The dynamics and scaling law for particles suspended in shear flow with inertia

Ding, E. J.; Aidun, Cyrus K.

doi:10.1017/s0022112000001932

Cited by 146 publications

(160 citation statements)

References 16 publications

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“…3(a) the external fluid lines are separated into two portions before approaching the vesicle at two saddle points (located close to the channel centerline at the back and at the front of the vesicle): One portion continues its flow (through the region between the wall and the membrane) and passes the vesicle, while the other portion is reflected back by the vesicle. Such flow recirculations are also observed for confined rotating rigid spheres [43] and rigid ellipsoids [44]. For the same degree of confinement (χ = 0.4), in Fig.…”

Section: Tank-treading Under Shear Flowsupporting

confidence: 65%

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: 65%

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

2011

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“…Note that φ cr < 11.7 • in the range studied, but does not vary monotonically with a/b. The implications of the torque on the elliptic cylinder in shear have been considered by Ding & Aidun (2000); these authors have found that above Re cr the system exhibits a saddle-node bifurcation, and that the scaling of the period of rotation, τ , for Re < Re cr as τ ∼ C(Re cr − Re) −1/2 with C independent of Re is thus a universal property owing to the behaviour near any saddle node. Similar to Ding & Aidun, we may assess the stability of the two torque-free points for Re = 50 and a/b = 1.25, representative of a general condition with Re > Re cr .…”

Section: Validation Of Flow Solver: Non-isotropic Bodies In Shear Flowmentioning

confidence: 99%

Stationary shear flow around fixed and free bodies at finite Reynolds number

2004

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Numerical solutions of stationary flow resulting from immersion of a single body in simple shear flow are reported for a range of Reynolds numbers. Flows are computed using finite-element methods. Comparisons to results of asymptotic low-Reynoldsnumber theory, experimental study, and other numerical techniques are provided. Results are presented primarily for isotropic bodies, i.e. the circular cylinder and sphere, for both of which the two conditions of a torque-free (freely-rotating) and fixed body are investigated. Conditions studied for the sphere are 0 < Re < 100, and for the circular cylinder 0 < Re < 500, with the shear-flow Reynolds number defined as Re =γ a 2 /ν;γ is the shear rate of the Cartesian simple shear flow u = (γ y, 0, 0), a is the cylinder or sphere radius, and ν is the kinematic viscosity of the fluid. In the torque-free case, the rotation rate of the body decreases with increasing Re. Qualitative dependence, seen in the Re = 0 fluid flow field, upon whether the body is fixed against rotation or torque-free vanishes as Re increases and the fluid flow is more similar to that around the fixed body: the influence of rotation of the body and the associated closed streamlines are confined to a narrow layer about the body for Re > O(1). Separation of the boundary layer is observed in the case of a fixed cylinder at Re ≈ 85, and for a fixed sphere at Re ≈ 100; similar separation phenomena are observed for a freely rotating cylinder. The surface stress and its symmetric first moment (the stresslet) are presented, with the latter providing information on the particle contribution to the mixture rheology at finite Re. Stationary flow results are also presented for elliptical cylinders and oblate spheroids, with observation of zero-torque inclinations relative to the flow direction which depend upon the aspect ratio, confirming and extending prior findings.

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“…The kinetic nature of the lattice Boltzmann method enables it to simulate complex geometry such as fluid flow in porous media (Ladd, 1994;Ladd and Verberg, 2001;Qi, 1999;Ding and Aidun, 2000;Qian, 1990;Qian et al, 1992;Chen and Doolen, 1998;Guo et al, 2002;He and Luo, 1997a,b). In the lattice Boltzmann (LB) method, fluid particles reside on the lattice nodes and move to their nearest neighbors along the links with unit spacing in each unit time step.…”

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

Flows With Inertia in a Three-Dimensional Random Fiber Network

Rong

2006

Chemical Engineering Communications

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A fiber web is modeled as a three-dimensional random cylindrical fiber network. Nonlinear behavior of fluid flowing through the fiber network is numerically simulated by using the lattice Boltzmann (LB) method. A nonlinear relationship between the friction factor and the modified Reynolds number is clearly observed and analyzed by using the Fochheimer equation, which includes the quadratic term of velocity. We obtain a transition from linear to nonlinear region when the Reynolds numbers are sufficiently high, reflecting the inertial effect of the flows. The simulated permeability of such fiber network has relatively good agreement with the experimental results and finite element simulations.

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The dynamics and scaling law for particles suspended in shear flow with inertia

Cited by 146 publications

References 16 publications

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

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

Stationary shear flow around fixed and free bodies at finite Reynolds number

Flows With Inertia in a Three-Dimensional Random Fiber Network

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