabczuk, 2022) to multicomponent vesicles, introducing Cahn–Hilliard equations while maintaining thermodynamic consistency. Additionally, we employ isogeometric analysis (IGA) for higher accuracy. We present a variety of two-dimensional numerical examples, including multicomponent vesicles in shear flow and Poiseuille flow with and without obstructions, using the resistive immersed surface method to handle obstructions. Furthermore, we provide three-dimensional simulations of multicomponent vesicles in Poiseuille flow.

AB - In this paper, we introduce a thermodynamically-consistent phase-field model to investigate the hydrodynamics of inextensible multicomponent vesicles in various fluid flows with inertial forces. Our model couples the fluid field, surface concentration field representing chemical species on the membrane, and vesicle dynamics, while enforcing global area and volume constraints through a Lagrange multiplier method. Specifically, we employ full Navier–Stokes equations for the fluid field, the Cahn–Hilliard equations for the species concentration on the membrane, a nonlinear advection–diffusion equation to describe the evolution of the vesicle membrane, and an additional equation to enforce local inextensibility. We utilize a residual-based variational multiscale method for the Navier–Stokes equations and a standard Galerkin finite element framework for the remaining equations. The PDEs are solved using an implicit, monolithic scheme based on the generalized-α time integration method. We extend previous models for homogeneous vesicles (Aland et al., 2014; Valizadeh and Rabczuk, 2022) to multicomponent vesicles, introducing Cahn–Hilliard equations while maintaining thermodynamic consistency. Additionally, we employ isogeometric analysis (IGA) for higher accuracy. We present a variety of two-dimensional numerical examples, including multicomponent vesicles in shear flow and Poiseuille flow with and without obstructions, using the resistive immersed surface method to handle obstructions. Furthermore, we provide three-dimensional simulations of multicomponent vesicles in Poiseuille flow.

KW - Hydrodynamics

KW - Isogeometric analysis

KW - Multicomponent vesicle

KW - Phase-field modeling

KW - Residual-based variational multiscale method

UR - http://www.scopus.com/inward/record.url?scp=85205323625&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2024.117390

DO - 10.1016/j.cma.2024.117390

M3 - Article

AN - SCOPUS:85205323625

VL - 432

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 117390

ER -