A discrete model for pattern formation in volatile thin films

M. Malik-Garbi, O. Agam

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)39-52
Number of pages14
JournalMathematical Modelling of Natural Phenomena
Volume7
Issue number4
DOIs
StatePublished - 2012

Keywords

  • Diffusion limited aggregation
  • Reaction-diffusion
  • Viscous fingering

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation

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