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264 4. Adsorption and Ion Exchange

Furthermore, in ion e the fluxes of at least two different ions are coupled with
xchange,
each other and this process cannot be described by the use of a simple dif fusion equation,
xchange. as in the case of adsorption and the exchange of isotopes, i.e. isotopic eThis elec-
tric coupling of the ionic fluxes and the stoichiometric nature of the ion-e xchange process
are the most important features, which distinguish ion exchange from adsorption and iso-
topic exchange (Helf 1962). As a result, the quantitatie treatment of ion e v xchange
ferich,
is much more complicated than adsorption or isotopic e xchange.
It is generally accepted that adsorption and ion exchange can be grouped together as
sorption for a unified treatment in practical applications. Most mathematical theories and
v
v
approaches hae been deeloped originally for adsorption rather than ion e xchange.
However, especially in the case of fed beds, they are suficiently general to be applica- f
ix
ble with minor, if an modif , y xclu- ications to a number of similar phenomena such as ion e
sion and ligand exchange. According to Helfferich, the applicability of a simplif ied theory
hinges on the mode of operation rather than on the particular mechanism of solute uptak e
(Helfferich, 1962). In the present book, the analysis of the ion exchange and adsorption
kinetics is based on a simplified unified approach and only some solutions are given, espe-
cially for ion exchange. On the other hand, the models for adsorption and isotopic
exchange are equialent. v
A significant feature of adsorption is that the rate of physical adsorption is generally too
,
v
high and consequently the oerall rate is controlled by mass transfer (or heat transfer)
en,
resistance, rather than by the intrinsic sorption kinetics (Ruthv 1984). Fwing this ollo
approach, adsorption is viewed and termed in the present book as a “dif fusion-controlled”
xchange.
process. The same holds for ion eAs long as the rate of adsorption and ion
exchange is determined by diffusion processes, the rate laws are deried by applying the v
ferich,
well-known diffusion equations (Helf 1962). In general, diffusion processes are
s f described in terms of Fick’ w: irst la
J gra d C (4.1)
D
i i
where J is the flux of the diffusing species i , C its concentration, and D the dif fusion coef-
i i
ficient. The diffusion of a species in a particle is a special case: the solid matrix occupies
a substantial fraction of the particle volume and obstructs diffusion. In addition, follo wing
a more rigorous approach, the solid matrix may consist of small microporous crystals
o distinct dif formed into a macroporous structure. In this case, twfusional resistances exist:
en,
macropore and micropore resistance (Ruthv 1984). In the related literature, macropore
diffusion is also termed “pore diffusion” while microporous dif fusion is termed “solid dif-
fusion” (Perry and Green, 1999). fusion” The term “intraparticle dif includes pore and solid
diffusion mechanisms. Pore diffusion is the diffusion of solutes in fluid-filled pores. These
pores are so large that the solute escapes the force field of the adsorbent surface (Perry and
Green, 1999). On the other hand, solid dif fusion is the dif fusion of solutes in the adsorbent
surface. In this case, the pores are so small that the solute neer escapes the force field of v
ace.
the adsorbent surfThe transport of solute molecules occurs by an actiated process v
involving jumps between adsorption sites (Perry and Green, 1999). Pore and solid dif fu-
sion act in parallel, and thus the dominant transport process is the faster one.