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Directional locking and deterministic separation in periodic arrays

Published online by Cambridge University Press:  25 May 2009

JOELLE FRECHETTE  and
GERMAN DRAZER
JOELLE FRECHETTE
Affiliation:
Chemical & Biomolecular Engineering Department, Johns Hopkins University, Baltimore, MD 21218, USA
GERMAN DRAZER*
Affiliation:
Chemical & Biomolecular Engineering Department, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the dynamics of a non-Brownian sphere suspended in a quiescent fluid and moving through a periodic array of solid obstacles under the action of a constant external force by means of Stokesian dynamics simulations. We show that in the presence of non-hydrodynamic, short-range interactions between the solid obstacles and the suspended sphere, the moving particle becomes locked into periodic trajectories with an average orientation that coincides with one of the lattice directions and is, in general, different from the direction of the driving force. The locking angle depends on the details of the non-hydrodynamic interactions and could lead to vector separation of different species for certain orientations of the external force. We explicitly show the presence of separation for a mixture of suspended particles with different roughness, moving through a square lattice of spherical obstacles. We also present a dilute model based on the two-particle mobility and resistance functions for the collision between spheres of different sizes. This simple model predicts the separation of particles of different size and also suggests that microdevices that maximize the differences in interaction area between the different particles and the solid obstacles would be more sensitive for size separation based on non-hydrodynamic interactions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 379 - 401
Copyright
Copyright © Cambridge University Press 2009

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