Hydrodynamics of multicomponent vesicles

A phase-field approach

authored by: Zuowei Wen, Navid Valizadeh, Timon Rabczuk, Xiaoying Zhuang
Abstract: 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.
Organisation(s): Institute of Photonics
External Organisation(s): Bauhaus-Universität Weimar
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 432
No. of pages: 29
ISSN: 0045-7825
Publication date: 01.12.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2024.117390 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{4b7b64e3011c4c36bde7beaa1709f8b7,
title = "Hydrodynamics of multicomponent vesicles: A phase-field approach",
abstract = "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.",
keywords = "Hydrodynamics, Isogeometric analysis, Multicomponent vesicle, Phase-field modeling, Residual-based variational multiscale method",
author = "Zuowei Wen and Navid Valizadeh and Timon Rabczuk and Xiaoying Zhuang",
note = "Publisher Copyright: {\textcopyright} 2024",
year = "2024",
month = dec,
day = "1",
doi = "10.1016/j.cma.2024.117390",
language = "English",
volume = "432",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier BV",
}

Back