The motion of an ellipsoid in tube flow at low Reynolds numbers

Sugihara‐Seki, Masako

doi:10.1017/s0022112096007926

Cited by 43 publications

(35 citation statements)

References 12 publications

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“…It is seen that the results agree very well (within 1 %). The particle trajectories presented in figure 7 of Sugihara-Seki (1996) also match those computed in this study. Sedimenting ellipsoids, simulated using this numerical scheme, also follow the wellknown property of turning their broadside orthogonal to the direction the flow for the case of non-zero Reynolds numbers (Cox 1965), and of moving in a direction between the directions of the gravity and the orientation of the long axis for Stokes flow (Jeffery 1922).…”

Section: Validationsupporting

confidence: 77%

“…The inertial terms in the Navier-Stokes equation are put to zero in the comparison tests. Sugihara-Seki (1996) presented (in his figure 4) the variation of translational and angular velocity of an ellipsoid, suspended in a Poiseuille flow within a tube of radius 1.0, as a function of its orientation angle inside the tube at different locations. These velocities have been computed here and compared, as shown in figure 1.…”

Section: Validationmentioning

confidence: 99%

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Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Swaminathan

Mukundakrishnan

2006

J. Fluid Mech.

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The motion of a heavy rigid ellipsoidal particle settling in an infinitely long circular tube filled with an incompressible Newtonian fluid has been studied numerically for three categories of problems, namely, when both fluid and particle inertia are negligible, when fluid inertia is negligible but particle inertia is present, and when both fluid and particle inertia are present. The governing equations for both the fluid and the solid particle have been solved using an arbitrary Lagrangian-Eulerian based finite-element method. Under Stokes flow conditions, an ellipsoid without inertia is observed to follow a perfectly periodic orbit in which the particle rotates and moves from side to side in the tube as it settles. The amplitude and the period of this oscillatory motion depend on the initial orientation and the aspect ratio of the ellipsoid. An ellipsoid with inertia is found to follow initially a similar oscillatory motion with increasing amplitude. Its orientation tends towards a flatter configuration, and the rate of change of its orientation is found to be a function of the particle Stokes number which characterizes the particle inertia. The ellipsoid eventually collides with the tube wall, and settles into a different periodic orbit. For cases with non-zero Reynolds numbers, an ellipsoid is seen to attain a steady-state configuration wherein it falls vertically. The location and configuration of this steady equilibrium varies with the Reynolds number.

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Section: Validationsupporting

confidence: 77%

Section: Validationmentioning

confidence: 99%

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Swaminathan

Mukundakrishnan

2006

J. Fluid Mech.

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“…To overcome this difficulty, we adopted the gradual h-refinement method, in which sizes of elements were progressively decreased toward the corners with size ratio = 0.15 (Babuska & Suri 1994;Karniadakis & Sherwin 2005). The finite-element scheme was formulated in terms of the primitive variables based on the variational principle δJ = 0 (Sugihara-Seki 1996, 2004. Here, the variational functional was chosen as…”

Section: Formulation and Methodsmentioning

confidence: 99%

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft

2008

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A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity L p , defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6 nm radius and 8 nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall.

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“…The emphasis throughout is on high flow rates corresponding to high Reynolds numbers. Apart from studies at low flow rates [9][10][11], previous work in the area is based mostly on direct numerical simulations and few experiments [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Movement of a finite body in channel flow

Smith¹,

Johnson²

2016

Proc. R. Soc. A.

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A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at mediumto-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos(π/7), i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

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The motion of an ellipsoid in tube flow at low Reynolds numbers

Cited by 43 publications

References 12 publications

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft

Movement of a finite body in channel flow

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