Page 309 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WITHOUT CONVECTION 289

Therefore, the initial molar flow rate of species A is
(41)(3 x 10-5)(0.9 - 0.25)
hA = = 1.88 x mol/s
4244.1
an
b) Fbm Eq. (0) Table 8.8
. C~AB(XA, - ~AL)A
nA =
L
- (41)(3 x 10-5)(0.9 - 0.25) [~(0.008)~/4]
- = 2.01 x 10-~ mol/ s
0.2

8.4.1.1 Electrical circuit analogy

The molar transfer rate of species A is given by &. (D) in Table 8.8 as

(8.414)

'DABA
Comparison of Q. (8.414) with Eq. (8.2-10) indicates that

Driving force = CA, - CA~ (8.415)

L
Resistance = - - Thickness (8.416)
VABA - ('lkansport property)(Area)

8.4.1.2 Transfer rate in terms of bulk fluid properties

Since it is much easier to measure the bulk concentrations of the adjacent solu-
tions to the surfaces at z = 0 and z = L, it is necessary to relate the surface
concentrations, XA, and XA~, to the bulk concentrations.
For energy transfer, the assumption of thermal equilibrium at a solid-fluid
boundary leads to the equality of temperatures and this condition is generally
stated as, "temperature is continuous at a solid-fluid boundary." In the case of
mass transfer, the condition of phase equilibrium for a nonreacting multicomp+
nent system at a solid-fluid boundary implies the equality of chemical potentials
or partial molar Gibbs free energies. Therefore, concentrations at a solid-fluid
boundary are not necessarily equal to each other with a resulting discontinuity in
the concentration distribution. For example, consider a homogeneous membrane
which is chemically different from the solution it is separating. In that case, the
solute may be more (or, less) soluble in the membrane than in the bulk solution.
A typical distribution of concentration is shown in Figure 8.28. Under these condi-
tions, a thermodynamic property H, called the partition coeficient, is introduced