Theoretical calculation of solute effective diffusion coefficient in hierarchical porous material

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 hierarchical 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.