The effect of the fixed charge distribution on the performance of a disk-shaped membrane is discussed theoretically. The present analysis generalizes the problem studied in the literature to a two-dimensional case. A parameter M characterizing the distribution of the fixed Charge in the membrane is proposed to predict its current efficiency, η. Four types of fixed Charge distribution, including linear, exponential, trigonometric, and piecewise continuous distributions, are examined. If M ＜ 0, the fixed charges are more concentrated on the left-hand side of the membrane, and the reverse is true if it is positive. If M = 0, the fixed charges are uniformly distributed. We find thatηincreases monotonically with M regardless of the level of the electrical potential applied across the membrane. This is different from the result for a one dimensional case, whereη has a local maximum as M varies. If M ＞ 0,η increases with the applied potential across the membrane, and the reverse is true If M ＜ O. If M→0,η is insensitive to the applied potential.
Journal of the Chinese Institute of Chemical Engineers=中國化學工程學會會誌 32(5)，頁437-444