Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 78

R 1

R 2

Figure 3.34 Tubular membrane.

where
1
K G =

1
k g +

m
k L ,

(3.86)

and

P A = mC A , b . (3.87)

Here, K G is an overall mass transfer coefficient. The equation for K G is analogous to the
resistance in series model for electrical circuits. P A is the value of the solute pressure that
would be in equilibrium with C A , b .
An analogous equation can be written in terms of liquid-phase concentrations:

K L ( C A , b − J A = C A , b ) , (3.88)

where

mC A , b . P A , b = (3.89)

More complicated mass transfer systems may not be amenable to determination of each
mass transfer resistance. The flux is written in terms of an overall coefficient.
One type of system to consider is one in which the surface area perpendicular (normal)
to the solute flux changes within the system, then the steady-state flux is not constant
but the mass transfer rate is. As an example, consider Figure 3.34, in which the material
between R 1 and R 2 is a membrane. At steady-state, mass can permeate from R 1 to R 2 . The
mass transfer rate R A (mass / time) is constant. The flux J A (mass / area · time) is related to

the rate by:

R A = J A × (surface area normal to the mass transfer direction) , (3.90)

since A 1 = J A 2 .

For this type of system, the flux needs to be specified at a location.

A 2 , J A 1 =