Physikalisch-Technische Bundesanstalt, 10587 Berlin, Germany.
J Chem Phys. 2011 Mar 7;134(9):094117. doi: 10.1063/1.3559154.
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.
采用有效介质理论推导出微乳液中形成图案的化学动力学反应的简单定性模型。这个具有空间异质性的体系由随机分布在油中的水纳米液滴组成。虽然反应的某些步骤仅在液滴内部进行，但通过中间化学反应物的扩散以及液滴的碰撞来实现通过扩展介质的传输。我们从异质反应扩散方程开始建模，然后通过使用关于非均匀反应扩散系统中的均匀化的早期结果，推导出等效的有效均匀空间反应扩散模型[SAlonso，MBär和RKapral，J.Chem.Phys.134,214102（2009）]。我们研究了有效模型中空间均匀状态的线性稳定性，并获得了图案形成的相图，该相图与在气溶胶 OT（AOT）-水-油微乳液中进行的Belousov-Zhabotinsky反应的早期实验结果定性相似[VKVanag和IREpstein，Phys.Rev.Lett.87,228301（2001）]。此外，我们通过直接数值模拟再现了在 AOT 水包油微乳液中进行的Belousov-Zhabotinsky 反应的实验中观察到的许多图案。
