Trevelyan P M J
Center for Nonlinear Phenomena and Complex Systems, Faculté des Sciences, Université Libre de Bruxelles (ULB), Brussels, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046118. doi: 10.1103/PhysRevE.80.046118. Epub 2009 Oct 22.
The small-time asymptotic properties of the reaction front formed by a reaction A+B-->C coupled to diffusion are considered. Reactants A and B are initially separately dissolved in two identical solvents. The solvents are brought into contact and the reactants meet through diffusion. The small-time asymptotic position of the center of mass of the reaction rate is obtained analytically. When one of the reactants diffuses much faster than the other reactant then the position of the local maximum in the reaction rate travels on a length scale related to the diffusion coefficient of the slowest diffusing reactant while the first moment of the reaction rate and the width of the reaction front are on a length scale related to the diffusion coefficient of the fastest diffusing reactant. If the sum of the initial reactant concentrations is fixed, then the fastest reaction rate is obtained when equal concentrations are used. The first-order solutions are analytically obtained, however, each solution involves an integral which requires numerical evaluation. Various small-time asymptotic analytical reaction front properties are obtained. In particular, one finds that the position of the center of mass of the product concentration distribution is initially located at three quarters of the position of the center of mass of the reaction rate.
考虑由反应A + B→C与扩散耦合形成的反应前沿的小时间渐近性质。反应物A和B最初分别溶解在两种相同的溶剂中。使溶剂接触，反应物通过扩散相遇。通过分析得到反应速率质心的小时间渐近位置。当一种反应物的扩散速度比另一种反应物快得多时，反应速率局部最大值的位置在与扩散最慢的反应物的扩散系数相关的长度尺度上移动，而反应速率的一阶矩和反应前沿的宽度在与扩散最快的反应物的扩散系数相关的长度尺度上。如果初始反应物浓度之和固定，那么使用相等浓度时可获得最快的反应速率。通过分析得到了一阶解，然而，每个解都涉及一个需要数值评估的积分。得到了各种小时间渐近分析反应前沿性质。特别地，人们发现产物浓度分布质心的位置最初位于反应速率质心位置的四分之三处。
