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Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow

Published online by Cambridge University Press:  02 November 2016

Arshad Kudrolli ,
David Scheff  and
Benjamin Allen
Arshad Kudrolli*
Affiliation:
Department of Physics, Clark University, Worcester, MA 01610, USA
David Scheff
Affiliation:
Department of Physics, Clark University, Worcester, MA 01610, USA
Benjamin Allen
Affiliation:
Department of Physics, Clark University, Worcester, MA 01610, USA
*
†Email address for correspondence: [email protected]
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Abstract

We advance a quantitative description of the critical shear rate $\dot{\unicode[STIX]{x1D6FE}_{c}}$ needed to dislodge a spherical particle resting on a surface with a model asperity in laminar and turbulent fluid flows. We have built a cone-plane experimental apparatus which enables measurement of $\dot{\unicode[STIX]{x1D6FE}_{c}}$ over a wide range of particle Reynolds number $Re_{p}$ from $10^{-3}$ to $1.5\times 10^{3}$. The condition to dislodge the particle is found to be consistent with the torque balance condition after including the torque component due to drag about the particle centre. The data for $Re_{p}<0.5$ are in good agreement with analytical calculations of the drag and lift coefficients in the $Re_{p}\rightarrow 0$ limit. For higher $Re_{p}$, where analytical results are unavailable, the hydrodynamic coefficients are found to approach a constant for $Re_{p}>1000$. We show that a linear combination of the hydrodynamic coefficients found in the viscous and inertial limits can describe the observed $\dot{\unicode[STIX]{x1D6FE}_{c}}$ as a function of the particle and fluid properties.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 397 - 409
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Copyright
© 2016 Cambridge University Press 

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References

Buffington, J. M. & Montgomery, D. R. 1997 A systematic analysis of eight decades of incipient motion studies, with special reference to gravel bedded rivers. Water Resour. Res. 33, 1993–2029.CrossRefGoogle Scholar
Charru, F., Mouilleron, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 55–80.CrossRefGoogle Scholar
Charru, F., Larrieu, E., Dupont, J.-B. & Zenit, R. 2007 Motion of a particle near a rough wall in a viscous shear flow. J. Fluid Mech. 570, 431–453.Google Scholar
Cheng, N.-S. 2008 Formula for the viscosity of a glycerol–water mixture. Ind. Engng Chem. Res. 47, 3285–3288.Google Scholar
Clark, A. H., Shattuck, M. D., Ouellette, N. T. & O’Hern, C. S. 2015 Onset and cessation of motion in hydrodynamically sheared granular beds. Phys. Rev. E 92, 042202.Google Scholar
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics, 2nd edn. Noordhoff, Leyden.Google Scholar
Hong, A., Tao, M. J. & Kudrolli, A. 2015 Onset of erosion of a granular bed in a channel driven by fluid flow. Phys. Fluids 27, 013301.CrossRefGoogle Scholar
Lee, H. & Balachandar, S. 2012 Critical shear stress for incipient motion of a particle on a rough bed. J. Geophys. Res.: Earth Surf. 117, F01026.Google Scholar
Leighton, D. & Acrivos, A. 1985 The lift on a small sphere touching a plane in the presence of a simple shear flow. Z. Angew. Math. Phys. 36, 174–178.CrossRefGoogle Scholar
Mollinger, A. M. & Nieuwstadt, F. T. M. 1996 Measurement of the lift force on a particle fixed to the wall in the viscous sublayer of a fully developed turbulent boundary layer. J. Fluid Mech. 316, 285–306.Google Scholar
O’Neill, M. E. 1968 A sphere in contact with a plane wall in a slow linear shear flow. Chem. Engng Sci. 23, 1293–1298.Google Scholar
Okamoto, S. 1980 Turbulent Shear Flow Behind a Sphere Placed on a Plane Boundary. In Turbulent Shear Flows, 2nd edn. (ed. Bradbury, L. J. S., Durst, F., Launder, B. E., Schmidt, F. W. & Whitelaw, J. H.), pp. 246–256. Springer.Google Scholar
Ouriemi, M., Aussillous, P., Medale, M., Peysson, Y. & Guazzelli, E. 2007 Determination of the critical shields number for particle erosion in laminar flow. Phys. Fluids 19, 061706.Google Scholar
Phillips, M. 1980 A force balance model for particle entrainment into a fluid stream. J. Phys. D: Appl. Phys. 13, 221–233.Google Scholar
Pozrikidis, C. 1997 Shear flow over a protuberance on a plane wall. J. Engng Maths 31, 29–42.Google Scholar
Shields, A.1936 Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Preussische Versuchsanstalt für Wasserbau und Schiffbau.Google Scholar
Sdougos, H. P., Bussolari, S. R. & Dewey, C. F. 1984 Secondary flow and turbulence in a cone-and-plate device. J. Fluid Mech. 138, 379–404.Google Scholar
Wiberg, P. L. & Smith, J. D. 1987 Calculations of the critical shear stress for motion of uniform and heterogeneous sediments. Water Resour. Res. 23, 1471–1480.Google Scholar
Zeng, L., Najjar, F., Balachandar, S. & Fischer, P. 2009 Forces on a finite-sized particle located close to a wall in a linear shear flow. Phys. Fluids 21, 033302.Google Scholar

Kudrolli et al. Movie 1

The particle is observed to move inside a U-shaped pocket at high particle Reynolds Numbers.

Download Kudrolli et al. Movie 1(Video)
Video 282.7 KB

Kudrolli et al. Movie 2

The particle is observed not to move inside a circular pocket even at high particle Reynolds Numbers.

Download Kudrolli et al. Movie 2(Video)
Video 308.3 KB

Kudrolli et al. Movie 3

Movie version of Figure 3 in the manuscript illustrates the dynamics of the flow. The movie corresponds to 41 seconds in real time and is 10x faster. The exposure is 1 second for each frame.

Download Kudrolli et al. Movie 3(Video)
Video 4.3 MB

Kudrolli et al. Movie 4

The particle is observed to roll over the barrier corresponding to a U-shaped pocket (Re_p \sim 0.2).

Download Kudrolli et al. Movie 4(Video)
Video 106.6 KB

Kudrolli et al. Movie 5

The particle is observed to roll over the barrier corresponding to a circular pocket (Re_p \sim 0.2).

Download Kudrolli et al. Movie 5(Video)
Video 190.6 KB