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284 4. Adsorption and Ion Exchange

unreacted core
Figure 4.16 Shrinking core model: the reaction proceeds at a narrow front, which mo es deeper v
into the solid particle as time passes.

It is well known that swelling of resins increases the particle radius. When resin beads
are immersed in the solution, water uptake takes place almost immediately resulting in a ,
ollen”
new “sw radius. The swollen radius is inersely proportional to the initial solution v
concentration (Hellferich, 1962). This effect has not been taken into account in the origi-
nal model of Levenspiel (1972). However, the actual swollen radius of the resin should be
used in the model equations, and so measurements should be performed in order to esti-
mate this radius.
enspiel,
Furthermore, in its original form (Le 1972), the assumption of constant and
v
uniform bulk concentration of A in the fluid phase was made. This is similar to the infinite
solution volume concept used in the analysis of adsorption and ion-exchange kinetics. In
wing, the follo the more general solutions are presented, i.e. for changing fluid concentra-
olume). tion (finite solution v
Film diffusion control

bk 3 f t
X B C A ∫ t d
Bo r 0 (4.89)

where:
k f the mass transfer coeficient in the fluid film surrounding the particle f
b the stoichiometric coef icient f
C A the fluid phase bulk concentration of A
the molar density of B in the solid phase (moles B/unit solid v olume),
B

q
B max p (4.90)

where is the particle density and p q max is the initial solid-phase concentration of B. In ion-
xperimental con- exchange systems, this quantity is equal to the MEL under the specif ied e
ditions. In most cases, if the ion e this v which xchanger is a resin, alue is equal to the REC,
is known beforehand by the producer .