The application of the space-charge model to the permeability properties of charged microporous membranes

One-dimensional axial simulation of electric double layer overlap effects in devices combining micro- and nanochannels

“…Our emphasis is on computational efficiency and producing a model suitable for numerically comparing device designs over large parameter spaces spaces, or iterative, model-based, parameter estimation. As is well known (Burgreen and Nakache 1964;Hildreth 1970;Levine et al 1975;Hijnen et al 1985), as the electrokinetic radius decreases, the electroosmotic contribution to ion transport also decreases, and the electrophoretic term becomes comparatively dominant. Li (2004) and Daiguji (2004) make similar observations.…”

“…The importance of this parameter in ion separation by charged membranes is well known, as seen, for example, in Hoffer and Kedem (1967), Cwirko and Carbonell (1990) and Wang et al (1995). Second, " u; the normalized electroosmotic velocity, depends on the ratio, denoted " G; of the average cross-channel potential to the zeta potential (Burgreen and Nakache 1964;Hildreth 1970;Levine et al 1975;Hijnen et al 1985). As " G approaches unity, transport due to the electroosmotic advection term decreases to zero, and the electrophoretic component becomes dominant.…”

“…This is supported by the correlation observed in our experiments between the apparent onset of EDL effects and two parameters that quantify the influence of EDL effects, namely the appropriately normalized fixed charge density and the ratio of average cross-channel potential to zeta potential. The normalized fixed charge density is known to be an important parameter in ion separation by charged membranes (Hoffer and Kedem 1967;Cwirko and Carbonell 1990;Wang et al 1995) and the ratio of average crosschannel potential to zeta-potential figures prominently in many studies of electroosmotic flow (for example, Burgreen and Nakache 1964;Hildreth 1970;Levine et al 1975;Hijnen et al 1985). Reflecting the relative contributions of the electrophoretic and electroosmotic terms, we numerically solve the fully coupled Poisson and NernstPlanck equations in the axial dimension, but use analytical approximations to the electroosmotic component.…”

Theoretical and Experimental Study of the Voltage–Current Characteristic of an Asymmetric Cellulose Acetate Membrane

“…For asymmetric membranes, it can be shown theoretically (17,25,26) that in the limit of very large volume flows ( J v 3 ϱ), the salt rejection coefficient approaches the value of the reflection coefficient () of the selective layer. In an earlier paper (27), we presented a general expression for the reflection coefficient of a selective membrane modeled as a bundle of cylindrical capillaries. For large electrolyte concentrations, where the influence of the membrane charge may be ignored and, as a consequence, the reflection coefficient is determined purely by dielectric exclusion, it can be shown that Eq.…”

Chromium (VI) separation from aqueous solution using anion exchange membrane

“…56 The model involves coupled nonlinear differential equations and is highly computationally intensive. [57][58][59][60][61][62] The system of governing equations represents a set of coupled nonlinear differential equation that is solved by making suitable assumptions and writing in terms of dimensionless quantities. The nondimensional Poisson-Boltzmann equation for the symmetric electrolytes (Eq.…”