二、三类边界条件下扩散方程的稳态近似分析  

Analysis of diffusion equation with the second and third boundary conditions based on steady state approximation

作　　者：王成善[1,2] 黄太镭[1] 穆小静[3] 

机构地区：[1]重庆大学材料科学与工程学院,重庆400044 [2]重庆大学重庆市冶金工程重点实验室,重庆400044 [3]重庆大学化学化工学院,重庆400044

出　　处：《重庆大学学报（自然科学版）》2013年第9期118-126,158,共10页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(50704040);重庆市自然科学基金资助项目(CSTC 2009BB4197)

摘　　要：描述反应器内团块、粉粒或液滴内的传质都离不开扩散方程。获得工程上可利用的扩散方程的近似解,既是实践需要,也是理论发展方向之一。在给出对有限长度区间内扩散方程进行稳态近似法处理过程的同时,将动力学中常用的浓度随时间不变的稳态假设发展为浓度变化率随时间不变的稳态假设,继而获得了一具体扩散问题的近似分析解。稳态近似法获得的结果和精确解随时间变化是同步的;近似解与接近最终稳态的情形吻合程度好,与远离最终稳态的情形吻合程度稍差些;稳态近似法获得的结果基本上满足总体质量守恒。One dimensional diffusion equation is widely used to describe mass transfer in particles or droplets in a reactor. The length of the definition domain of the one-dimension Fick equation is limited, because it is determined by the scale of the particles or the droplets. The diffusion equation with a certain length of definition domain has no analytic solution unless series solution. So, to obtain approximate solutions of diffusion equation is of theoretical significance and practical significance. Firstly, assumption of constant concentration variance ratio is used instead of assumption of constant concentration frequently used in kinetics of process metallurgy. Secondly, a detail process to deal with diffusion equation based on steady state approximation is given, and the approximate solutions of the diffusion equation at certain conditions are obtained at the same time. By comparing the approximate solutions with the numerical solutions, it is concluded that the diffusive process of non-steady state is considerably well predicted by the approximate solutions, and approximate solutions accord with the situations being close to the final steady state a little better than accord with the situations being close to the begin of the diffusion, and it fairly satisfies the total mass balance.

关 键 词：提取冶金 动力学 扩散方程 非稳态 稳态近似法 分析解 

分 类 号：T[一般工业技术]