Motion of a tank-treading ellipsoidal particle in a shear flow

Keller, Stuart Ronald; Skalak, Richard

doi:10.1017/s0022112082002651

Cited by 431 publications

(541 citation statements)

References 18 publications

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“…In Fig. 3(b) we report The same qualitative tendency is observed in the unbounded geometry [3,39,41]. Figure 3(d) shows the behavior of the tank-treading velocity normalized by γ R 0 /2, which is the tank-treading velocity of a circular vesicle [45].…”

Section: Tank-treading Under Shear Flowsupporting

confidence: 70%

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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Section: Tank-treading Under Shear Flowsupporting

confidence: 70%

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

2011

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“…Algorithm 2 corresponds to a sequence of steepest descent steps for the constrained minimization problem (33). One could use a line search approach for nonlinear programming (e.g., with an 2 merit function [46]) but this requires access to F and is more complex to implement.…”

Section: Algorithm 2 Explicit Reparametrizationmentioning

confidence: 99%

“…For example, at equilibrium (i.e., in a quiescent fluid), healthy red blood cells have a biconcave shape that corresponds to a minimal membrane bending energy. Under nonequilibrium conditions, as experienced in a simple shear flow, the best-studied features of red cell dynamics, formation of tank-treading ellipsoids and tumbling motion, are shared with vesicles [6,33,35]. has a non-equilibrium 2-1 ellipsoidal shape and they are arranged in a rectangular lattice.…”

Section: Introductionmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

137

143

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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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“…We note that the dynamics of RBC and vesicles in fluid flow has been studied both experimentally (see [1,2,19,20,26,37]) and theoretically (cf. [6,7,21,22,32,34]). For the numerical study of the rheology of RBC in microchannels, the IB has been applied in [5,17,27,38], whereas the FE-IB has been used recently in [16].…”

Section: % Iterationmentioning

confidence: 99%

An adaptive Newton continuation strategy for the fully implicit finite element immersed boundary method

Hoppe

Linsenmann

2012

Journal of Computational Physics

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Abstract. The Immersed Boundary Method (IB) is known as a powerful technique for the numerical solution of fluid-structure interaction problems as, for instance, the motion and deformation of viscoelastic bodies immersed in an external flow. It is based on the treatment of the flow equations within an Eulerian framework and of the equations of motion of the immersed bodies with respect to a Lagrangian coordinate system including interaction equations providing the transfer between both frames. The classical IB uses finite differences, but the IBM can be set up within a finite element approach in the spatial variables as well (FE-IB). The discretization in time usually relies on the Backward Euler (BE) method for the semidiscretized flow equations and the Forward Euler (FE) method for the equations of motion of the immersed bodies. The BE/FE FE-IB is subject to a CFL-type condition, whereas the fully implicit BE/BE FE-IB is unconditionally stable. The latter one can be solved numerically by Newton-type methods whose convergence properties are dictated by an appropriate choice of the time step size, in particular, if one is faced with sudden changes in the total energy of the system. In this paper, taking advantage of the well developed affine covariant convergence theory for Newton-type methods, we study a predictor-corrector continuation strategy in time with an adaptive choice of the continuation steplength. The feasibility of the approach and its superiority to BE/FE FE-IB is illustrated by a representative numerical example.Key words. finite element immersed boundary method, fully implicit scheme, predictorcorrector continuation, red blood cells AMS subject classifications. 65H20, 65M60, 74L15, 76D05, 92C101. Introduction. A computationally attractive methodology for the numerical simulation of the motion and deformation of elastic and viscoelastic bodies in external flows is the Immersed Boundary Method (IB), which has been originally developed by Peskin [28] and further studied in [11,29,30,31,33]. The IBM uses an Eulerian coordinate system for the flow equations and Lagrangian coordinates for the boundary of the immersed bodies together with appropriate interaction equations to transform Eulerian to Lagrangian quantities and vice versa. The interaction equations feature multidimensional Dirac delta functions that have to be approximated appropriately within a finite difference approach. More recently, a variational formulation of the IBM has been provided in [8] and [9, 10] as a basis for a finite element realization referred to as the Finite Element Immersed Boundary Method (FE-IB). Both for the classical IB and the FE-IB, the most common approach with regard to discretization in time is to use the Backward Euler (BE) method for the flow equations and the Forward Euler (FE) method for the equation describing the motion and deformation of the immersed bodies which gives rise to the BE/FE IB and BE/FE FE-IB, respectively. However, these schemes typically require a CFL-type condition (cf., e.g., [9,16]). B...

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Motion of a tank-treading ellipsoidal particle in a shear flow

Cited by 431 publications

References 18 publications

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

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

A fast algorithm for simulating vesicle flows in three dimensions

An adaptive Newton continuation strategy for the fully implicit finite element immersed boundary method

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