Ionic separation in electrodialysis : analyses of boundary layer, cationic partitioning, and overlimiting current

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Title: Ionic separation in electrodialysis : analyses of boundary layer, cationic partitioning, and overlimiting current
Author: Kim, Younggy
Abstract: Electrodialysis performance strongly depends on the boundary layer near ion exchange membranes . The thickness of the boundary layer has not been clearly evaluated due to its substantial fluctuation around the spacer geometry . In this study , the boundary layer thickness was defined with three statistical parameters : the mean , standard deviation , and correlation coefficient between the two boundary layers facing across the spacer . The relationship between the current and potential under conditions of the competitive transport between mono - and di -valent cations was used to estimate the statistical parameters . An uncertainty model was developed for the steady -state ionic transport in a two -dimensional cell pair . Faster ionic separations were achieved with smaller means , greater standard deviations , and more positive correlation coefficients . With the increasing flow velocity from 1 .06 to 4 .24 cm /s in the bench -scale electrodialyzer , the best fit values for the mean thickness reduced from 40 to less than 10 μm , and the standard deviation was in the same order of magnitude as the mean . For the partitioning of mono - and di -valent cations , a CMV membrane was examined in various KCl and CaCl₂ mixtures . The equivalent fraction correlation and separation factor responded sensitively to the composition of the mixture ; however , the selectivity coefficient was consistent over the range of aqueous -phase ionic contents between 5 and 100 mN and the range of equivalent fractions of each cation between 0 .2 and 0 .8 . It was shown that small analytic errors in measuring the concentration of the mono -valent cation are amplified when estimating the selectivity coefficient . To minimize the effects of such error propagation , a novel method employing the least square fitting was proposed to determine the selectivity coefficient . Each of thermodynamic factors , such as the aqueous - and membrane -phase activity coefficients , water activity , and standard state , was found to affect the magnitude of the selectivity coefficient . The overlimiting current , occurring beyond the electroneutral limit , has not been clearly explained because of the difficulty in solving the singularly perturbed Nernst -Planck -Poisson equations . The steady -state Nernst -Planck -Poisson equations were converted into the Painlevé equation of the second kind (P[subscript II] equation ) . The converted model domain is explicitly divided into the space charge and electroneutral regions . Given this property , two mathematical formulae were proposed for the limiting current and the width of the space charge region . The Airy solution of the P[subscript II] equation described the ionic transport in the space charge region . By using a hybrid numerical scheme including the fixed point iteration and Newton Raphson methods , the P[subscript II] equation was successfully solved for the ionic transport in the space charge and electroneutral regions as well as their transition zone . Above the limiting current , the sum of the ionic charge in the aqueous -phase electric double layer and in the space charge region remains stationary . Thus , growth of the space charge region involves shrinkage of the aqueous -phase electric double layer . Based on this observation , a repetitive mechanism of expansion and shrinkage of the aqueous -phase electric double layer was suggested to explain additional current above the limiting current .
URI: http : / /hdl .handle .net /2152 /ETD -UT -2010 -08 -1724
Date: 2010-11-09

Citation

Ionic separation in electrodialysis : analyses of boundary layer, cationic partitioning, and overlimiting current. Doctoral dissertation, University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2010 -08 -1724 .

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