Velocity, electro-osmotic

Fig. 4.22 Normalized electro-osmotically driven velocity profiles as a function of z for circular tube. Reprinted from Maynes and Webb (2003) with permission...

Reversed-phase separations currently dominate in CEC. As a result, the vast majority of the mobile phases are mixtures of water and an organic solvent, typically acetonitrile or methanol. In addition to the modulation of the retention, the mobile phase in CEC also conducts electricity and must contain mobile ions. This is achieved by using aqueous mixtures of salts instead of pure water. The discussion in Sect. 2 of this chapter indicated that the electro osmotic flow is created by ionized functionalities. The extent of ionization of these functionalities that directly affects the flow rate depends on the pH value of the mobile phase. Therefore, the mobile phase must be buffered to a pH that is desired to achieve the optimal flow velocity. Obviously there are at least three parameters of the mobile phase that have to be controlled (i) percentage of the organic solvent, (ii) the ionic strength of the aqueous component, and (iii) its pH value. 

Thus the coefficient a2 describes the electro-osmotic flow velocity per unit of potential gradient, i.e., the electro-osmotic mobility. 

But v/X is the electro-osmotic velocity of the fluid per unit of electric field, i.e., the electro-osmotic mobility. It is interesting to note that both the electro-osmotic mobility v/X = a2 and the streaming-current coefficient j/AP = a3 have beat proved to be equal to each other and to ltfZ/4nr. This only means that the Onsager reciprocity relation has been shown to be consistent with a simple model of some electrokinetic phenomena. 

If one compares Eqs. (6.317) and (6.314) everything is fine, except that this Stokes law approach gives a numerical factor / =, whereas the electro-osmotic approach gives/= f. It turns out that each is right for a particular set of conditions. This conclusion comes out of an accurate mathematical treatment that results in the following expression for the electrophoretic velocity ... 

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. ... 

Equations (6.4.43a-c) yield the central result of this section—the following expression for the electro-osmotic slip velocity ua under an applied potential and concentration gradient, in the Debye-Hiickel approximation for a thin double layer... 

Figure 8.5—Effect of the nature of the capillary inner wall on migration velocities If the inner wall has not been treated (glass or silica naturally have a negative polyanionic layer) the liquid is pumped from the anodic towards the cathodic reservoir. This is called the electro-osmotic flow. Thus an anion can move towards the cathode. Between pH 7 and 8. vE0S can increase by 35%. However, if the wall is coated with a nonpolar film (e.g. octadecyl) this flow does not exist.

By combining the apparent mobility and the electro-osmotic flow, which is responsible for the migration of the bulk electrolyte, it is possible to calculate the migration velocity or the electrophoretic mobility of charged species. Using equation (8.3), equation (8.5) can be written as ... 

Electrophoretic measurements by the microscope method are complicated by the simultaneous occurrence of electro-osmosis. The internal glass surfaces of the cell are usually charged, which causes an electro-osmotic flow of liquid near to the tube walls together with (since the cell is closed) a compensating return flow of liquid with maximum velocity at the centre of the tube. This results in a parabolic distribution of liquid speeds with depth, and the true electrophoretic velocity is only observed at locations in the tube where the electro-osmotic flow and return flow of the liquid cancel. For a cylindrical cell the stationary level is located at 0.146 of the internal diameter from... 

Figure 7.11 illustrates a suitable apparatus for studying electro-osmotic flow through a porous plug. Reversible working electrodes are used to avoid gas evolution. A closed system is employed, the electro-osmotic flow rate being determined by measuring the velocity of an air bubble in a capillary tube (c. 1 mm diameter) which provides a return path for the electrolyte solution. 

In electrophoresis an electric field is applied to a sample causing charged dispersed droplets, bubbles, or particles, and any attached material or liquid to move towards the oppositely charged electrode. Their electrophoretic velocity is measured at a location in the sample cell where the electric field gradient is known. This has to be done at carefully selected planes within the cell because the cell walls become charged as well, causing electro-osmotic flow of the bulk liquid inside the cell. From hydrodynamics it is found that there are planes in the cell where the net flow of bulk liquid is zero, the stationary levels, at which the true electrophoretic velocity of the particles can be measured. 

The flow velocity is linearly dependent on the electric field strength applied (veo= peo , where peo denotes the electro osmotic mobility). In glass or fused silica, linear flow velocities of 100 pm/s to 1 mm/s can be achieved with field strengths in the order of several 100 V/cm. For a typical channel cross section of 10 5 cm2 (50 x 20 pm) this results in corresponding volume flowrates in the order of 100 pl/s to 1 nl/s. 

FIGURE 3.6 A neutral (TRITC-Arg A and D), a singly charged anion (TRITC-Gly B and E), or a doubly charged anion (TRITC-Asp C and F) is continuously electrophoresed. Preferential transport of anions into the field-free channel (ff) at a tee intersection. The electro-osmotic velocity in the side or ground channel (g) has been reduced relative to that in the separation channel (sep) by selectively coating the ground channel with a viscous polymer [387]. Reprinted with permission from the American Chemical Society. 

A smooth curve is obtained which indicates a reasonable migration velocity whose value is relatively independent of pH near pH 8. Although the pH 5 value is missing as noted above, the interpolated curve crosses the velocity axis at about pH 5.25, essentially identical to the accepted pi value of 5.2 where the electrophoretic velocity is expected to be zero. (However, the net velocity at all pH values is towards the detector due to the presence of electro-osmotic flow.)... 

Another factor affecting particle velocity is the relative contribution of electro-osmotic fluid flow and electrophoresis on the particle. Since the observed velocity is the sum of the intrinsic electrophoretically induced particle velocity and fluid velocity, there exist situations where the two combine to render the particle velocity unobservable within the range discussed above. For similar reasons. there are situations where particle velocity may be observable outside the range discussed above. Choice of particle is important in being able to extract the electrokinetic information. 

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