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A Discrete Model For Pattern Formation In Volatile Thin Films

Published online by Cambridge University Press:  09 July 2012

M. Malik-Garbi  and
O. Agam
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Abstract

We introduce a model, similar to diffusion limited aggregation (DLA), which serves as a discrete analog of the continuous dynamics of evaporation of thin liquid films. Within mean field approximation the dynamics of this model, averaged over many realizations of the growing cluster, reduces to that of the idealized evaporation model in which surface tension is neglected. However fluctuations beyond the mean field level play an important role, and we study their effect on the conserved quantities of the idealized evaporation model. Assuming the cluster to be a fractal, a heuristic approach is developed in order to explain the distinctive increase of the fractal dimension with the cluster size.

Keywords

viscous fingeringdiffusion limited aggregationreaction-diffusion
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 39 - 52
Copyright
© EDP Sciences, 2012

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Here the Hamiltonian which defines the evolution does not account for the constraint that A particle cannot be born on a site ocuupied by B particle. This constraint can be taken into account by replcing the term with , where Θ(x) is the haviside function and ϵ is a positive infintesimal number.