Correction factor of the Stokes force undergone by a sphere in the axis of a cylinder in uniform and Poiseuille flows

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

doi:10.1051/epjap:2003066

Cited by 9 publications

(14 citation statements)

References 20 publications

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“…In recent years, numerical values of λ(k) have also been reported by Ben Richou et al 14 in an extended range of confinement, i.e., 0.05 < k < 0.98. Since the relative error between the results of Bungay and Brenner 13 and those of Ben Richou et al 14 is less than 2% in this range (as shown by Table III in Ben Richou et al 14 ), we can equally use the expression (2) or the interpolated numerical data obtained in our laboratory by Ben Richou et al 14 We shall use these results in this work to obtain the condition of levitation of a free sphere suspended in a Poiseuille flow in Stokes type regimes.…”

Section: Formulation and Analysissupporting

confidence: 55%

“…The nondimensional flow rate f(k) depends solely on the confinement parameter k. Based on the studies quoted above (Bungay and Brenner 13 or Ben Richou et al 14 ), this functional relationship between f(k) and k is shown in Fig. 2.…”

Section: Formulation and Analysismentioning

confidence: 88%

“…Since the relative error between the results of Bungay and Brenner 13 and those of Ben Richou et al 14 is less than 2% in this range (as shown by Table III in Ben Richou et al 14 ), we can equally use the expression (2) or the interpolated numerical data obtained in our laboratory by Ben Richou et al 14 We shall use these results in this work to obtain the condition of levitation of a free sphere suspended in a Poiseuille flow in Stokes type regimes. We consider an upward Poiseuille flow in a vertical cylindrical tube in which we place a non-neutrally buoyant sphere.…”

Section: Formulation and Analysismentioning

confidence: 93%

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Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

Champmartin

Ambari

Chhabra

2012

Review of Scientific Instruments

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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. In this study, a theoretical framework is developed to predict the equilibrium conditions of a nonneutrally buoyant sphere placed in a vertical conical tube as encountered in liquid rotameters. The analysis presented herein is applicable for a sphere heavier than the surrounding fluid, situated on the axis of a slightly tapered tube. The sphere is subject to the laminar flow conditions with the Reynolds numbers ranging between the Stokes type regimes up to values corresponding to slightly inertial regimes. In this work, we assume that the aperture angle of the tube is small and that the drag force is mainly due to the dissipation located in the gap between the tube and the sphere. Under these conditions, it is possible to consider the tube as locally cylindrical and we can use the results previously obtained for the correction factor of the Stokes force on a sphere subject to a Poiseuille flow in a tube of constant cross-section. We obtain an equation relating the flow rate to the vertical position of the sphere in the tube and the validity of this analysis is demonstrated by applying it to a commercially available rotameter. The present study provides a simple but sound theoretical method to calibrate such flowmeters.

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Section: Formulation and Analysissupporting

confidence: 55%

Section: Formulation and Analysismentioning

confidence: 88%

Section: Formulation and Analysismentioning

confidence: 93%

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Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

Champmartin

Ambari

Chhabra

2012

Review of Scientific Instruments

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“…For this lateral confinement (k = 10 À2 ), at least at a distance of ten sphere radii to the bottom, the lateral correction factor is negligible (k(k = 10 À2 , e ? 1) = F(k = 10 À2 )/(6plaU) = 1.017 [10] and d(e = 10) = 1.109). This successful result confirms the validity of the dynamic mesh numerical method used for this unsteady problem.…”

Section: Newtonian Fluidmentioning

confidence: 96%

“…Still in the Newtonian case, the effect of the lateral confinement induced by the wall of an infinitely long circular cylinder has been calculated numerically and experimentally by Ambari et al [9] and Ben Richou et al [10]. Apart from the asymptotic calculation given by Rodin [11] in lateral unbounded power-law fluid, for the squeezing motion of two nearly-touching rigid spheres, there are other similar asymptotic solutions for non-Newtonian fluids [12] to the same problem.…”

Section: Introductionmentioning

confidence: 96%

Slow motion of a sphere towards a plane through confined non-Newtonian fluid

Despeyroux,

Ambari

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. a b s t r a c tThe time needed for the contact of two spheres or a sphere with a rigid plane is mainly controlled by the hydrodynamic drainage of the film located in the gap as long as its thickness is out of range of the Van der Waals interactions. In fact, this time controls the dynamics of aggregation of concentrated dispersions. This fundamental problem has an exact solution in Newtonian fluid which has been used to confirm the validity of the numerical dynamic mesh method employed in this geometrically unsteady problem. Following this validation, we applied it to calculate the correction factor of the drag undergone by a sphere approaching a plane, at constant Reynolds number, in a cylindrical tube filled with a non-Newtonian fluid having negligible viscoelastic component and roughly behaving as a power-law fluid. After a justification for using this useful model, we studied the influence of the lateral confinement on the frontal correction factor of the drag. In the lubrication limit, we recall the asymptotic solution of Rodin to this problem in lateral unbounded power law fluid. The comparison of both asymptotical and numerical results confirms their validity. The results obtained in this study may find an application to Dynamic Surface Force Apparatus for nanorheology.

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Physics of Hydrodynamic Interactions

2024

Some Complex Phenomena in Fluid and Solid Mechanics

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Correction factor of the Stokes force undergone by a sphere in the axis of a cylinder in uniform and Poiseuille flows

Cited by 9 publications

References 20 publications

Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

Slow motion of a sphere towards a plane through confined non-Newtonian fluid

Physics of Hydrodynamic Interactions

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