Drag force on a circular cylinder midway between two parallel plates at very low Reynolds numbers—Part 1: Poiseuille flow (numerical)

Richou, A. Ben; Ambari, Abdelhak; Naciri, Jâafar Khalid

doi:10.1016/j.ces.2003.10.031

Cited by 37 publications

(43 citation statements)

References 12 publications

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“…(4); its values in the oscillating and stationary regimes are plotted in Figure 4. In both cases, the experimental variation of λ s with D/H is similar to that predicted by Ben Richou et al 8,9 (also plotted on the figure). The difference between the experimental and predicted data is at most 15% and is likely due to the difference between the Reynolds numbers used by these authors, which are lower by a factor of 10 or more than in the present work; as shown by Hu 6 and Ben Richou, 9 the higher Reynolds number leads to a larger value of λ s .…”

Section: Relations Between Force and Flow/cylinder Velocitiessupporting

confidence: 74%

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Oscillations and translation of a free cylinder in a viscous confined flow

2013

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An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H. The vertical motion of the cylinder, its rotation about its axis, and its transverse motion across the gap have been investigated as a function of its diameter D, its density ρs, of the mean vertical velocity U of the fluid, and of its viscosity ν. The relevant Reynolds number Re is shown to be based on the cell aperture H and on the relative velocity Vr between the fluid and the cylinder. For a blockage ratio D/H above 0.5 and Re above 20, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap were observed together with periodic variations of the vertical velocity. For a given fluid-cylinder pair, the relative velocity Vr as well as the frequency f and the amplitude of the transverse velocity for these oscillations are nearly independent of the flow velocity U. For given cylinder density and fluid characteristics, f is also nearly independent of the ratio D/H in the range investigated. The oscillations could be observed down to values of Re as low as 30: this is lower than usual values for vortex shedding in confined geometries, which suggests that one might deal with a different instability mechanism.

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Section: Relations Between Force and Flow/cylinder Velocitiessupporting

confidence: 74%

“…For particles placed in the centre of the channel, Faxen 7 derived the expression of the drag for a confinement D/H less then 0.5; the case of higher confinements has been recently considered by Ben Richou and co-workers. 8,9 An eccentered a) Electronic mail: vdangelo@fi.uba.ar. b) Electronic mail: hulin@fast.u-psud.fr.…”

Section: Introductionmentioning

confidence: 99%

Oscillations and translation of a free cylinder in a viscous confined flow

2013

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“…The drag coefficient of a single circular pillar placed midway between two long, flat plates as a function of the ratio of the pillar's diameter and the distance between the plates is available in Harrison (1924), Faxen (1946) andBen Richou et al (2004). There's also a wealth of data for drag coefficients of pressure driven flow around pillar arrays.…”

Section: Mhd Flow In a Conduit Patterned With A Pillar Arraymentioning

confidence: 99%

When MHD-based microfluidics is equivalent to pressure-driven flow

Qin

Bau

2010

Microfluid Nanofluid

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Magnetohydrodynamics (MHD) provides a convenient, programmable means for propelling liquids and controlling fluid flow in microfluidic devices without a need for mechanical pumps and valves. When the magnetic field is uniform and the electric field in the electrolyte solution is confined to a plane that is perpendicular to the direction of the magnetic field, the Lorentz body force is irrotational and one can define a "Lorentz" potential. Since the MHD-induced flow field under these circumstances is identical to that of pressure-driven flow, one can utilize the large available body of knowledge about pressure-driven flows to predict MHD flows and infer MHD flow patterns. In this note, we prove the equivalence between MHD flows and pressure-driven flows under certain conditions other than flow in straight conduits with rectangular crosssections. We determine the velocity profile and the efficiency of MHD pumps, accounting for current transport in the electrolyte solutions. Then, we demonstrate how data available for pressure driven flow can be utilized to study various MHD flows, in particular, in a conduit patterned with pillars such as may be useful for liquid chromatography and chemical reactors. Additionally, we examine the effect of interior obstacles on the electric current flow in the conduit and show the existence of a particular pillar geometry that maximizes the current. solution is confined to a plane that is perpendicular to the direction of the magnetic field, the Lorentz body force is irrotational and one can define a "Lorentz" potential. Since the MHDinduced flow field under these circumstances is identical to that of pressure-driven flow, one can utilize the large available body of knowledge about pressure-driven flows to predict MHD flows and infer MHD flow patterns. In this note, we prove the equivalence between MHD flows and pressure-driven flows under certain conditions other than flow in straight conduits with rectangular cross-sections. We determine the velocity profile and the efficiency of MHD pumps, accounting for current transport in the electrolyte solutions. Then, we demonstrate how data available for pressure driven flow can be utilized to study various MHD flows, in particular, in a conduit patterned with pillars such as may be useful for liquid chromatography and chemical reactors. Additionally, we examine the effect of interior obstacles on the electric current flow in the conduit and show the existence of a particular pillar geometry that maximizes the current.

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“…(1) and (2) are rewritten in a curvilinear and orthogonal frame ðX; YÞ matching perfectly the boundaries of the cylinder and the walls [11]. Using the singularities method we generate a conformal mapping from curved borders to a rectangular one.…”

Section: Methodsmentioning

confidence: 99%

Wall effects on the transportation of a cylindrical particle in power-law fluids

Despeyroux

Ambari

Richou

2011

Journal of Non-Newtonian Fluid Mechanics

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/8454 To cite this version :Antoine DESPEYROUX, Abdelhak AMBARI, Abderrahim BEN RICHOU -Wall effects on the transportation of a cylindrical particle in power-law fluids -Journal of Non-Newtonian Fluid Mechanics -Vol. 166, n°19-20, p.1173-1182 -2011 Any correspondence concerning this service should be sent to the repository b s t r a c tThe present work deals with the numerical calculation of the Stokes-type drag undergone by a cylindrical particle perpendicularly to its axis in a power-law fluid. In unbounded medium, as all data are not available yet, we provide a numerical solution for the pseudoplastic fluid. Indeed, the Stokes-type solution exists because the Stokes' paradox does not take place anymore. We show a high sensitivity of the solution to the confinement, and the appearance of the inertia in the proximity of the Newtonian case, where the Stokes' paradox takes place. For unbounded medium, avoiding these traps, we show that the drag is zero for Newtonian and dilatant fluids. But in the bounded one, the Stokes-type regime is recovered for Newtonian and dilatant fluids. We give also a physical explanation of this effect which is due to the reduction of the hydrodynamic screen length, for pseudoplastic fluids. Once the solution of the unbounded medium has been obtained, we give a solution for the confined medium numerically and asymptotically. We also highlight the consequence of the confinement and the backflow on the settling velocity of a fiber perpendicularly to its axis in a slit. Using the dynamic mesh technique, we give the actual transportation velocity in a power-law ''Poiseuille flow'', versus the confinement parameter and the fluidity index, induced by the hydrodynamic interactions.

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Drag force on a circular cylinder midway between two parallel plates at very low Reynolds numbers—Part 1: Poiseuille flow (numerical)

Cited by 37 publications

References 12 publications

Oscillations and translation of a free cylinder in a viscous confined flow

Oscillations and translation of a free cylinder in a viscous confined flow

When MHD-based microfluidics is equivalent to pressure-driven flow

Wall effects on the transportation of a cylindrical particle in power-law fluids

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