Electroosmosis effect

Our theoretical model considers both the pressure gradient and electroosmosis. If there is no electroosmosis effect involved, such as in the case where no external electric field is applied, the theoretical model reduces to a simple pressure-driven flow. In Fig. 9, the dimensionless velocity profiles for different electric fields are shown. When there is no electric field, the three-liquid flow is in fact a pressure-driven flow of a single liquid, showing parabohc velocity profile. The holdup of nonconducting liquids for different viscosity ratio /I2 is shown in Fig. 10. In this figure, = I- P2 changes from 1.46 to 3.17. We note that under constant flow rates and electric fields, the liquid holdups depend on flie viscosity ratio between the two liquids. 

The interface position and velocity profile of the liquid-liquid stratified flow in microchannel can be controlled using the electroosmosis effect, which can retard or aid the flow of one liquid. The experiment demonstrated a new method to solve the unmatched viscosity problem of the hquid-liquid flow in diffusion-based microfluidic apphcations. Other potential uses include development of microlens, flow switching, or flow focusing for multi-liquids flow in microfluidics. 

Our theoretical model considers both the pressure gradient and electroosmosis. If there is no electroosmosis effect... 

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

The simple treatment of this and of other electrokinetic effects was greatly clarified by Smoluchowski [69] for electroosmosis it is as follows. The volume flow V (in cm /sec) for a tube of radius r is given by applying the linear velocity V to the body of liquid in the tube... 

There are four related electrokinetic phenomena which are generally defined as follows electrophoresis—the movement of a charged surface (i.e., suspended particle) relative to astationaiy hquid induced by an applied ectrical field, sedimentation potential— the electric field which is crested when charged particles move relative to a stationary hquid, electroosmosis—the movement of a liquid relative to a stationaiy charged surface (i.e., capiUaty wall), and streaming potential—the electric field which is created when liquid is made to flow relative to a stationary charged surface. The effects summarized by Eq. (22-26) form the basis of these electrokinetic phenomena. 

Theory Cross-flow-electrofiltration can theoretically be treated as if it were cross-flow filtration with superimposed electrical effects. These electrical effects include electroosmosis in the filter medium and cake and electrophoresis of the particles in the slurry. The addition of the applied electric field can, nowever, result in some qualitative differences in permeate-flux-parameter dependences. 

Electroosmosis is an electrokinetic effect, so a direct electric potential causes a movement of liquid through stationary particles. From primary electrode reactions,... 

The streaming potential (Dorn effect) relates to a movement of liquid that generates electric potential, and electroosmosis occurs when a direct electric potential causes movement of the liquid. The sedimentation potential relates to sedimentation (directed movement) of charged particles that generates electric potential, and electrophoresis occurs when a direct electric potential causes a movement of charged particles. 

With regard to the movement of liquid versus particles under direct current, electrophoresis is the reverse of the effect of electroosmosis.33 If particles move through a liquid that is stationary, this is called electrophoresis conversely, if the liquid moves through particles that are stationary, that is called electroosmosis. 

In step 2, the migration times of the solute and the marker of the electroosmosis, such as mesityl oxide, were measured at each pH and converted to the effective mobility. When the CE instrument is equipped with a photodiode array detector, the spectrophotometric method is available simultaneously. The buffers should be exchanged every five runs, because the pH of the buffer was changed by electrolysis during CE analyses. The details of the experimental conditions are described in Ref. 20. 

The word electrokinetic implies the joint effects of motion and electrical phenomena. We are interested in the electrokinetic phenomena that originate the motion of a liqnid within a capillary tube and the migration of charged species within the liquid that surrounds them. In the first case, the electrokinetic phenomenon is called electroosmosis whereas the motion of charged species within the solution where they are dissolved is called electrophoresis. This section provides a brief illns-tration of the basic principles of these electrokinetic phenomena, based on text books on physical chemistry [7-9] and specialized articles and books [10-12] to which a reader interested to stndy in deep the mentioned theoretical aspects should refer to. 

Electrokinetic phenomena such as electroosmosis, streaming potential, and viscoelectric effects (Chapter 12)... 

It will be noted that the importance of the correction for surface conductivity increases as Rc decreases and vanishes as Rc - oo. Equation (54) also suggests that the numerical evaluation of ks may be accomplished by studying electroosmosis in a set of capillaries identical in all respects except for variability in Rc. Finally, the expansion of Equation (50) to Equation (54) in correcting for surface conductivity explicitly assumes a cylindrical capillary. Experiments made with porous plugs cannot be corrected for surface conductivity by Equation (54), but the qualitative conclusion that the effect of surface conductivity increases as the pore radius decreases is valid in this case also. 

Two conditions must be met to justify comparisons between f values determined by different electrokinetic measurements (a) the effects of relaxation and surface conductivity must be either negligible or taken into account and (b) the surface of shear must divide comparable double layers in all cases being compared. This second limitation is really no problem when electroosmosis and streaming potential are compared since, in principle, the same capillary can be used for both experiments. However, obtaining a capillary and a migrating particle wiih identical surfaces may not be as readily accomplished. One means by which particles and capillaries may be compared is to coat both with a layer of adsorbed protein. It is an experimental fact that this procedure levels off differences between substrates The surface characteristics of each are totally determined by the adsorbed protein. This technique also permits the use of microelectrophoresis for proteins since adsorbed and dissolved proteins have been shown to have nearly identical mobilities. 

Solution-. The observed effect is the sum of two contributions, one of which is the electro-osmotic flow of the medium through the cell. The latter has its maximum value at the center since the layer of fluid adjacent to the walls is stationary. The particles tracked at the center of the cell therefore possess the maximum increment in velocity due to electroosmotic flow. Since the cell is a closed compartment, the liquid displaced by electroosmosis along the walls must circulate by a backflow down the center of the tube. Since the total liquid flow in a closed cell must be zero, the appropriate value from Figure 12.10a to use for the velocity is the average of observations made at all depths. ... 

This result shows that electroosmotic flow and backflow in the capillary cancel when the factor (2r1/R — 1) equals zero. This condition corresponds to r/Rc = 0.707. Thus at 70.7% of the radial distance from the center of the capillary lies a circular surface of zero liquid flow. Any particle tracked at this position in the capillary will display its mobility uncomplicated by the effects of electroosmosis. This location may also be described as lying 14.6% of the cell diameter inside the surface of the capillary. Experimentally, then, one establishes the inside diameter of the capillary and focuses the microscope 14.6% of this distance inside the walls of the capillary. Corrections for the effect of the refractive index must also be included. Additional details of this correction can be found in the book by Shaw (1969). 

Under optimum conditions the dimensions of the cross section of the cell are such that the effects of electroosmosis are minimal. The rectangular profile of the cross section allows for both good thermal equilibration (because one dimension is short) and good optical precision (because the other dimension is longer). 

As is shown, the authors include in their derivations the influence of electro-osmotic flow. In an earlier publication R. Schlogl (144) neglected this effect. Comparing the results, one has to conclude that electroosmosis has a big influence on the concentration profiles. 

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