1) The permselectivity coefficient (
TBA) between two ions, B and A, of the same electric charge, but of different valence, can be expressed by Equation (15):
(15)
where
uA, uB: transfer velocity of A and B ions across membrane
C0A,
C0B: concentration of A and B ions in the bulk of dialysate
KBA: separation factor
i: current density
δ: thickness of diffusion layer
DA,
DB: diffusion constant of A and B ions in dialysate
t±: total transport number of A and B ions in membrane
tA,
tB: transport number of A and B ions in dialysate
F: Faraday's constant
By Equation (15),
iδ can be regarded as one parameter for
T BA.
2) Equations (20) and (21), which express the critical current density (
icrit) and the critical permselectivity (
TBA crit), can be derived.
icrit=
F/δ·
DACOA+
DBCOB (20)
(21)
3) The permselectivity coefficient (
TBA) and separation factor (
KBA) at the moment when the concentration of B ion in the bulk of dialysate (
C0B) becomes equal to that in the diffusion layer on a membrane surface (
CSB), can be given by Equations (23) and (26), respectively. Further, Equation (28) giving the separation factor (
KBAcrit) at the moment when TBA becomes equal to
TBA crit, is also derived.
4) Results of numerical analysis by using Equations (15),(20) and (21) are shown in Fig. 8, 9 and 11. From these results, the tendency of changing in the value of
TBA with current density (
i), with
TBA successively approaches to and reaches
TBAcrit at the critical current density (
icrit), becomes clear.
The very similar tendency of changing in
TBA value with current density can be found among the results of our previous experiments. This indicates that the assumption on a mass transfer model across an ion exchange membrane is appropriate.
5) By Equation (15), the concentration of A and B ions in the solution of diffusion layer (
CSA and
CSB) and the value of
KBA, as well as the value of T
BA, is calculated. And, relations between these calculated values and the values of
TBA,
KBA and
KBAcrit obtained by Equations (23),(26) and (28) are discussed.
It it found that:
(1) When
KBA>
KBAcritTBAapproaches to
TBAcrit with a value larger than
TBAcrit, but when
KBA<
KBAcrit,
TBA approaches to
TBAcrit with a value smaller than
TBAcrit.
(2) When
KBA<
KBA,
CSB is larger than
C0B, but when
KBA becomes larger than
KBA with an increase in current density,
CSB becomes smaller than
C0B. At the critical current density (
icrit), both
CSB and
CSA reach to zero.
抄録全体を表示