Electroosmotic potential

Electroosmotic flow is also dependent on the zeta potential at the immobilized surface and the strength of the electric field. For electroosmosis, the flow rate generated is... 

Electroosmotic flow, 195 End column detection, 89 Energy barrier, 16 Enzyme electrodes, 172, 174 Enzyme immunoassays, 185 Enzyme inhibition, 181 Enzyme reconstitution, 178 Enzyme wiring, 178 Equilibrium potential, 15 Ethanol electrodes, 87, 178 Exchange current, 14... 

Qian and Bau [144] have analyzed such electroosmotic flow cells with embedded electrodes on the basis of the Stokes equation with Helmholtz-Smoluchowski boimdary conditions on the channel walls. They considered electrode arrays with a certain periodicity, i.e. after k electrodes the imposed pattern of electric potentials repeats itself An analytic solution of the Stokes equation was obtained in the form of a Eourier series. Specifically, they analyzed the electroosmotic flow patterns with regard to mixing applications. A simple recirculating flow pattern such as the one... 

FIGURE 31.1 Schematic design of cells for studying electroosmosis (a) and streaming potentials (b), the velocity of electroosmotic transport can be measured in terms of the rate of displacement of the meniscus in the capillary tube (in the right-hand part of the cell). 

Streaming Potential When the solution is forced through the porous solid under the effect of an external pressure P, the character of liquid motion in the cylindrical pores will be different from that in electroosmotic transport. Since the external pressure acts uniformly on the full pore cross section, the velocity of the liquid will be highest in the center of the pore, and it will gradually decrease with decreasing distance from the pore walls (Fig. 31.5). The velocity distribution across the pore is quantitatively described by the Poiseuille equation. 

Of the four electrokinetic phenomena, two (electroosmotic flow and the streaming potential) fall into the region of membrane phenomena and will thus be considered in Chapter 6. This section will deal with the electrophoresis and sedimentation potentials. 

The electroosmotic pumping is executed when an electric field is applied across the channel. The moving force comes from the ion moves in the double layer at the wall towards the electrode of opposite polarity, which creates motion of the fluid near the walls and transfer of the bulk fluid in convection motion via viscous forces. The potential at the shear plane between the fixed Stem layer and Gouy-Champmon layer is called zeta potential, which is strongly dependent on the chemistry of the two phase system, i.e. the chemical composition of both solution and wall surface. The electroosmotic mobility, xeo, can be defined as follow,... 

According to the Helmholtz-Yon Smoluchowski [2,16-18,20,21] equation, the electroosmotic velocity, veof, is related to the potential in the following way ... 

The potential is the potential difference between the plane of shear (or slipping plane) and the bulk solution. From Eq. (4), it is clear that for a given situation of water (electrolyte) in the interstitium, the Ueo is proportional to the zeta potential and to the applied field strength. Also in a real situation of EOD, it is necessary to use the so called length-averaged value of the zeta potential in order to take into account the effect of the axially variable zeta potential on the electroosmotic velocity. 

The electroosmotic velocity as defined in Eq. (1) is directly proportional to the , potential at the surface of shear defined as... 

The second parameter influencing the movement of all solutes in free-zone electrophoresis is the electroosmotic flow. It can be described as a bulk hydraulic flow of liquid in the capillary driven by the applied electric field. It is a consequence of the surface charge of the inner capillary wall. In buffer-filled capillaries, an electrical double layer is established on the inner wall due to electrostatic forces. The double layer can be quantitatively described by the zeta-potential f, and it consists of a rigid Stern layer and a movable diffuse layer. The EOF results from the movement of the diffuse layer of electrolyte ions in the vicinity of the capillary wall under the force of the electric field applied. Because of the solvated state of the layer forming ions, their movement drags the whole bulk of solution. 

While the external electrical field approach is a method directly modifying the zeta-potential of the capillary wall, it is not applicable with commercial apparatuses. The back-pressure technique, on the other hand, has the disadvantage that the flat electroosmotic flow profile is disrupted by superposition of a pressure-driven laminar flow profile hence, the efficiency of separation deteriorates. 

It has been pointed out above that electroosmotic and electrophoretic mobilities are converse manifestations of the same underlying phenomena therefore the Helmholtz-von Smoluchowski equation based on the Debye-Huckel theory developed for electroosmosis applies to electrophoresis as well. In the case of electrophoresis, is the potential at the plane of share between a single ion and its counterions and the surrounding solution. 

In the presence of EOF, the observed velocity is due to the contribution of electrophoretic and electroosmotic migration, which can be represented by vectors directed either in the same or in opposite direction, depending on the sign of the charge of the analytes and on the direction of EOF, which depends on the sign of the zeta potential at the plane of share between the immobilized and the diffuse region of the electric double layer at the interface between the capillary wall and the electrolyte solution. Consequently, is expressed as... 

Following this we derive the equation for electroosmotic flow and relate it to the zeta potential of the charged surface (Section 12.6). Section 12.7 focuses on the streaming potential and compares the zeta potentials obtained by the different methods. 

FIG. 12.6 Electroosmotic flow through a pore. If the fluid flow occurs as a result of applied pressure difference along the length of the pore, the resulting potential difference is known as the streaming potential. (Adapted with permission from Probstein 1994.)... 

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