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Nonlinear dynamics of spherical particles in Poiseuille flow under creeping-flow condition

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10.1063/1.4809989

### Abstract

We study the nonlinear dynamics of spherical colloids under the influence of a pressure driven flow at vanishing Reynolds number. The colloids are confined between two parallel planar walls with a distance comparable to the particle diameter and they interact hydrodynamically via the solvent. We show that the bounded Poiseuille flow gives rise to new classes of trajectories resulting in cross-streamline migration. Two particles moving on these new trajectories exhibit either bound or unbound states. In the first case they oscillate on closed trajectories in the center-of-mass frame. In the second case, they exhibit cross-swapping trajectories in addition to swapping trajectories which were already observed in unbounded or bounded linear shear flow. The different classes of trajectories occur depending on the initial positions of the two particles and their size. We present state diagrams in the lateral positions, where we categorize the trajectories and color code the oscillation frequencies of the bound states. Finally we discuss how the results on the two-particle system help to understand the stability of particle trains composed of several particles.

© 2013 AIP Publishing LLC

Received 08 April 2013
Accepted 24 May 2013
Published online 17 June 2013

Acknowledgments: We thank A. Mikhailov for helpful discussions. This work was supported by the Deutsche Forschungsgemeinschaft through the research training group GRK 1558.

Article outline:

I. INTRODUCTION

II. MODELING

A. System geometry

B. Stokes equations

C. The grand mobility matrix

D. *L*-multipole approximation and lubrication correction

E. Numerical implementation and parameters

III. RESULTS

A. Two-particle system

1. Unbound and oscillatory bound states

2. Dependence on particle size

B. Linear array of particles

IV. SUMMARY AND CONCLUSION

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/content/aip/journal/jcp/138/23/10.1063/1.4809989

2013-06-17

2014-04-18

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