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