Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions

Du, Qiang; Liu, Chun; Wang, Xiaoqiang

doi:10.1016/j.jcp.2005.07.020

Cited by 248 publications

(215 citation statements)

References 28 publications

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“…If h and k f vanish, the above two equations degenerate into the shape equation of achiral lipid vesicles, which has been fully discussed in Refs. [23,24,25,26,27]. Two remarks are necessary concerning Eq.…”

Section: A Euler-lagrange Equationsmentioning

confidence: 99%

Concise theory of chiral lipid membranes

Seifert

2007

Phys. Rev. E

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A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur et al., Science 264, 945 (1994) (2005)] on self-assembled chiral lipid membranes of DC8,9PC. A torus with the ratio between its two generated radii larger than √ 2 is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0 • and 35 • , which are close to the most frequent values 5 • and 28 • observed in the experiment [N. Mahajan et al., Langmuir 22, 1973]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left-and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda et al., Nature (London) 399, 566 (1999)].

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Section: A Euler-lagrange Equationsmentioning

confidence: 99%

Concise theory of chiral lipid membranes

Seifert

2007

Phys. Rev. E

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“…In addition, this method is valid for Stokes flow only (no inertia). Other classes of methods are phase-field [7][8][9] and level set approaches [10] that can be applied both in the Stokes and Navier-Stokes regimes. Their advantage is the ability of handling, in principle, many particles by just specifying the initial condition (in any new run with different vesicles, a number specifying only initial conditions is required in principle).…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional vesicle dynamics under shear flow: Effect of confinement

2011

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Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.

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“…In this vein, a parametric approach is advocated in [6,4] while a phase field method is used in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Biomembranes: Effect of the Bulk Fluid

Bonito

Nochetto

Pauletti

2011

Math. Model. Nat. Phenom.

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Abstract. We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow: the geometric model which does not take into account the bulk fluid and the biomembrane model for two different regimes of parameters.

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Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions

Cited by 248 publications

References 28 publications

Concise theory of chiral lipid membranes

Concise theory of chiral lipid membranes

Two-dimensional vesicle dynamics under shear flow: Effect of confinement

Dynamics of Biomembranes: Effect of the Bulk Fluid

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