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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: akudrolli@clarku.edu
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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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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