Stabilization of long-wavelength modes on the interface in electrodeposition

Takashi Nagatani
Phys. Rev. A 40, 2154 – Published 1 August 1989

Abstract

A model is proposed for electrochemical deposition that can describe the flat, dense pattern constituting an assembly of needles with a flat envelope. The model is represented by a pair of diffusion equations that govern mass transport in the electrostatic field. A linear-stability theory is applied to investigate whether or not the interface of the aggregate is stable, following Saffman and Taylor [Proc. R. Soc. London, Ser. A 245, 312 (1958)]. It is found that the disturbances with a wavelength longer than a critical wavelength become stable on the interface of the aggregate. When the destabilizing force of the Saffman-Taylor instability becomes smaller than the stabilizing force of the electrostatic field at the long-wavelength modes, then the flat, dense pattern occurs.

  • Received 6 February 1989

DOI:https://doi.org/10.1103/PhysRevA.40.2154

©1989 American Physical Society

Authors & Affiliations

Takashi Nagatani

  • College of Engineering, Shizuoka University, Hamamatsu 432, Japan

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Issue

Vol. 40, Iss. 4 — August 1989

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