Skip to main content Accessibility help
×
Home

Motion of a particle near a rough wall in a viscous shear flow

  • F. CHARRU (a1), E. LARRIEU (a1), J.-B. DUPONT (a1) and R. ZENIT (a2)

Abstract

The motion of a spherical particle along a rough bed in a simple shear viscous flow is studied experimentally for a wide range of parameters, varying the particle size and density, the fluid viscosity and the shear rate γ. The instantaneous particle velocity is calculated in the stream, transverse and vertical directions, using a high-speed video imaging system. It is found that the normalized streamwise mean particle velocity U/US, where US is the Stokes settling velocity, depends only on the dimensionless shear rate μ γ/(Δ ρ g d), this relationship being independent of the particle Reynolds number Rep. This result holds for small Rep, which was the case in our experiments (Rep < 10). The characteristic amplitude and frequency of the velocity fluctuations are also given and discussed. A model is then proposed for the mean streamwise velocity, based on ideas of Bagnold (Proc. R. Soc. Lond. A, vol. 332, 1973, p. 473) and calculations of Goldman et al. (Chem. Engng Sci., vol. 22, 1967b, p. 653) for the velocity of a particle close to a smooth plane. From this model an equivalent bed roughness and an effective friction coefficient are deduced.

Copyright

References

Hide All
Abbot, J. E. & Francis, J. R. D. 1977 Saltation and suspension trajectories of solid grains in a water stream. Phil. Trans. R. Soc. Lond. A 284, 225254.
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 4963.
Bagnold, R. A. 1973 The nature of saltation and of ‘bed-load’ transport in water. Proc. R. Soc. Lond. A 332, 473504.
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, 19932029.
Chaoui, M. & Feuillebois, F. 2003 Creeping flow around a sphere in a shear flow close to a wall. Q. J. Mech. Appl. Maths 56, 381410.
Charru, F., Mouilleron-Arnould, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 5580.
Cherukat, P. & McLaughlin, J. B. 1994 The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263, 118.
Chin, C. O., Melville, B. W. & Raudkivi, A. J. 1994 Streambed armoring. J. Hydraul. Engng 120, 899918.
Francis, J. R. D. 1973 Experiments on the motion of solitary grains along the bed of a water stream. Proc. R. Soc. Lond. A 332, 443471.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967a Slow viscous motion of a sphere parallel to a plane wall - I Motion through a quiescent fluid. Chem. Engng Sci. 22, 637651.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967b Slow viscous motion of a sphere parallel to a plane wall - II Couette flow. Chem. Engng Sci. 22, 653660.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice Hall.
Hunt, M. L., Zenit, R., Campbell, C. S. & Brennen, C. E. 2002 Revisiting the 1954 suspension experiments of R. A. Bagnold. J. Fluid Mech. 452, 124.
King, M. R. & Leighton, D. T. 1997 Measurement of the inertial lift on a moving sphere in contact with a plane wall in a shear flow. Phys. Fluids 9, 12481255.
Krishnan, G. P. & Leighton, D. T. 1995 Inertial lift on a moving sphere in contact with a plane wall in a shear flow. Phys. Fluids 7, 25382545.
Midi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341365.
O'Neill, M. E. 1968 A sphere in contact with a plane wall in a slow linear shear flow. Chem. Engng Sci. 23, 12931298.
Quartier, L., Andreotti, B., Douady, S. & Daerr, A. 2000 Dynamics of a grain on a sandpile model. Phys. Rev. E 62, 106114.
Riguidel, F.-X., Jullien, R., Ristow, G. H., Hansen, A. & Bideau, D. 1994 Behaviour of a sphere on a rough inclined plane. J. Phys. Paris I 4, 261272.
Samson, L., Ippolito, I., Batrouni, G. G. & Lemaitre, J. 1998 Diffusive properties of motion on a bumpy plane. Eur. Phys. J. B 3, 377385.
Williams, P. S., Koch, T. & Giddings, J. C. 1992 Characterization of near-wall hydrodynamic lift forces using sedimentation field-flow fractionnation. Chem. Engng Sci. 111, 121127.
Zhao, Y., Galvin, K.P. & Davis, R. H. 2002 Motion of a sphere down a rough plane in a viscous fluid. Intl J. Multiphase Flow 28, 17871800.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Motion of a particle near a rough wall in a viscous shear flow

  • F. CHARRU (a1), E. LARRIEU (a1), J.-B. DUPONT (a1) and R. ZENIT (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed