Dynamic Self-Assembly of Spinning Particles

[+] Author and Article Information
Eric Climent

Laboratoire de Génie Chimique, UMR 5503,  CNRS∕INPT∕UPS, 5 Rue Paulin Talabot, 31106 Toulouse, Franceeric.climent@ensiacet.fr

Kyongmin Yeo

Center for Fluid Mechanics, Division of Applied Mathematics,  Brown University, Box F, Providence, RI 02912kyeo@dam.brown.edu

Martin R. Maxey

Center for Fluid Mechanics, Division of Applied Mathematics,  Brown University, Box F, Providence, RI 02912maxey@dam.brown.edu

George E. Karniadakis

Center for Fluid Mechanics, Division of Applied Mathematics,  Brown University, Box F, Providence, RI 02912gk@dam.brown.edu

J. Fluids Eng 129(4), 379-387 (Oct 18, 2006) (9 pages) doi:10.1115/1.2436587 History: Received May 24, 2006; Revised October 18, 2006

This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a plane in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain, and flow-induced interactions. A hydrodynamic repulsion balances the centripetal attraction of the magnetized particles and leads to the formation of an aggregate of several particles that rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The repulsion force between the particles is shown to be the result of the secondary flow generated by each particle at low but nonzero Reynolds number. Comparisons are made with analogous experiments of spinning disks at a liquid–air interface, where it is found that the variation in the characteristic scales of the aggregate with the rotation rate of individual particles are consistent with the numerical results.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Sketch of the experimental configuration (15)

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Figure 2

Profile of the azimuthal velocity uφ in the equatorial plane: Stokes flow (solid line); force coupling method–Stokes flow (open circles); force coupling method −Reω=8(+)

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Figure 3

Nondimensional torque coefficient M against Reynolds number Reω: solid line, Lamb’s theory (Stokes flow); dashed line, correlation from the experiments of Sawatzki (30) and simulations of Dennis (31); filled circles, FCM-T results; open circles, FCM-TS results

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Figure 4

Secondary flow in x, z plane for sphere spinning about the z axis at Reω=2

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Figure 5

Trajectories of two spinning particles without magnetic attraction: closed circular trajectories (Stokes flow); open trajectories (low, but finite Reynolds number)

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Figure 6

Secondary flow for two spheres, spinning about axes parallel to the z axis, at Reω=2

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Figure 9

Comparison of simulation results with experiments for the separation distance of the stable pattern (two particles) at different rotation rates ω: (stars) experiments of Grzybowski (15) (dashed line is only a guide for the eye); (triangles) FCM results with a constant magnetic attraction force; (circles) FCM results with a linear magnetic attraction force

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Figure 10

Definition of length scales for a rotating aggregate

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Figure 11

Fluid velocity vectors for a stable aggregate of rotating spheres, N=7, at Reω=2. The aggregate precesses about the center particle in this common plane.

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Figure 12

Stable aggregation patterns for N=10 at Reω=2

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Figure 13

Stable aggregation patterns for N=12 at Reω=2

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Figure 7

Repulsion force F between two corotating particles against distance R, where 2R is the distance between particles. Results at Reω=0.25 (open circles), 2 (triangles), and 8 (cross)

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Figure 8

Precession angular velocity Ω for a pair of corotating spheres against R: (a) comparison of results at Reω=0.25 with estimate from Stokes flow; and (b) comparison of results at Reω=0.25, 2, and 8




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