Velocity electroosmotic

This leads to a body force pgE on the Debye layer, which begins to move and then by viscous drag pulls the charge neutral bulk liquid along. If no electrochemical processes occurs at the electrodes, the motion stops after a very short time (of the order of microseconds) when the electrodes are screened by the formation of a Debye layer around them. If, however, electrochemical processes, for example, electrolysis, take place at the electrodes, such a charge buildup is prevented, and electrical currents can flow in the system. We derive an expression for the resulting EO velocity fleld in the liquid below. 

Let us estimate the EO velocity produced in a fine capillary by uniform electric field applied along the axis. It may be remembered from the previous section that for electrolyte flow, when electroneutrality is not satisfied, the Lorentz force should be added to the momentum equation. The momentum equation is 

/surf is the surface force, that is, V f, and is the body force, that is, gravitational ipg) or electric body force per unit volume peE). For incompressible flow of constant velocity, /surf = We write the momenmm equation as 

Assuming inertia free flow with no pressure gradient, the above equation simplifies to 

For a long capillary, fully developed condition can be assumed, that is, = 0 and u = u y). Therefore, we have 

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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 electroosmotic velocity is also characterized by a mobility, namely, the electroosmotic mobility ( eofX... 

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... 

Equation (6) confirms that the electroosmotic velocity decreases with the square root of the salt concentration in the buffer. This trend is demonstrated in Fig. 26 [110]. However, the increase in concentration of the electrolyte also increases the conductivity of the mobile phase and leads to a rapid increase in current. High... 

In the section General Principles, a comprehensive description is given of the basic principles of the capillary electrophoretic separation process. The concepts of electrophoretic mobility and electroosmotic mobility as well as band dispersion phenomena and resolution are described, using the equations listed in Table 3. A remarkable difference exists between the equations in both chapters in which the electroosmotic velocity and/or the electroosmotic mobility is used. In the Ph.Eur., the terms 4-feo and 4-/teo are used, whereas in the USP the terms feo and Pco are used in the corresponding equations, with the sentence added The sum or the difference between the two velocities (v p and v o) is used depending on whether the mobilities act in the same or opposite directions. ... 

The electroosmotic velocity n od in CEC can be defined from the von Smoluchowski equation ... 

Dittmann, M. M., and Rozing, G. P. (1997). Capillary electrochromatography investigation of the influence of mobile phase and stationary phase properties on electroosmotic velocity, retention, and selectivity. J. Microcolumn Sep. 9, 399-408. 

The analysis of this effect in a closed cylindrical cell is obtained by subtracting from the electroosmotic velocity vEO the velocity of flow vP through a capillary given by Poiseuille s equation (Equation (4.18)) ... 

The constant of proportionality between electroosmotic velocity, ueo, and applied field is called electroosmotic mobility, p.eo. 

Electroosmotic velocity is measured by adding to the sample a neutral molecule to which the detector responds. 

Solution Electroosmotic velocity is found from the migration time of the neutral marker ... 

The inside capillary wall controls the electroosmotic velocity and provides undesired adsorption sites for multiply charged molecules, such as proteins. A fused-silica capillary should be prepared for its first use by washing for 15 min each (> 20 column volumes) with 1 M NaOH and 0.1 M NaOH, followed by run buffer ( —20 mM buffer). For subsequent use at high pH, wash for 10 s with 0.1 M NaOH, followed by deionized water and then by at least 5 min with run buffer.28 If the capillary is being run with pH 2.5 phosphate buffer, wash between runs with 1 M phosphoric acid, deionized water, and run buffer.29 When changing buffers, allow at least 5 min of flow for equilibration. For the pH range 4-6, at which equilibration of the wall with buffer is very slow, the capillary needs frequent regeneration with... 

Electroosmotic velocities of buffered solutions are shown for a bare silica capillaiy and one with aminopropyl groups (silica—Si—CHiCHiCHjNlL) covalently attached to the wall. A positive sign means that flow is toward the cathode. Explain the signs and relative magnitudes of the velocities. 

Optimal detection potential, separation voltage, and injection time/ voltage are used to determine parameters such as electroosmotic velocity (ueo = Leff/tm) and mobility (/[Pg.1282]

Figure 1.17 Schematic of a micro channel equipped with many electrodes at the upper (U ) and lower (Lf) walls for control of the C, potential. The arrows in the channel denote the directions of the electroosmotic velocities creating one type of flow pattern, here a counter-current arrangement of top and bottom flows (top) alternating-flow arrangement, demonstrating another type of control over the potential (bottom) [28] (by courtesy of ACS).

In electroosmosis, the stationary and mobile phases are exchanged in relation to electrophoresis. As measurement of the rate of movement of a liquid through a capillary is difficult, the force that it exerts is measured, i.e. the electroosmotic pressure, or, alternatively, the volume of liquid transported through a capillary in a given time interval. The electroosmotic velocity, veo, is... 

Electroosmotic mobility (in capillary electromigration), u or (teo -> Electroosmotic velocity, i/eo, divided by -> electric field (strength), E. 

Electroosmotic velocity, i/eo — See electroosmosis. In -> capillary electromigration, this velocity is... 

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