Tsang Yue-Kin
Scripps Institution of Oceanography, University of California-San Diego, La Jolla, California 92093, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026305. doi: 10.1103/PhysRevE.80.026305. Epub 2009 Aug 18.
We study the fast irreversible bimolecular reaction in a two-dimensional chaotic flow. The reactants are initially segregated and together fill the whole domain. Simulations show that the reactant concentration decays exponentially with rate lambda and then crosses over to the algebraic law of chemical kinetics in the final stage of the reaction. We estimate the crossover time from the reaction rate constant and the flow parameters. The exponential decay phase of the reaction can be described in terms of an equivalent passive scalar problem, allowing us to predict lambda using the theory of passive scalar advection. Depending on the relative length scale between the velocity and the concentration fields, lambda is either related to the distribution of the finite-time Lyapunov exponent of the flow or given in terms of an effective diffusivity which is independent of the small-scale stretching properties of the flow. For the former case, we suggest an optimal choice of flow parameters at which lambda is maximum.
我们研究二维混沌流中的快速不可逆双分子反应。反应物最初是分离的，共同填充整个区域。模拟表明，反应物浓度以速率λ呈指数衰减，然后在反应的最后阶段转变为化学动力学的代数定律。我们根据反应速率常数和流动参数估计交叉时间。反应的指数衰减阶段可以用等效的被动标量问题来描述，这使我们能够利用被动标量平流理论预测λ。根据速度场和浓度场之间的相对长度尺度，λ要么与流的有限时间李雅普诺夫指数的分布有关，要么由与流的小尺度拉伸特性无关的有效扩散率给出。对于前一种情况，我们提出了一个使λ最大的流动参数的最优选择。
