Journal of Fluid Mechanics

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

M. ZURITA-GOTORa1 c1, J. BŁAWZDZIEWICZa1 and E. WAJNRYBa2

a1 Department of Mechanical Engineering, P.O. Box 20-8286, Yale University, New Haven, CT 06520-8286, USA

a2 IPPT, Świetokrzyska 21, Warsaw, Poland

Abstract

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.

(Received October 15 2006)

(Revised August 06 2007)

Correspondence:

c1 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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