任意Damköhler数下剪切流混合锋中增强的反应动力学和反应混合尺度动力学
Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damköhler numbers
摘要：
不同化学成分的流体相互混合的混合前沿通常受到速度梯度的影响，由于渗透率变化和流线几何形状，速度梯度的范围从孔隙尺度到集水尺度。这些过程的一个共同特征是混合界面因剪切而产生应变。根据代表特征扩散时间与特征平流时间之比的Péclet数$Pe$和代表特征扩散时间与特征反应时间之比的Damköhler数$Da$，局部反应速率可受到混合界面动力学的强烈影响。这种影响主要在动力学限制或混合限制条件下表征，即对于非常低或非常高的$Da$。在这里的耦合的剪切流和化学反应性的任意Damköhler数，为双分子反应和初始界面与分离的反应物进行了研究。近似的分析表达式的全球生产率和反应混合规模的基础上得到的反应层的方法，允许拉伸增强混合和化学反应之间的一般耦合。而对于$Pe<Da$，反应动力学和拉伸效应是解耦的，我们称之为“弱拉伸”的情况下，对于$Pe>Da$，我们发现了一个“强拉伸”的情况下，新的标度律出现从反应动力学，扩散和拉伸之间的相互作用。分析结果与数值模拟进行了验证。这些研究结果揭示了流动的非均匀性对增强化学反应的影响，以及从动力学限制到混合限制情况的广泛系统的反应性的空间局部热点的创建。
英文摘要：
Mixing fronts, where fluids of different chemical compositions mix with each other, are typically subjected to velocity gradients, ranging from the pore scale to the catchment scale due to permeability variations and flow line geometries. A common trait of these processes is that the mixing interface is strained by shear. Depending on the Péclet number $Pe$, which represents the ratio of the characteristic diffusion time to the characteristic advection time, and the Damköhler number $Da$, which represents the ratio of the characteristic diffusion time to the characteristic reaction time, the local reaction rates can be strongly impacted by the dynamics of the mixing interface. This impact has been characterized mostly either in kinetics-limited or in mixing-limited conditions, that is, for either very low or very high $Da$. Here the coupling of shear flow and chemical reactivity is investigated for arbitrary Damköhler numbers, for a bimolecular reaction and an initial interface with separated reactants. Approximate analytical expressions for the global production rate and reactive mixing scale are derived based on a reactive lamella approach that allows for a general coupling between stretching enhanced mixing and chemical reactions. While for $Pe<Da$, reaction kinetics and stretching effects are decoupled, a scenario which we name "weak stretching", for $Pe>Da$, we uncover a "strong stretching" scenario where new scaling laws emerge from the interplay between reaction kinetics, diffusion, and stretching. The analytical results are validated against numerical simulations. These findings shed light on the effect of flow heterogeneity on the enhancement of chemical reaction and the creation of spatially localized hotspots of reactivity for a broad range of systems ranging from kinetic limited to mixing limited situations.
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