Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-30T17:57:16.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Shear-induced dispersion in a dilute suspension of rough spheres

Published online by Cambridge University Press:  26 April 2006

F. R. Da Cunha  and
E. J. Hinch
F. R. Da Cunha
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Current address: University of Brazilia, Department of Mechanical Engineering, Campus Universitario-Asa Norte, Brasilia-DF, Brazil 70910-900.
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
Get access Rights & Permissions [Opens in a new window]

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.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 309 , 25 February 1996 , pp. 211 - 223
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

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, 651–657.Google Scholar
Arp, P. A. & Mason, S. G. 1977 The kinetics of flowing dispersions. IX. Doublets of rigid spheres. J. Colloidal Interface Sci. 61, 44–61.Google Scholar
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, 375–400.Google Scholar
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, 401–127.
Biemfohr, S., Looby, T, Biemfohr, S. & Leighton, D. T. 1993 Measurement of shear-induced coefficient of self-diffusion in dilute suspensions. In the Proc. DOE/NSF Workshop on Flow of Particles and Fluids, Ithaca, NY.
Bossis, G. & Brady, J. F. 1987 Self-diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys. 87, 5437–5448.Google Scholar
Davis, R. H. 1992 Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres. Phys. Fluids A 4, 2607–2619.Google Scholar
Eckstein, E. C, Bailey, D. G. & Shapiro, A. H. 1977 Self-diffusion of particles in shear flow of a suspension. J. Fluid Mech. 79, 191–208.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Leighton, D. T. & Acrivos, A. 1987a The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Leighton, D. T. & Acrivos, A. 1987b Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109–131.Google Scholar
Lin, C. J., Lee, K. J. & Sather, N. F. 1970 Slow motion of two spheres in a shear flow. J. Fluid Mech. 43, 35–47.Google Scholar
Nir, A. & Acrtvos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209–223.Google Scholar
Smart, J. R., Beimfohr, S. & Leighton, D. T. 1993 Measurement of translational and rotational velocities of a non-colloidal sphere rolling down a smooth inclined plane at low Reynolds number. Phys. Fluids A 5, 13–24.Google Scholar
Smart, J. R. & Leighton, D. T. 1989 The measurement of the hydrodynamics surface roughness of non-colloidal spheres. Phys. Fluids A 1, 52–60.Google Scholar
Wakiya, S. 1971 Slow motion in shear flow of a doublet of two spheres in contact. J. Phys. Soc. Japan 31, 1581–1587.Google Scholar
Wang, Y., Mauri, R. & Acrivos, A. 1995 Transverse shear-induced diffusion of spheres in a dilute suspension. J. Fluid Mech. (submitted)Google Scholar