微观混合与快速反应过程的模型及模拟──（Ⅰ）片状结构模型及其简化

THE MODEL AND SIMULATION FOR MICROMIXING AND FAST CHEMICAL REACTION──(Ⅰ) The Slice Structure Model and Simplification

液相快速反应往往难于排除小尺度混合过程的影响。本文根据作者提出的片状结构模型，将微观混合与快速复杂反应用一组无限区域上的非线性对流扩散方程描述。在主反应为瞬时反应的情况下，引入适当的变换，结合有关的解析解，将这一数学问题简化为有限区间上一个弱非线性方程的初边值问题，为进一步的数值模拟提供了方便。

Fast chemical reaction is usually disguised by micromixing, or mixing on the molecular scale. According to the slice-structure model, which was proposed by the auther in 1990, micromixing and fast chemical reactions are described by a set of nonlinear convective-diffusive equations on a infinite domain. When the main reaction can be regarded as instantaneous, the number of equations can be reduced to one by use of proper transformations. Furthermore, the equation can be simplified to a weak-nonlinear one on a finite domain by combination with certain analytical solutions.