Abstract
A bidisperse model for transient diffusion and adsorption processes in porous materials is presented in this paper. The mathematical model is solved by numerical methods based on finite elements combined with the linear driving force approximation. A criterion based on the model to identify the diffusion controlling mechanism (macropore diffusion, micropore diffusion, or both) is proposed. The effects of different adsorption isotherms (linear, Freundlich, or Langmuir) on the concentration profiles and on curves of fractional uptake versus time are investigated. In addition, the influences of model parameters concerning the pore networks on the fractional uptake are studied as well.
Highlights
Porous materials are widely used in chemical industries, such as in heterogeneous catalytic reactions, adsorption, separation and ion exchange
The porous materials with bidisperse pore structures have attracted the extensive interests of chemical engineers, because in these materials, macropores can be used for intensifying the mass transport and micropores for reaction and adsorption (Bhatia 1997; Lee et al 1991; LeinekugelLe-Cocq et al 2007)
The diffusion path is divided into two parallel paths: (1) molecules diffuse into macropores, and are adsorbed on the macropore walls, diffuse into micropores and are adsorbed on the micropore walls; (2) molecules diffuse through micropores and are adsorbed on the micropore walls
Summary
Porous materials are widely used in chemical industries, such as in heterogeneous catalytic reactions, adsorption, separation and ion exchange. For description of the diffusion processes inside bidisperse pore structures, a bidisperse pore model of random pores was proposed by Wakao and Smith (Wakao and Smith 1962), who considered a parallel diffusion mechanism as shown in Fig. 1a: (1) diffusion through the macropores; (2) diffusion through the micropores; (3) diffusion through the macropores and micropores in series. A model is proposed for transient diffusion and adsorption in porous materials with bidisperse pore structures In this model, the diffusion path is divided into two parallel paths (as shown in Fig. 2c): (1) molecules diffuse into macropores, and are adsorbed on the macropore walls, diffuse into micropores and are adsorbed on the micropore walls (only this path was involved in Ruckenstein and Turner’s models); (2) molecules diffuse through micropores and are adsorbed on the micropore walls. The effects of model parameters on the curves of fractional uptake are studied as well and a criterion to identify the controlling mechanisms which reflect the competing effects of macropore and micropore diffusion is proposed
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