扩散方程的稳态近似分析:Ⅰ.稳态近似法处理过程

Analysis of diffusion equation based on steady state assumption:Ⅰ.the process of steady state approximation

反应器内层状渣(锍)、金液界面两侧内扩散、团块、气泡、粉粒或液滴内的扩散,都是有限长度区间上传质问题;获得有限长度区间上扩散方程的近似分析解,可兼有学术和应用价值。以质量守衡原理、菲克扩散定律为物理基础,以对方程的离散化处理为手段,以基于浓度变化率随时间不变的假设获得扩散速率近似式为必要步骤,给出了对有限长度区间内扩散方程进行稳态近似法处理的过程;同时获得了二、三类边界条件下扩散方程的一个稳态近似解。对近似解和精确解偏差进行了分析。笔者对扩散方程的稳态近似法处理过程可以应用于工程上。

The Fick diffusion equation is widely used to describe mass transfer in a particle ,a droplet or a liquid layer in a chemical reactor ,w here the definition domain of the diffusive equation is limited ,because it is decided by the scale of those particles or droplets .The diffusive equation with a definition domain of certain length has no analytic solutions unless the series solution .So ,to obtain approximate solutions of a diffusive equation is of theoretical and practical significance .After an assumption of constant concentration variance ratio is made and substituted for the presumption of constant concentration frequently used in kinetics of multi-phase reaction ,a detail process to deal with diffusion equation based on steady state approximation is given ,and the approximate solutions of the diffusive equation with the second boundary condition and the third boundary condition are obtained in the meantime .The method to deal with diffusion equation by steady state approximation may be applied to many fields in engineering .