An immersed boundary projection method for simulating the inextensible vesicle dynamics

Ong, Kian Chuan; Lai, Ming Chih

doi:10.1016/j.jcp.2020.109277

Cited by 16 publications

(6 citation statements)

References 41 publications

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“…However, in certain scenarios bending contributions become important, for example, to describe biomembranes and red blood cells, e.g. [10,11,12,13,14]. In this case the bending stiffness force can be easily added to the interfacial stress balance by modifying Eq.…”

Section: Parameters and Limit Casesmentioning

confidence: 99%

“…Most numerical methods that couple surface rheology to surrounding fluids are designed for membranes and red blood cells. These models include bending stiffness and describe the surface either as an inextensible membrane (infinite dilational modulus) [10,11,12,13,14] or as an elastic shell (with finite shear and dilational modulus) [15,16,17,18]. Only in the last decade the first numerical models were proposed to simulate fluidic surfaces, yet assuming purely viscous behavior [19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

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A numerical method for the simulation of viscoelastic fluid surfaces

de Kinkelder,

Sagis,

Aland

2021

Preprint

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

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Section: Parameters and Limit Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A numerical method for the simulation of viscoelastic fluid surfaces

de Kinkelder,

Sagis,

Aland

2021

Preprint

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“…In addition, Kim et al [25] introduced a penalty immersed boundary method to simulate the dynamics of inextensible vesicles in an incompressible viscous fluid by using two Lagrangian immersed boundaries connected through stiff springs to represent the real immersed boundary for different purposes. Also, Ong et al [26] developed an immersed boundary projection method based on an unconditionally energy stable scheme to simulate the vesicle dynamics in a viscous fluid.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Immersed Boundary/Coarse-Graining Method for Modeling Inextensible Semi-Flexible Filaments in Thermally Fluctuating Fluids

Papadopoulos¹

2021

Computer Modeling in Engineering &Amp; Sciences

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A new and computationally efficient version of the immersed boundary method, which is combined with the coarse-graining method, is introduced for modeling inextensible filaments immersed in low-Reynolds number flows. This is used to represent actin biopolymers, which are constituent elements of the cytoskeleton, a complex network-like structure that plays a fundamental role in shape morphology. An extension of the traditional immersed boundary method to include a stochastic stress tensor is also proposed in order to model the thermal fluctuations in the fluid at smaller scales. By way of validation, the response of a single, massless, inextensible semiflexible filament immersed in a thermally fluctuating fluid is obtained using the suggested numerical scheme and the resulting time-averaged contraction of the filament is compared to the theoretical value obtained from the worm-like chain model.

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“…Models based on interface tracking or capturing such as level set method [13,14,15] were also developed [16,17,18,19] to take into consideration the fluidcell-structure interaction. In numerical treatment, various methods such as immersed boundary method [20,21,22,23,24], immersed interface method [25,26], and fictitious domain method [19] using finite difference or finite element formulation have been introduced to solve governing equations of these models.…”

Section: Introductionmentioning

confidence: 99%

“…Dirichlet or Neumann type conditions were simply added to these models at the end to close the governing equations [43,27,37]. Moreover, in our model derivation, the incompressibility of the fluid, the local and global inextensibility of the vesicle membrane and the conservation of vesicle mass are taken into account by introducing two Lagrangian multipliers, hydrostatic pressure p and surface pressure λ [22] and penalty terms, respectively.…”

Section: Introductionmentioning

confidence: 99%

An Energy Stable C0 Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation

Shen¹,

Zhang²,

Lin³

et al. 2020

Preprint

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A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between vesicles and the wall of the fluid domain. A second-order accurate in both space and time C 0 finite element method is proposed to solved the model governing equations. Various numerical tests confirm the convergence, energy stability, and conservation of mass and surface area of cells of the proposed scheme. Vesicles with different mechanical properties are also used to explain the pathological risk for patient with sickle cell disease.

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An immersed boundary projection method for simulating the inextensible vesicle dynamics

Cited by 16 publications

References 41 publications

A numerical method for the simulation of viscoelastic fluid surfaces

A numerical method for the simulation of viscoelastic fluid surfaces

A Hybrid Immersed Boundary/Coarse-Graining Method for Modeling Inextensible Semi-Flexible Filaments in Thermally Fluctuating Fluids

An Energy Stable C0 Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation

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