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Induced Self-Aggregation of Metallic Spheres in Highly Viscous Medium

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Peter Fleck and Alfred Hubler, Center for Complex Systems Research, Department of Physics, University of Illinois at Urbana-Champaign
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We study the classical dynamics of metallic spheres confined to a plane and immersed in highly viscous, but weakly conducting medium
while exposed to the electro-static field of external line electrodes [1].
We represent the system's charge dynamics by the spheres' multipole moments as induced by the electrodes.
We theoretically derive and reformulate dimensionlessly the equations of motion of and force contributions on an individual sphere.
We find the system's dynamics to depend on the dimensionless effective viscosity and its geometry alone.
We discuss the system's parameter ranges necessary for line arrangements of multiple spheres to emerge.
[1] J. Jun, A. Hübler, "Formation and structure of ramified charge transportation networks in an electromechanical system", PNAS 102, 536–540 (2005)