Electroosmotic height

Four different electrokinetic processes are known. Two of them, electroosmosis and electrophoresis, were described in 1809 by Ferdinand Friedrich Renss, a professor at the University of Moscow. The schematic of a cell appropriate for realizing and studying electroosmosis is shown in Fig. 31.1a. An electrolyte solution in a U-shaped cell is divided in two parts by a porous diaphragm. Auxiliary electrodes are placed in each of the half-cells to set up an electric held in the solution. Under the inhuence of this held, the solution starts to how through the diaphragm in the direction of one of the electrodes. The how continues until a hydrostahc pressure differential (height of liquid column) has been built up between the two cell parts which is such as to compensate the electroosmotic force. 

The standard deviation of the Gaussian zones expresses the extent of dispersion and corresponds to the width of the peak at 0.607 of the maximum height [24,25]. The total system variance (ofot) is affected by several parameters that lead to dispersion (Eq. 17.22). According to Lauer and McManigill [26] these include injection variance (of), longitudinal (axial) diffusion variance (of), radial thermal (temperature gradient) variance (of,), electroosmotic flow variance (of,), electrical field perturbation (electrodispersion) variance (of) and wall-adsorption variance (of ). Several authors [9,24,27-30] have described and investigated these individual variances further and have even identified additional sources of variance, like detection variance (erf,), and others... 

A micro channel of height 2 H is equipped with electrodes at the upper (L/,) and lower (L walls [28], These electrodes are used to control the C, potential at the solid-liquid interface. In this way, the direction of the electroosmotic flow near the interface can be changed locally. The external electric field is given as Ex. 

Electroosmotic flow, described in Section 4.9, is another complicating factor in electrophoresis. The electroosmotic flow process is often responsible for nonselective ion transport superimposed on the electrophoretic transport. When electroosmotic displacement is significant, it must be kept in mind that the distance X in the preceding plate height equations is the displacement distance due to electrophoresis alone it does not include electroosmotic displacement. Also the voltage V must be calculated as that applied over the path of electrophoretic displacement only, not including the distance of electroosmotic displacement [41]. 

A high electroosmotic flow through the stationary-phase particles may be created when the appropriate conditions are provided. This pore flow has important consequences for the chromatographic efficiency that may be obtained in CEC. From plate height theories on (pressure-driven) techniques such as perfusion and membrane chromatography, it is known that perfusive transport may strongly enhance the stationary-phase mass transfer kinetics [30-34], It is emphasised... 

Unfortunately, Eq. (8) is not fully satisfactory since it results in negative values for the Cs term at high pore flow (to + k" >1). Such high flow ratios may be created when a pressure-driven flow is directed against the electroosmotic flow. Also, when the interior of the particles has a much higher surface potential than the exterior, surface flow ratios > 1 may be expected. Of course, negative contributions to the total plate height are physically impossible and Eq. (9) cannot be valid. 

Consider electroosmotic flow in a rectangular microcharmel of width 2W, height 2H and length L, as illustrated in Figure 1 [5]. Because of the symmetry in the potential and velocity fields, the solution domain can be reduced to a quarter section of the channel (as shown by the shaded area in Figure 1). 

The flow of medium leads to the appearance of difference in fluid levels in vessels attached to the capillary. The resulting pressure drop, Ap=pg A//, causes the counter-flow of dispersion medium, and the flow profile in the capillary is such as that shown in Fig. (V-13, c), i.e., near the walls and in the center of a capillary the medium moves in opposite directions. Under the steady-state conditions, when the net flux of medium is zero (QE + Qp=0), the height of electroosmotic rise, HE, is given by... 

H height of the disperse system volume (in sedimentation analysis) He height of electroosmotic rise... 

Since for small Debye length the situation is completely complementary to the electroosmotic case, we may apply the result of Eq. (7.4.5), identifying Ap as the force per unit particle cross-sectional area exerted by the fluid on the particle. Assuming Stokes flow, we use STTixaU for the force on a single particle if there are n particles per unit volume, then the total force per unit volume is taken to be nF. With the potential drop measured over the suspension height H, it readily follows that... 

Electroosmotic flow-driven chromatography yields higher separation efficiencies than HPLC because of the use of small particles and reduction of plate heights as a result of the plug-flow profile. 

As an application, the flow in rough microchannels was applied theoretically in the nucleic acid extraction process [8], which is the first critical step for many nucleic acid probe assays. Using a microchannel with 3D prismatic elements on the channel wall can dramatically increase the surface area-to-volume ratio and hence enhance the nuclei acid adsorption on the wall. The opportunity for molecule adsorption is also increased due to the induced pressure resisting the central bulk electroosmotic flow. It is found that decreasing the electroosmotic flow velocity or the channel height enhances nuclei adsorption. 

The Smoluchowski equation is used to relate average flow velocity (Vav) to electric field strength E in electroosmotic flows. Under the conditions of a thin double layer or a large channel height (i.e., a plug-like or constant velocity profile), it can be expressed as follows ... 

A van Deemter plot for capillary electrophoresis is a graph of plate height versus migration velocity, where migration velocity is governed by the net sum of electroosmotic flow and electrophoretic flow. 

In the majority of microfluidic cases where 1/k is much smaller than the chaimel height the Helmholtz-Smoluchowski equation provides a reasonable estimate of the flow velocity at the edge of the double layer field. As such when modelling two and three dimensional flow systems it is common to apply this equation as a shp boundary condition on the bulk flow field. Since beyond the double layer by definition pe = 0, the flow equation reduces to (assuming pure electroosmotic flow) to a simple Lapla-... 

Lattice Poisson-Boltzmann Method, Analysis of Electroosmotic Microfludics, Figure 11 Variation of flow rate with height of roughness Coo lO- M, = 5x102v/m, =-50mV, // = 0.4 xm,... 

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