| Summary: | 碩士 === 國立臺灣大學 === 化學工程學系研究所 === 86 === The effects of fixed charge distribution C3 in an ion-selective membrane and
of the convective boundary layer near the outer boundary of the membrane on it
s current efficiency η are investigated. An intuitive parameter M2, which is
a measure for the nature of C3, is proposed, and three families of fixed char
ge distribution, including linear, exponential, and trigonometric, are examine
d. Under the condition that the total amount of fixed charges is constant, M2
has a positive maximum M2max if all fixedcharges are near the right membrane-
liquid interface, and a negative minimum M2min if all fixed charges are near t
he left membrane-liquid interface. Any other type of fixed charge distributio
n has an M2 between these two extremes, and if C3 is uniform, M2=0. It is fou
nd that η is closely related to M2. In other words, the latter can be used t
o predict the former. We conclude that: (1) The value of η for M2 < 0 is sma
ller than that for M2=0. (2) If M2> 0, the variation of η as a function of M
2 has amaximumm. (3) If M2 < 0, η decreases with the increase in current den
sity; the reverse is true for M2 > 0. (4) If M2=0, η is independent of appl
ied current density.
The effect of the bounda
ry layer near the membrane-liquid interface on η is also discussed in the pre
sent study. We consider two types of fixed charge distribution : a class of li
near distribution and a class of exponential distribution. The result of numer
ical simulation reveals that , if the flow velocity in the membrane phase is s
mall, increasing the inhomogeneity of fixed charge distribution is capable of
raising η. However, if it is appreciable, the reverse is true. If a boundary
layer is present, ηdecreases with the increase in current density; the revers
e is true if it is absent. The former is due to that the degree of concentrati
on polarization in the boundary layer increases with current density. Although
the existence of a boundary layer has the effect of reducing η, the convecti
ve flow of fluid perpendicular to membrane has a positive effect on η. If a
boundary layer is absent, and the fixed charges are distributed homogeneously,
η is independent of current density I; if the boundary layer ispresent, η w
ill vary with I.
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