* Corresponding author. Chemical Engineering Science 54 (1999) 4285} 4291 Concentration dependence of di!usion}adsorption rate in activated carbon German Drazer, Ricardo Chertco!, Luciana Bruno, Marta Rosen* Grupo de Medios Porosos, Facultad de Ingenieria, Universidad de Buenos Aires, Paseo Colon 850, CP 1063 Buenos Aires, Argentina Received 18 March 1998; received in revised form 6 January 1999; accepted 25 January 1999 Abstract A new method based on transfer rate measurements of a radioactive solute inside activated carbon grains is presented which allows to isolate the relative contributions of the chemical (reversible adsorption) and geometrical (tortuous di!usion paths) e!ects on the overall e!ective di!usion coe$cient. Transfer rate measurements were performed with two di!erent initial conditions: carbon grains either initially saturated with a solution of the same concentration as the bath (self-di+usion) or free of solute. In the self-di!usion case the adsorption equilibrium for the solute is undisturbed during the process and the adsorption dynamics for tracer particles becomes linear. These processes can be analyzed in terms of an e!ective self-di!usion coe$cient (D  ). The concentration dependence of the transfer rate is shown to be controlled by nonlinearities of the adsorption isotherm. We also show that the self-di!usion coe$cient (D  ) is one order of magnitude lower than in free bulk di!usion. Finally, in the second case (grains initially free of solute) we predict satisfactorily sorption rate curves, as well as the dependence of the transfer rate on the initial concentration, using results obtained in the self-di!usion case.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Nonlinear adsorption; Di!usion; Activated carbon; Fractal structure; Radioactive tracer; Transfer rate 1. Introduction Activated carbon (an amorphous and porous form of carbon, which is specially treated to produce a very large surface area) is generally used as an adsorbent, catalyst and catalyst support (Knaebel, 1995). Transport proper- ties of molecules in solution in these porous media are of great technological relevance. The purpose of the present work is to study the rate of mass transfer inside porous activated carbon grains, and its concentration depend- ence. Di!usive mass transfer processes such as between the interior of the grains and the surrounding #uid are of particular importance in many porous samples with a bi- disperse pore size distribution, like "nely divided powder or catalysts or adsorbents made by pelletizing an active powder. In particular, in "xed-bed systems made by packing activated carbon grains, the intraparticle di!us- ivity is the only exchange mechanism: this is due to the high permeability contrast between the large pores corre- sponding to spaces between the grains (macropores) and small pores (micropores) inside the grains themselves (Cui et al., 1989; Magnico et al., 1993). The particular features of intraparticle di!usivity inside porous carbon grains have a considerable in#uence on macroscopic transport in practical applications (Dawson et al., 1996; Rasmuson and Neretnieks, 1980; Burghardt et al., 1988; Ruckenstein et al., 1971; Neogi and Ruckenstein, 1980). We shall more particularly seek to separate the re- spective in#uence of structural and adsorptive properties on di!usion phenomena. Di!usion measurements in por- ous activated carbon are in#uenced by its geometry (tor- tuosity and number of dead ends in #ow paths inside the pore space) and chemistry (amount of adsorbed di!using particles on surface sites) (Dozier et al., 1986). It is worth mentioning that geometrical e!ects on di!usivity strongly depend on the size of di!using particles when- ever they are not negligible compared to the typical pore sizes. Large particles are then excluded from a fraction of the pore volume. The e!ective tortuosity and number of dead ends seen by such di!using particles is therefore increased in similar ways as in percolation models (Sahimi and Jue, 1989; Sahimi, 1992). 0009-2509/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 0 8 8 - 3