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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41354


    Title: Current efficiency of a disk-shaped ion-xchange membrane
    Authors: Hsu, Jyh-ping;Jiang, J. M.;曾琇瑱;Tseng, Shio-jenn
    Contributors: 淡江大學數學學系
    Keywords: Current efficiency;Ion-exchange membrane;Fixed charge distribution;Electro Dialysis;Nernst-Planck equation;Poisson equation
    Date: 2001-07
    Issue Date: 2010-01-28 07:22:18 (UTC+8)
    Publisher: 中國化學工程學會
    Abstract: 本文以理論方式探討了固定電荷分佈對圓盤型薄膜之分離效率的影響,主要的工作是將文獻中之相關分析延伸至二維的問題。吾人以參數M來定性薄膜內之固定電荷分佈,並探討其與電流效率η之相關性。若M為負,表示固定電荷較集中於薄膜的左側;反之,若M為正,則較集中於薄膜的右側;如果M為零,表示固定電荷是均勻地分佈於薄膜中。文中考慮了線性、指數、三角函數、與區段連續等四類固定電荷分佈。數值模擬的結果顯示無論施加於薄膜兩端的電位差為何,η隨著M呈單調遞增的變化。這個行為與一維薄膜的是不間的,其中當M變化時可有一局部最大值。另外,如果M為正,則η隨著薄膜兩端之電壓差增加而增加,反之,若M為負,則隨著薄膜兩端之電壓差增加而減小。當M趨近零時, η與薄膜兩端之電壓差的關係不密切。
    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.
    Relation: Journal of the Chinese Institute of Chemical Engineers 32(5),頁437-444
    DOI: 10.6967%2fJCICE.200109.0437
    Appears in Collections:[數學學系暨研究所] 期刊論文

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