Three-dimensional vesicles under shear flow: Numerical study of dynamics and phase diagram

Biben, Thierry; Farutin, Alexander; Misbah, Chaouqi

doi:10.1103/physreve.83.031921

Cited by 109 publications

(121 citation statements)

References 39 publications

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“…Taking advantage of the linearity of the Stokes equations, boundary integral methods (BIM) (Pozrikidis 1992(Pozrikidis , 2010 are efficient techniques to solve the dynamics of fluidic particles in an external flow. These methods have been successfully applied to red blood cells (Pozrikidis 1995;Zhao et al 2010;Zhao & Shaqfeh 2011), capsules (Lac et al 2007;Walter et al 2011;Hu et al 2012) and vesicles (Ghigliotti et al 2010;Veerapaneni et al 2011;Biben et al 2011;Boedec et al 2012). An appealing feature of BIM is their precision, as they do not need the discretisation of the fluid domain (Pozrikidis 1992).…”

Section: Introductionmentioning

confidence: 99%

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

2014

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We propose a procedure -partly analytical and partly numerical -to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The unsteady Stokes equations for the stream function are decomposed onto normal modes for the angular and temporal variables, leading to a fourth-order linear ordinary differential equation in the radial variable. The forcing terms are dictated by the properties of the membrane, and result into jump conditions at the interface between the internal and external media. The equation can be solved numerically, and an excellent agreement is found with a fullycomputational approach we developed in parallel. Comparisons are also shown with the results available in the scientific literature for drops, and a model based on the concept of embarked fluid is presented, which allows for a good representation of the results and a consistent interpretation of the underlying physics.

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Section: Introductionmentioning

confidence: 99%

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

2014

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“…7 For notational convenience, we suppress the (u, v) dependence. Using these definitions, we now derive the spectra of various operators.…”

Section: Spectral Analysis On the Unit Spherementioning

confidence: 99%

“…Several authors [6,7,16,17,35,57] have used direct integral equation formulation for simulating vesicle flows. This formulation results in a single-layer potential for flows with no viscosity contrast and a combination of a single-layer and a double-layer for flows with viscosity contrast [35,48,57,69].…”

Section: Related Workmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

133

142

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Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows", Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general non-axisymmetric vesicle flows in three dimensions.Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere.By introducing these algorithmic components, we obtain a time-stepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.

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“…A widely used method is the boundary integral method that is based on the use of Green's function techniques [2]. It has been successfully applied to vesicles [3][4][5][6]. The advantage of this method is the high precision.…”

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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Three-dimensional vesicles under shear flow: Numerical study of dynamics and phase diagram

Cited by 109 publications

References 39 publications

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

A fast algorithm for simulating vesicle flows in three dimensions

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

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