Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 77

P A ,b

BULK
GAS
PHASE

BULK
LIQUID
PHASE

P A ,i

C A ,i

C A ,b

LIQUID - PHASE FILM
(BOUNDARY LAYER)

GAS FILM
(BOUNDARY LAYER)

GAS/ LIQUID
INTERFACE

Figure 3.33 Region near a gas / liquid interface.

Using the above two equations, an equation can be obtained for the flux of A in terms of a
driving force based on the bulk-phase concentrations (see Problem 3.2 at end of chapter):

P A , b −

mC A , b .

1

1
k g +

J A = (3.83)

m
k L

There are some important points to note. As written, the driving force is in terms of the
gas phase since mC A , b is the pressure that would be in equilibrium with the liquid-phase
bulk concentration. An equation for J A could also be derived in terms of liquid-phase
concentration. The overall mass transfer resistance ( R T ) has two contributions:

1
k g
Gas-Phase Resistance

m
k L

.

R T = + (3.84)

Liquid-Phase Resistance

Some implications of this resistance term can be observed immediately. First, the larger
the value of k , the smaller the resistance. Second, the value of each resistance can be
different. When one resistance is significantly larger than the other (or the mass transfer
coefficient for one phase is significantly smaller), it is dominant and is termed the con-
trolling resistance. Mass transfer across both films is controlled (limited) by the dominant
resistance. Third, the larger the value of m , the larger the liquid-phase resistance (can you
see why physically?).
The flux equation can be written as:

P A )

J A = K G ( P A , b − , (3.85)