Membrane and Desalination Technologies - TCE Moodle Website

294 J. Paul Chen et al.
Approximating ln cAm by ðDcAmÞ=cAm and using the relation f Am = RT/D Am, we obtain
DcAm
JA ¼ DAm : (22)
l
Assuming further thermodynamic equilibrium at both sides of the membrane and a
proportional relationship between the concentration inside the membrane, cAm, and outside
the membrane, cA,
cAm ¼ KAcA; (23)
where K A is the distribution constant. Hence, Eq. (22) can be written as
JA ¼
DcA
DAmKA :
l
(24)
Therefore, the fluxes of the solvent and solute can be described by Eq. (18) and Eq. (24), or
JB ¼ cBmDBmvB
ðDp DPÞ and JA ¼ DAmKA
RTl
DcA
:
l
Other than the flux of solvent, the process is also evaluated in terms of solute rejection, R,
defined as
R ¼ 1
cAF
where cAP is the concentration of solute in the permeate (mol/m 3 ) and cAF is the concentration
of solute in the feed (mol/m 3 ).
Because
Rearranging,
R ¼ 1
JA
JB
R ¼ 1
cAP
; (25)
¼ cAP
; (26)
cBP
JAcBP
JBcAF
DAmKARTDcAcBP
cBmDBmvBðDp DPÞcAF
¼ 1 DAmKARTðcAP cAFÞcBP
cBmDBmvBðDp DPÞcAF
DAmKARTcBP
¼ 1 þ
cBmDBmvBðDp DPÞ
; (27)
cAF cAP
cAF
DAmKARTcBP
¼ 1 þ
R: (28)
cBmDBmvBðDp DPÞ