表面调制和搅拌下的化学反应
Chemical reactions in the presence of surface modulation and stirring
摘要：
我们研究简单反应的动力学，其中的化学物种被限制在一个一般的，时间调制的表面，并受到外部施加的搅拌。这些非均匀效应的研究需要一个模型的基础上的反应-对流-扩散方程，我们得出。我们使用均匀化方法表明，在一个小的尺度参数的第二阶，调制效应的浓度场是渐近等效的系统有或没有搅拌。这证明了我们对更简单的反应扩散模型的考虑，在该模型中，我们发现通过调节底物，我们可以修改反应速率、反应的总产率和前沿传播的速度。这些观察结果证实了在三个数值案例研究涉及的自催化和反应的环面和正弦调制基板
英文摘要：
We study the dynamics of simple reactions where the chemical species are confined on a general, time-modulated surface, and subjected to externally-imposed stirring. The study of these inhomogeneous effects requires a model based on a reaction-advection-diffusion equation, which we derive. We use homogenization methods to show that up to second order in a small scaling parameter, the modulation effects on the concentration field are asymptotically equivalent for systems with or without stirring. This justifies our consideration of the simpler reaction-diffusion model, where we find that by modulating the substrate, we can modify the reaction rate, the total yield from the reaction, and the speed of front propagation. These observations are confirmed in three numerical case studies involving the autocatalytic and bistable reactions on the torus and a sinusoidally-modulated substrate
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