【摘要】 讨论了两类不同的边界条件, 并比较了由这些边界条件导出的球形颗粒固相扩散方程的分析解和数值解， 还评估其他吸附速率的近似模型. 本文指出了前人导出的并广泛应用的分析解其边值条件在物理意义上的不合理性， 使用在颗粒球心处的浓度梯度为零作为有实际物理意义的边界条件， 推出固相内扩散方程的数值解， 并分别比较用两种模型计算颗粒内溶质浓度分布以及吸附剂颗粒体积平均吸附量的差别. 结果表明： 在吸附发生的初期， 二者计算的吸附量有较小的误差， 以固相内扩散方程的数值解为基准， 在吸附发生初期， 二次方推动力吸附速率近似模型的相对误差为29％， LDF模型的相对误差高达95％. 若以不超过±10％误差为基准作为判断一个近似模型是否有效， 当τ＞0.0007时， 二次推动力吸附速率模型是有效的， 而只有当τ＞0.05时， LDF模型才是有效的.更多还原

【Abstract】 This paper discusses different boundary conditions(B.C.) in which the different solutions of solid diffusion equation are deduced, makes the comparison between the analytical solution and the numerical solution deduced respectively under these B.C., and then evaluates some other approximations for adsorption rate. Result shows that the some B.C. used previously to deduce the analytical solution is unreasonable or physically ambiguous. The reasonable boundary condition(B.C.) for the diffusion in the spherical particle should be that the concentration gradient at the particle central is equal to zero. The numerical method of the solid diffusion equation corresponding to this B.C. is suggested. The concentration profiles and the volume_average adsorbed amounts q-(t) are calculated respectively by using the numerical and analytical solutions, and then LDF model and a quadratic driving force model are evaluated on the basis of the q-(t) calculated by the numerical solution. The results indicate that there exits slight difference between the q-(t) calculated separately from the numerical and analytical solutions in the initial period of the adsorption, and that, in the initial period of the adsorption, the relative error of the LDF model is up to 95%, and that of the quadratic driving force model is about 29%. By taking ±10% error as the limit of the validity of the approximations, the LDF model is valid at τ＞0 05, and the quadratic driving force model is valid at τ＞0.0007.更多还原