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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Complex wave patterns in an effective reaction-diffusion model for chemical reactions in microemulsions
Author(s): S. Alonso, K. John and M. Bär
Journal: J. Chem. Phys.
Year: 2011
Volume: 134
Issue: 9
Pages: 094117
AIP Publishing
DOI: 10.1063/1.3559154
ISSN: 1089-7690
Web URL: http://scitation.aip.org/content/aip/journal/jcp/134/9/10.1063/1.3559154
Keywords: Aerosols,Aerosols: chemistry,Chemical,Diffusion,Emulsions,Emulsions: chemistry,Models,Oils,Oils: chemistry,Water,Water: chemistry
Tags: 8.41, RD
Abstract: An effective medium theory is employed to derive a simple qualitative model of a pattern forming chemical reaction in a microemulsion. This spatially heterogeneous system is composed of water nanodroplets randomly distributed in oil. While some steps of the reaction are performed only inside the droplets, the transport through the extended medium occurs by diffusion of intermediate chemical reactants as well as by collisions of the droplets. We start to model the system with heterogeneous reaction-diffusion equations and then derive an equivalent effective spatially homogeneous reaction-diffusion model by using earlier results on homogenization in heterogeneous reaction-diffusion systems [S.Alonso, M.Bär, and R.Kapral, J. Chem. Phys. 134, 214102 (2009)]. We study the linear stability of the spatially homogeneous state in the resulting effective model and obtain a phase diagram of pattern formation, that is qualitatively similar to earlier experimental results for the Belousov-Zhabotinsky reaction in an aerosol OT (AOT)-water-in-oil microemulsion [V.K.Vanag and I.R.Epstein, Phys. Rev. Lett. 87, 228301 (2001)]. Moreover, we reproduce many patterns that have been observed in experiments with the Belousov-Zhabotinsky reaction in an AOT oil-in-water microemulsion by direct numerical simulations.

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