中文摘要：

双级孔材料中扩散与吸附现象广泛存在于化工过程中,准确预测其传递性质对指导过程设计具有重要意义。从最小尺度的孔隙开始采用体积平均方法推导出一个扩散型方程,并且得到该孔隙尺度下有效扩散系数的表达式。然后以此扩散方程为基础逐级扩大孔隙尺度,直至获得最大尺度孔隙中对应的扩散型方程及其对应的有效扩散系数的理论表达式。基于此,推导出一个扩散型方程描述双级孔材料内的组分扩散与吸附过程。孔隙结构、扩散速率、吸附强度的影响由有效扩散系数衡量。将上述理论模型与孔尺度模拟方法结合,对多孔圆柱阵列内的扩散吸附过程进行预测,预测结果与文献报道的直接数值模拟的结果吻合。结果表明：体积平均理论以及推导得到的封闭方程可用于预测双级孔材料内组分的有效扩散系数,为理解孔隙结构对有效扩散系数的影响以及调控相关过程性能提供了新的方法。

英文摘要：

Solute diffusion and adsorption in hierarchical porous materials widely exist in various chemical processes, and accurate prediction of the transfer performance is important. A diffusion equation was first derived from zones with the minimal pores in the hierarchica] porous material by the volume averaging method, and an expression of the effective diffusion coefficient for the corresponding zone was obtained. The derived diffusion equation was used to get another diffusion equation and the related effective diffusion coefficient for zones with larger pores by the volume averaging method. By this way, a diffusion equation which describes the diffusion and adsorption behavior in the hierarchical porous material is obtained. The influences of porous structure, diffusion rate, adsorption amount on the transfer performance are measured by the effective diffusion coefficient. Solute diffusion and adsorption behavior in porous cylinder array was predicted, and the results agree well with the results reported in literature. The results show that the volume averaging theory and the closed equation are used to predict the effective diffusion coefficient in the hierarchical porous material, a new way is provided to understand the effect of effective diffusion coefficient on porous structure and adjust related process performances.