CHEMICAL ENGINEERING

240 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

constant fractional rate of surface renewal,s, but an upper limit on surface age equal to
the life of the jet, 4 , show that the surface age frequency distribution function,ft
,for
this case is given by:

ft

Dsexpst/[1expst

] for 0 <t<4

ft

D0fort>4.

Hence, show that the enhancement,E, for the increase in value of the liquid-phase mass
transfer coefficient is:

ED[s4

^1 /^2 erfs4

^1 /^2 ]/f2[1exps4

]g

whereEis defined as the ratio of the mass transfer coefficient predicted by conditions
described above to the mass transfer coefficient obtained from the penetration theory for
a jet with an undisturbed surface. Assume that the interfacial concentration of acetone is
practically constant.

Solution

For the penetration theory:
∂CA
∂t

DD

∂^2 CA

∂y^2

(equation 10.66)

As shown in Problem 10.19, this equation can be transformed and solved to give:

CNADAe

p

p/D

yCBe

p

p/D

y

The boundary conditions are:

WhenyD 0 ,CADCAi,BDCAi/p

and whenyD1,CAD0andAD 0

∴ CNAD

CAi

p

e

p

p/D

y

dCNA

dy

DCAi

√

1

D

√

1

p

e

p

p/D

y

From Volume 1, Appendix, Table 12, No 84, the inverse:

dCA

dy

DCAi

√

1

D

√

1

t

ey

(^2) / 4 Dt
At the surface: NA (^) tDD

(

dCA

dy

)

yD 0

DCAi

√

D

t

at timet

The average rate over a time 4 is:

1

4

CAi

√

D



∫ 4

0

dt

p

t

D 2 CAi

√

D

4