Page 310 - Modelling in Transport Phenomena A Conceptual Approach

290 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

which relates the concentration of species in the membrane at equilibrium to the
concentration in bulk solution. For the problem depicted in Figure 8.28, the par-
tition coefficients can be defined as
(8.417)

(8.418)

t-z
Figure 8.28 Concentration distribution across a membrane.

The molar rate of transfer of species across the membrane under steady condi-
tions can be expressed as
+
LA = Ak:(cib - cAi) = AIc,+(cii - cAa) (8.419)
On the other hand, the use of Eqs. (8.417) and (8.418) in Eq. (8.414) leads to
ADAB(H-cA, - H+cii)
nA = (8.420)
L
Equations (8.419)-(8.4-20) can be rearranged in the form

(8.421)

(8.422)

(8.423)