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  • Journal of Fluid Mechanics, Volume 592
  • December 2007, pp. 447-469

Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres

  • DOI:
  • Published online: 10 December 2007

Binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of the particles. The spheres on these new trajectories do not pass each other (as they would in free space) but instead they swap their cross-streamline positions. To determine the significance of the wall-induced particle migration, we have evaluated the hydrodynamic self-diffusion coefficient associated with a sequence of uncorrelated particle displacements due to binary particle encounters. The results of our calculations quantitatively agree with the experimental value obtained by Zarraga & Leighton (Phys. Fluids, vol. 14, 2002, p. 2194) for the self-diffusivity in a dilute suspension of spheres undergoing shear flow in a Couette device. We thus show that the wall-induced cross-streamline particle migration is the source of the anomalously large self-diffusivity revealed by their experiments.

Corresponding author
Present address: Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Camino de los descubrimientos s/n, Sevilla 41092, Spain.
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P. A. Arp & S. G. Mason 1977 Kinetics of flowing dispersions. VIII. Doublets of rigid spheres (theoretical). J. Colloid Interface Sci. 61, 2143.

S. Bhattacharya & J. Blawzdziewicz 2002 Image system for Stokes-flow singularity between two parallel planar walls. J. Math. Phys. 43, 5720–31.

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S. Bhattacharya , J. Blawzdziewicz & E. Wajnryb 2006 aFar-field approximation for hydrodynamic interactions in parallel-wall geometry. J. Comput. Phys. 212, 718738.

S. Bhattacharya , J. Blawzdziewicz & E. Wajnryb 2006 bHydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls. Phys. Fluids 18, 053301.

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I. E. Zarraga & D. T. Leighton 2001 Shear-induced diffusivity in a dilute bidisperse suspension of hard spheres. J. Colloid Interface Sci. 243, 13.

I. E. Zarraga & D. T. Leighton 2002 Measurement of an unexpectedly large shear-induced self-diffusivity in a dilute suspension of spheres. Phys. Fluids 14, 21942201.

M. Zurita-Gotor , J. Blawzdziewicz & E. WAjnryb 2007 Motion of a rod-like particle between parallel walls with application to suspension rheology. J. Rheol. 51, 7197.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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