作　　者： ; ;

机构地区： 华南理工大学化学与化工学院

出　　处： 《离子交换与吸附》 2000年第4期289-295,共7页

摘　　要： 吸附质在球形颗粒的内扩散可用固相内扩散偏微分方程描述，当使用吸附剂球心的浓度为零时，可得到解析解模型；当使用在球心的浓度梯度为零时，只能得到数值解。本文分析了在这两种不同的边界条件下导出的分析解和数值解模型之间的差别，当分别用两种模型计算颗粒内瞬时溶质浓度分布和吸附剂颗粒体积平均吸附量的结果表明：在吸附发生的初期(如τ= 0.0001)，二者的相对误差为24%，当吸附持续较长时间时，二者的数值基本相同。若以固相内扩散方程的数值解为基准，在吸附发生初期，二次方推动吸附速率近似模型的误差为29%，LDF模型的相对误差高达95%。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。作为吸附速率的近似模型，前者比后者有更高的精度。 The diffusion behavior of adsorbate in spherical particles can be described by diffusion equation a partial differential equation. The analysis solution of the equation can be obtained at the boundary condition that the concentration of the adsorbate is equal to zero at the center of a spherical particle. The numerical solution of the equation can be only gotten at the boundary condition that the concentration gradient of the adsorbate is equal to zero at the center of the spherical particle. The concentration profiles of the adsorbate within the particle and the average-volume amounts adsorbed were calculated separately from these analytical solution and the numerical. It was demonstrated that the relative error of the volume-average amounts adsorbed calculated respectively from these two solutions was about 24% in the initial period of the adsorption, and however, the amounts adsorbed would be nearly identical with adsorption time lasting. On the base of the numerical solution, during the initial period of the adsorption the relative errors of LDF model was up to 95%, and the relative error of quadratic driving force approximation was about 29%. If ones take ±10% error as the limit for the validity of the approximations, the quadratic driving force approximation is valid at non-dimensional time τ>0.0007 and the LDF approximation is valid atτ>0.05. The former is more accurate than the later.

关 键 词： 边界条件 分析解 数值解 球形颗粒吸附剂 内扩散

领　　域： [理学] [理学]