Concentration Profile for Linear Driving Force Model for Diffusion in a Particle

Diffusional resistance in the porous particle is important in adsorption and reaction engineering. For a porous adsorbent particle subjected to an arbitrary change in the surrounding Ž . fluid-phase concentration, Glueckauf 1955 derived the linŽ . ear driving force LDF approximation that relates the average adsorbate concentration inside the particle directly with the concentration in the fluid phase. By using the LDF approximation, the mass balance equation is eliminated from the model, leaving only the mass balance equation in the fluid Ž . phase to be dealt with Yang, 1987 . This results in a tremendous simplification of the model that is to be solved either analytically or numerically. Since Glueckauf’s work, the LDF approximation has played an important role in studies of fixed bed adsorber dynamics and various adsorption processes, such Ž as breakthrough behavior Miura et al., 1979; Haas et al., . 1988; Farooq and Ruthven, 1991 , simulated moving bed sysŽ tems Ma and Wang, 1997; Pais et al., 1997; Zhong and . Guiochon, 1997; Ching and Lu, 1998 , and pressure swing Ž adsorption Doong and Yang, 1986; Serbezov and Sotirchos, . 1997; Sundaram and Yang, 1998 . The LDF approximation is Ž also useful in studying reaction in a catalyst particle Kim, . 1989; Goto et al., 1990; Goto and Hirose, 1991 . An equivalent approach to the use of the LDF approximation is to have a concentration profile within the particle. Knowing the concentration profile, the mass balance equation for the particle is also eliminated from the governing equations. Since the LDF works well, it provides a clue for deriving a concentration profile within the particle. This was Ž . indeed done by Liaw et al. 1979 . In their work, they assumed a parabolic concentration profile, and showed that the parabolic profile led directly to Glueckauf’s LDF approximation. Since the work of Liaw et al., the parabolic concentration profile has been widely accepted and has been applied Ž to adsorption processes Bhaskar and Do, 1989; Yao and . Tien, 1993; Zhang and Ritter, 1997; Ching and Lu, 1998 and Ž used as a basis for other approximations Goto and Hirose, 1991; Do and Rice, 1995; Xiu, 1996; Zhang and Ritter, 1997; . Xiu et al., 1997; Yao and Tien, 1998 .