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Growth model for ramified electrochemical deposition in the presenceof diffusion, migration, and electroconvection
Phys. Rev. E 55, 549 – Published 1 January, 1997
DOI: https://doi.org/10.1103/PhysRevE.55.549
Abstract
A growth pattern formation model for the macroscopic description of ramified electrochemical deposition is presented. The model describes the diffusive, migration and electroconvective motion of ions and its deposition in thin cells through the evolutionary two-dimensional Nernst-Planck equations for cation and anion concentration, the Poisson equation for the electric field, the Navier-Stokes equations for the laminar fluid flow and a dielectric breakdown model scheme for the random deposition of ions. A new set of dimensionless numbers governing the model regimes is introduced. We present numerical results showing that, for a given set of dimensionless numbers, the electroconvective forces produce vortex-tip interaction yielding a basic growth pattern formation mechanism, i.e., tip splitting and fanning. This mechanism gives a reasonable picture of reality.
References (35)
- B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
- T. Vicsek, Fractal Growth Phenomena 2nd ed. (World Scientific, Singapore, 1992).
- On Growth and Form, Vol. 100 of NATO Advanced Study Institute, Ser. B: Physics, edited by G. Stanley and N. Ostrowsky (Kluwer, Boston, 1986).
- L. Kadanoff, J. Stat. Phys. 39, 267 (1985).
- F. Argoul, J. Huth, P. Merzeau, A. Arneodo and H. L. Swinney, Physica D 62, 170 (1993).
- J. S. Newman, Electrochemical Systems (Prentice Hall, New Jersey, 1973).
- T. A. Witten and L. M. Sander, Phys. Rev. B 27, 5686 (1983).
- L. Pietronero and H. J. Weismann, J. Stat. Phys. 36, 909 (1984).
- P. Meakin, Phys. Rev. B. 28, 5221 (1983).
- G. Marshall, Comput. Phys. Commun. 56, 51 (1989).
- G. Marshall (unpublished).
- L. Lam, R. D. Pochy, and V. M. Castillo, in Nonlinear Structures in Physical Systems, edited by L. Lam and H. C. Morris (Springer, New York, 1990).
- G. Marshall and E. Arguijo, Chaos, Solitons Fractals 5, 531 (1992).
- G. Marshall, S. Tagtachian and L. Lam, Chaos, Solitons Fractals 6, 325 (1995).
- J. N. Chazalviel, Phys. Rev. E 42, 7355 (1990).
- J. R. Melrose, D. B. Hibbert and R. C. Ball, Phys. Rev. Lett. 65, 3009 (1990).
- V. Fleury, J. N. Chazalviel, M. Rosso and B. Sapoval, Phys. Rev. A 44, 6693 (1991).
- V. Fleury, M. Rosso and J. N. Chazalviel, Phys. Rev. A 43, 6908 (1991).
- V. Fleury, J. N. Chazalviel and M. Rosso, Phys. Rev. Lett. 68, 2492 (1992).
- V. Fleury, J. N. Chazalviel and M. Rosso, Phys. Rev. E 48, 1279 (1993).
- P. P. Trigueros, F. Mas, J. Claret and F. Sagues, J. Electro- anal. 348, 221 (1993).
- V. Fleury, J. Kaufman and B. Hibbert, Nature 367, 435 (1994).
- D. Barkey, J. Electrochem. Soc. 138, 2912 (1991).
- R. H. Kork, D. C. Pritchard and W. Y. Tam, Phys. Rev. A 44, 6940 (1991).
- M. Wang and N. Ming, Phys. Rev. A 45, 2493 (1992).
- A. Kuhn and F. Argoul, Fractals 3, 451 (1993).
- C. Livermore and Po-zen Wong, Phys. Rev. Lett. 72, 3847 (1994).
- K. A. Linehan and J. R. de Bruyn, Can. J. Phys. 73, 177 (1995).
- D. Otero, G. Marshall and S. Tagtachian, Fractals 4, 7 (1996).
- V. Fleury, J. Kaufman and B. Hibbert, Phys. Rev. E 48, 3831 (1993).
- J. Huth, H. L. Swinney, W. D. McCormick, A. Kuhn and F. Argoul, Phys. Rev. E 51, 3444 (1995).
- G. Marshall, E. Perone, P. Tarela and P. Mocskos, Chaos, Solitons Fractals 6, 315 (1995).
- R. Bruinsma and S. Alexander, J. Chem. Phys. 92, 3075 (1990).
- I. Rubinstein, Electro-Diffusion of Ions (SIAM Studies in Appl. Math., Philadelphia, 1990).
- Suzuki and Sawada, Phys. Rev. A 27, 478 (1983).