EDL configuration on a dissimilarly charged protrusion array via double Fourier series and perturbation method.

In this study, through the extension of an one-dimensional, dissimilarly charged protrusions surface model set up in our previous work, a novel dissimilarly charged protrusion array (DCPA) model immersed in an electrolyte solution, which could simulate realistically both the surface morphology and the surface charged condition profoundly concerned on a biological cell membrane, or on the surface of a micro-scale, modified particle used in biomedical engineering and water treatment, is proposed. Considering the condition of small protrusions, the electrical potential field due to the electrical double layer (EDL) on DCPA model is solved semi-analytically using both the double Fourier series and the perturbation method. The analysis from the numerical result reveals that, a small, dissimilarly charged protrusion can lead to a steep variation in the local EDL configuration, especially compared with that in the condition when the charged surface is taken roughly as a flat surface using a lumped, mean surface charge density.

Solving EDL configuration near a dissimilarly charged protrusions surface model using perturbation method.

In this work, an elementary, novel dissimilarly charged protrusions (DCP) surface model in an electrolyte solution considering simultaneously the complexity of both surface morphology and surface charged condition, which are concerned frequently on a biological cell membrane, on a modified micro-particle surface, or in a lab-on-a-chip biosensor device, is proposed. Based on Fourier series and the perturbation technique, the configuration of electrical double layer (EDL) near this complicated charged surface model is successfully solved semi-analytically. The numerical calculation reveals that, the methodology suggested in present study could deal with charged surface systems of arbitrary geography and of arbitrary charge distribution. In the analysis, three special subjects are discussed, including an isolated dissimilarly charged protrusion, the effect of protrusions, and the effect of dissimilarly charged condition on protrusions.

Electrokinetic flow near an undulated, charged surface.

In this study, using the iterative finite difference method, the effect of an irregular condition at boundary, the surface undulation, in a charged surface system on the two dimensional electrokinetic flow near the surface is analyzed. The results reveal that, for the electrokinetic flow, the undulation of charged surface may have two major effects: one is that it changes the flow pattern of electrolyte solution, especially in the region close to the undulated surface; the other is that, due to the increase of effective surface area, the magnitude of velocity field may be increased considerably. In addition, when either the amplitude of undulation is increased, or the period of undulation is decreased, both the maximum velocity and the tangential flow rate will be raised to an extent. This is important for applications, for example, the electrophoresis of a biological cell, the electroosmosis of electrolyte solution in a micro-channel, etc.

Charged layer with undulated surface: configuration of electrical double layer.

A charged layer with undulated surface exists commonly in natural entities (for example the biological membrane layer and the surface of charged colloid) and in artificial fabrications (for example the peripheral surface of ion-exchange membrane pores). When the micro- or nano-scale charged layer systems are concerned, the effect of undulation of charged layer surface on the electrical phenomenon may become great significant. In this work, using the perturbation method, the significance of undulated surface on a charged layer in the electrical phenomenon is investigated. Under assumptions that the undulation amplitude is small and that the Debye-Huckel approximation is applicable, the electrical potential field in three regions is solved simultaneously. Based on the analytical results it is found that, if compared with that in condition of flat surface, the undulation of charged layer surface decreases/increases the magnitude of electrical potential field near the wave crest/trough, due to the curvature of undulated surface. In addition, the surface potential on the undulated surface shows a wavelike distribution. The analytical results also show that, the significance of undulated surface is determined by the physical parameters, including the geometry of undulated surface, the amplitude and the period of undulation, and the fixed charge density in charged layer.

Ionic separation efficiency of a novel electric-field-assisted membrane module comprising an array of microchannel units.

The ionic separation efficiency of a novel membrane module comprising an array of microchannel units is analyzed. Under the Debye-Hückel approximation, we derive a semianalytical expression for the ionic separation efficiency. Analyses reveal that the effects of the size of the microchannel, the fixed charge density in the membrane layer, and the permittivity of the membrane layer on ionic separation efficiency depend strongly on the valence type of electrolyte in treated water. Under the condition of a symmetric electrolyte, the ionic separation efficiency is found to be about unity and unresponsive to variation of system parameters. If the valence of the cation is higher than that of the anion, the ionic separation efficiency is larger than unity, and decreases to unity as the size of the microchannel increases. In contrast, if the valence of the cation is lower than that of the anion, the ionic separation efficiency is smaller than unity and increases to unity as the size of the microchannel increases. Under the latter two conditions, the effects of both fixed charge density in the membrane layer and permittivity of the membrane layer on the ionic separation efficiency are found to be reversed.

Theoretical analysis of a novel electrical field assisted membrane module comprising an array of microchannel units.

A novel electrical field assisted membrane module consisting of an array of microchannel units, each microchannel unit comprised of a cylindrical pore and a charged ion-selective membrane layer, is analyzed theoretically. The governing equations for the flow and the electrical fields are solved analytically under the Debye-Huckel condition and the influences of the key parameters on the flow behavior of the system under consideration are investigated through numerical simulation. We show that for a fixed microchannel radius, the volumetric flow rate through a microchannel unit has a maximal value as the radius of the cylindrical pore varies. This maximum is independent of both the strength of the applied field and the density of the fixed charges in the membrane layer, but varies with the permittivity of the membrane layer.

Analytical expressions for the electrical potential near planar, cylindrical, and spherical surfaces for symmetric electrolytes.

The conjecture of Tuinier (J. Colloid Interface Sci. 258 (2003) 45) for the electrical potentials near a cylindrical surface and near a spherical surface under the conditions of symmetric electrolyte and large scaled radius are derived by solving the corresponding Poisson-Boltzmann equation. The surface charge density-surface potential relations for these surfaces are also derived under the conditions of constant surface potential. We show that the level of surface charge density for planar, cylindrical, and spherical surfaces follows the order spherical surface > cylindrical surface > planar surface.