DYNAMIC HETEROGENEITY: Bifurcations, Patterns and a New Mechano-Chemical Instability

9803752研究人员模拟并分析了最近在非常薄的晶体上的催化化学反应研究中发现的一种机械力-化学不稳定性：反应速度的时空变化加上热释放导致催化剂表面的空间变化的热膨胀和弯曲。这改变了催化性能，关闭了反应、放热和变形之间的循环；据观察，这会导致持续的机械力-化学振荡。该项目以在机械和化学反应系统中独立研究花纹形成和不稳定性的经验为基础。扩展了梁在约束下的非线性屈曲的理论和计算研究，以考虑梁的静态和动态特性的变化，包括热应变。早期对催化剂表面图案形成的计算机辅助研究被用来通过由此产生的温度场来驱动催化剂的机械变形。最后，通过允许变形改变表面催化性质来闭合环路，从而尝试重现在实验中观察到的振荡。建模、稳定性分析和计算机辅助工作是在与普林斯顿(关于不均匀的光束)和柏林(关于变形催化晶体)的实验小组的持续对话中进行的。多相催化反应构成了与工业和环境相关的化学过程的支柱：例如，项目解决的CO氧化反应发生在每个汽车催化转化器中。对反应条件下原位催化剂上发生的事情进行精细的空间和时间细节分析的技术的发展，正在彻底改变对这些过程进行建模的方式，并使新现象的发现成为可能。这将反过来改善催化过程的设计。具体地说，该项目旨在了解最近才在一氧化碳氧化中观察到的一种现象：与温度和化学浓度有关的催化剂机械变形的振荡。对该过程的计算机辅助分析产生了更好的预测模型，可用于优化该过程的材料特性和操作条件。该项目的资金由MPS的计算数学计划和多学科活动办公室以及ENG的化学反应过程计划提供。

9803752The investigators model and analyze a mechano-chemical instability recently discovered in the study of catalytic chemical reactions on very thin crystals: spatiotemporal variation in the reaction rate coupled with heat release causes spatially varying thermal expansion and buckling of the catalyst surface. This changes the catalytic properties, closing the loop between reaction, heat release and deformation; it has been observed to lead to sustained mechano-chemical oscillations. The project builds on experience in studying pattern formation and instability independently in mechanical and in chemically reacting systems. Theoretical and computational studies of nonlinear buckling of beams under constraints are extended to account for static as well as dynamic variations of the beam properties, including thermally-induced strains. Earlier computer-assisted studies of pattern formation on catalytic surfaces are used to drive, through the temperature fields thereby generated, mechanical deformations of the catalyst. Finally, the loop is closed by allowing the deformation to change the surface catalytic properties, thus attempting to reproduce the oscillations observed in experiments. The modeling, stability analysis and computer-assisted work are performed in constant dialogue with experimental groups in Princeton (on inhomogeneous beams) and in Berlin (on deforming catalytic crystals).Heterogeneous catalytic reactions constitute the backbone of chemical processes of industrial and environmental relevance: the CO oxidation reaction the project addresses occurs, for example, in every automotive catalytic converter. The development of techniques for analyzing in fine spatial and temporal detail what occurs on the catalyst in situ under reaction conditions is revolutionizing the way modeling of these processes is done and enabling the discovery of new phenomena. This will in turn improve the design of catalytic processes. Specifically, this project aims at understanding a phenomenon only recently observed in CO oxidation: oscillations involving mechanical deformations of the catalyst coupled to temperature and chemical concentrations. Computer-aided analyses of the process lead to better, predictive models, which can be exploited in optimizing both the material properties and the operating conditions of the process. Funding for the project is provided by the program of Computational Mathematics and the Office of Multidisciplinary Activities in MPS and by the Chemical Reaction Processes program in ENG.