CHEMICAL ENGINEERING

MASS TRANSFER 275

The rising velocity is given by a force balance:

3 d 1 uD^16 d^31 + 1 + 2 

g

or: u 1 D

d^21 g

18 

+ 1 + 2

 DKd^21 relative to continuous phase

The downward liquid velocity is^12 Kd^21

The upward droplet velocity relative to container is:

Kd^21 ^12 Kd^21 D^12 Kd^21

and the time of contact during rise through heightHis:

tcD

H

1

2 Kd

2

1

. (i)

The mass transfer rate is:D∂CA/∂y

.

Thus:

1

CAS

∂CA

∂y

D

∂

∂y

{

erfc

y

2

p

Dt

}

D

∂

∂y

{

2

p



∫ 1

y/ 2

p

Dt

ey

(^2) / 4 Dt
d

(

y

2

p

Dt

)}

D

∂

∂y

Ð

1

2

p

Dt



2

p



∫ 1

y

ey

(^2) / 4 Dt
dt.
or:

∂CA

∂y

D

CAS

p

Dt

ey

(^2) / 4 Dt

(

∂CA

∂y

)

yD 0

D

CAS

p

Dt

The mass transfer rate at the surface is: (moles/areaðtime).

D

(



CAS

p

Dt

)

D

√

D

t

CAS

The mass transfer in timete 1 is:
√
D


CAS

∫te 1

0

t^1 /^2 dtD 2

√

D



t^1 e 1 /^2 CASDKte^1 / 12

Substituting from equation (i):

Mass transfer in moles per unit area of drop/

p

2 H

p

Kd 1

The mass transfer per drop is proportional to:

p

2

√

H

K

d 11 d^21 /

p

2

√

H

K

d 1

The mass transfer per unit timeDMass transfer per dropðdrops/time

or: proportional to:

p

2

√

H

K

d 1 ð

6 Q 1

d^31

/ 8. 48

√

H

K

Q 1

d^21