Buoyancy and electrically driven convection models in thin-layer electrodeposition

Guillermo Marshall, Pablo Mocskos, Harry L. Swinney, and John M. Huth
Phys. Rev. E 59, 2157 – Published 1 February 1999
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Abstract

Recent work demonstrates the inevitable role of convection during the growth of patterns in thin-layer electrochemical deposition. Convection is driven mainly by Coulombic forces due to local charges and by buoyant forces due to concentration gradients that lead to density gradients. Here we study by theoretical and numerical modeling the limiting regimes under which electroconvection or gravitoconvection prevail. The model describes the diffusive, migratory, and convective motion of ions in a fluid subject to an electric field. The equations are written in terms of dimensionless quantities, in particular, the gravity Grashof and the electrical Grashof numbers. The simulations reveal that gravitoconvection becomes increasingly important as the gravity Grashof number increases, while electroconvection becomes increasingly important as the electrical Grashof number increases. For both regimes the model predicts concentration, electric potential, and velocity patterns that are in qualitative agreement with typical electrodeposition experiments. In gravitoconvection, the model predicts the evolution, before collision, of the convection rolls near each electrode growing first as t4/5 and then slowing down to t1/2; the same scaling behavior was observed in experiments. After collision, the cathodic and anodic rolls merge into a single roll. In electroconvection, the model predicts the existence of vortex pairs formed by the electrical force on space charge accumulating near the growing filament tip. Such vortex rolls and pairs have been observed in experiments.

  • Received 15 May 1998

DOI:https://doi.org/10.1103/PhysRevE.59.2157

©1999 American Physical Society

Authors & Affiliations

Guillermo Marshall and Pablo Mocskos

  • Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina

Harry L. Swinney and John M. Huth

  • Center for Nonlinear Dynamics and The Department of Physics, The University of Texas, Austin, Texas 78712

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Vol. 59, Iss. 2 — February 1999

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