Convergence of a regularization method for creeping flow of a Bingham material about a rigid sphere

2002 ◽  
Vol 102 (2) ◽  
pp. 179-191 ◽  
Author(s):  
Benjamin T Liu ◽  
Susan J Muller ◽  
Morton M Denn
Keyword(s):  
Regularization Method ◽  
Creeping Flow ◽  
Rigid Sphere ◽  
Bingham Material

Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow

1995 ◽  
Vol 284 ◽  
pp. 97-135 ◽  
Author(s):  
Jacques Magnaudet ◽  
Mayela Rivero ◽  
Jean Fabre
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Creeping Flow ◽  
Viscous Drag ◽  
Rigid Sphere ◽  
Mass Force ◽  
Spherical Bubble ◽  
High Reynolds Numbers ◽  
High Reynolds

This work reports the first part of a series of numerical simulations carried out in order to improve knowledge of the forces acting on a sphere embedded in accelerated flows at finite Reynolds number, Re. Among these forces added mass and history effects are particularly important in order to determine accurately particle and bubble trajectories in real flows. To compute these hydrodynamic forces and more generally to study spatially or temporally accelerated flows around a sphere, the full Navier–Stokes equations expressed in velocity–pressure variables are solved by using a finite-volume approach. Computations are carried out over the range 0.1 ≤ Re ≤ 300 for flows around both a rigid sphere and an inviscid spherical bubble, and a systematic comparison of the flows around these two kinds of bodies is presented.Steady uniform flow is first considered in order to test the accuracy of the simulations and to serve as a reference case for comparing with accelerated situations. Axisymmetric straining flow which constitutes the simplest spatially accelerated flow in which a sphere can be embedded is then studied. It is shown that owing to the viscous boundary condition on the body as well as to vorticity transport properties, the presence of the strain modifies deeply the distribution of vorticity around the sphere. This modification has spectacular consequences in the case of a rigid sphere because it influences strongly the conditions under which separation occurs as well as the characteristics of the separated region. Another very original feature of the axisymmetric straining flow lies in the vortex-stretching mechanism existing in this situation. In a converging flow this mechanism acts to reduce vorticity in the wake of the sphere. In contrast when the flow is divergent, vorticity produced at the surface of the sphere tends to grow indefinitely as it is transported downstream. It is shown that in the case where such a diverging flow extends to infinity a Kelvin–Helmholtz instability may occur in the wake.Computations of the hydrodynamic force show that the effects of the strain increase rapidly with the Reynolds number. At high Reynolds numbers the total drag is dramatically modified and the evaluation of the pressure contribution shows that the sphere undergoes an added mass force whose coefficient remains the same as in inviscid flow or in creeping flow, i.e. CM = ½, whatever the Reynolds number. Changes found in vorticity distribution around the rigid sphere also affect the viscous drag, which is markedly increased (resp. decreased) in converging (resp. diverging) flows at high Reynolds numbers.

Enterovirus Concentration Using Automated Hollow Fiber Ultrafiltration

1982 ◽  
Vol 14 (4-5) ◽  
pp. 257-272 ◽  
Author(s):  
G Belfort ◽  
A Paluszek ◽  
L S Sturman
Keyword(s):  
Drinking Water ◽  
Hollow Fiber ◽  
Enhanced Recovery ◽  
Tap Water ◽  
Membrane Surface ◽  
Creeping Flow ◽  
Hollow Fibers ◽  
Virus Concentration ◽  
Concentration Technique ◽  
Solution Interface

The Automated Hollow Fiber Ultrafiltration (AHFU) method is proposed here as a simple, efficient and rapid virus concentration technique from tap and drinking water sources. The results reported here extend the testing of the AHFU method to include two Picornaviruses [Poliovirus 2 (vaccine) and Echovirus 1] and Reovirus 3. Their respective mean virus recoveries from between 3 and 100 l of tap water is 88 ± 26, 79 ± 60, and 104 ± 48%. Various approaches including membrane surface modification, changes in backwash hydrodynamics, modification of the feed and backwash composition, and the use of S35-methionine labelled Poliovirus 2, are used to study the recovery of sorbed Poliovirus 2 from the hollow fiber/solution interface. An increase in the backwash pH to between 9.5 and 10.5 significantly improved Poliovirus 2 recovery. This, together with the labelled experiments, indicates that the virus-membrane interactions are probably electrostatic in nature. Convective polarization during filtration probably brings the virus close enough to the surface for these interactions to occur since virus losses were not detected for a non-permeation recycle experiment. Because very low Reynold's numbers are used, the flow is in the creeping-flow-regime for both filtration and backwashing (axial and radial). Unless significantly higher Reynolds could be used, enhanced recovery due to purely hydrodynamic forces is unlikely. High Reynold's numbers, of course, are limited by the pressure constraints of the hollow fibers.

Kelvin–Helmholtz creeping flow at the interface between two viscous fluids

2015 ◽  
Vol 55 ◽  
pp. 317
Author(s):  
Lawrence Forbes ◽  
Rhys Paul ◽  
Michael Chen ◽  
David Horsley
Keyword(s):  
Creeping Flow ◽  
Viscous Fluids
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