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Shear-induced dispersion in a dilute suspension of rough spheres

  • F. R. Da Cunha (a1) (a2) and E. J. Hinch (a1)
Abstract

In the absence of Brownian motion, inertia and inter-particle forces, two smooth spheres collide in a simple shear flow in a reversible way returning to their initial streamlines. Because the minimum separation during the collision can be less than 10−4 of the radius, quite a small surface roughness can have a significant irreversible effect on the collision. We calculate the change between the initial and final streamlines caused by roughness. Repeated random collisions in a dilute suspension lead to a diffusion of the particles across the streamlines. We calculate the shear-induced diffusivity for both self-diffusion and down-gradient diffusion.

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Acrivos, A., Batchelor, G. K., Hinch, E. J., Koch, D. L. & Mauri, R. 1992 Longitudinal shear-induced diffusion of spheres in a dilute suspension. J. Fluid Mech. 240, 651657.

Arp, P. A. & Mason, S. G.1977The kinetics of flowing dispersions. IX. Doublets of rigid spheres. J. Colloidal Interface Sci.61, 4461.

Batchelor, G. K. & Green, J. T. 1972a The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375400.

Batchelor, G. K. & Green, J. T. 1972b The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401127.

Bossis, G. & Brady, J. F.1987Self-diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys.87, 54375448.

Davis, R. H.1992Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres. Phys. Fluids A 4, 26072619.

Leighton, D. T. & Acrivos, A. 1987a The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415439.

Leighton, D. T. & Acrivos, A. 1987b Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109131.

Lin, C. J., Lee, K. J. & Sather, N. F. 1970 Slow motion of two spheres in a shear flow. J. Fluid Mech. 43, 3547.

Nir, A. & Acrtvos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209223.

Smart, J. R., Beimfohr, S. & Leighton, D. T.1993Measurement of translational and rotational velocities of a non-colloidal sphere rolling down a smooth inclined plane at low Reynolds number. Phys. Fluids A 5, 1324.

Smart, J. R. & Leighton, D. T.1989The measurement of the hydrodynamics surface roughness of non-colloidal spheres. Phys. Fluids A 1, 5260.

Wakiya, S.1971Slow motion in shear flow of a doublet of two spheres in contact. J. Phys. Soc. Japan31, 15811587.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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