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4.2 Design of Adsorption and Ion-Exchange Processes 277

1.5

1

0.5
f(p n ) 0

-0.5

-1

-1.5
0 5 10 15
p n
Figure 4.14 The function f ( p ) for w = 2. n

Furthermore, Helfferich (1962) gies Ps equation, which can be used as an
v
atterson’
approximation:
w 1
f 1
Ut () 1 ff 1 f 3 4 f (4.52)
1
2
5
w
where (Figure 4.15)
1
f (4.53)
1
ab
f a ex p a T 2 (4.54)
2

f erf a T (4.55)
3
f b ex p b T 2 (4.56)
4

f erf b T (4.57)
5
with a and b being the nee and the positie roots respecti of the equation , ely gati v v v

x 2 wx3 w 3 0 (4.58)

In ion exchange, for the estimation of w , the total concentration in solid phase Q M is taken
equal to the REC. This concentration expresses the real total charge of the solid, which is