American Institute of Mathematical Sciences

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2010, 7(2): 237-258. doi: 10.3934/mbe.2010.7.237

Morphological spatial patterns in a reaction diffusion model for metal growth

Benedetto Bozzini 1, , Deborah Lacitignola 2, and  Ivonne Sgura 3,

1. 

Dipartimento di Ingegneria dell’Innovazione, Università del Salento - Lecce, via per Monteroni, I-73100 Lecce, Italy
2. 

Dipartimento di Scienze Motorie e della Salute, Università di Cassino, Campus Folcara, Loc. S.Angelo, I-03043 Cassino, Italy
3. 

Dipartimento di Matematica, Università del Salento - Lecce, via per Arnesano, I-73100 Lecce, Italy

Received  May 2009 Revised  December 2009 Published  April 2010

In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate - within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space analysis is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability and selection of solutions are also provided. By the numerical approximation of the equations, simulations are presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd alloys.
Keywords: Turing instability, pattern formation, electrodeposition, numerical simulations..
Mathematics Subject Classification: 35K57, 62P30, 65.
Citation: Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. Morphological spatial patterns in a reaction diffusion model for metal growth. Mathematical Biosciences & Engineering, 2010, 7 (2) : 237-258. doi: 10.3934/mbe.2010.7.237
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