Electro-osmosis flow velocity

This phenomenon of electro-osmosis can be treated in mathematical form. The fact is that the velocity of flow of electrolyte, v, depends not only on its usual driving... 

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... 

To characterize a surface electrokinetically involves the measurement of one of the above electrokinetic effects. With disperse colloidal systems it is practical to measure the particle electrophoretic mobility (induced particle velocity per unit applied electric field strength). However, for a nondisperse system one must measure either an induced streaming potential or an electro-osmosis fluid flow about the surface. 

Electro-osmosis in a closed cell leads to a hydrodynamic pressure which, in turn, causes a Poiseuille-type back flow (sec. 1.6.4d and fig. 1.6.10), leading to a velocity profile as in fig. 4.8. For the, most common, cylindrical cell, the resulting velocity profile is as in fig. 4.15. The mathematical elaboration is as follows. Let 2 be the axial direction in the cylinder and r the radial one, then the fluid velocity in the z-direction at a distance r from the axis can be written as... 

Using SI units, the velocity of the electro-osmotic flow is expressed in meters per second (m/s) and the electric field in volts per meter (V/m). Consequently, in analogy to the electrophoretic mobility, the electro-osmotic mobility has the dimension square meters per volt per second. Because electro-osmotic and electrophoretic mobilities are converse manifestations of the same underlying phenomenon, the Hehnholtz-von Smoluchowski equation applies to electro-osmosis as well as to electrophoresis. In fact, when an electric field is applied to an ion, this moves relative to the electrolyte solution, whereas in the case of electro-osmosis, it is the mobile diffuse layer that moves under an appUed electric field, carrying the electrolyte solution with it. 

The flow of liquid caused by electro-osmosis displays a pluglike profile because the driving force is uniformly distributed along the capillary tube. Consequently, a uniform flow velocity vector occurs across the capillary. The flow velocity approaches zero only in the region of the double layer very close to the capillary surface. Therefore, no peak broadening is caused by sample transport carried out by the electro-osmotic flow. This is in contrast to the laminar or parabolic flow profile generated in a pressure-driven system, where there is a strong pressure drop across the capillary caused by frictional forces at the liquid-solid boundary. A schematic representation of the flow profile due... 

Alternatively, the velocity of the electro-osmotic flow can be measured by weighing the volume of the electrolyte solution displayed by electro-osmosis from the anodic to the cathodic reservoir. When detection is performed by ultraviolet (UV) absorbance, a solvent dip equal to the electro-osmotic flow appears in the electropherogram after any sample injection. In most cases, the sample solvent has a lower UV absorbance than the electrolyte... 

Figure 4. A schematic diagram of the electro-osmotic flow of medium (e.g., an electrolyte) in a capUlary caused by the flow of counter-ions as a plug, under the influence of the applied electric field, E is the convective liquid velocity from elecfro-osmosis. 43...

The above equations neglected the electro-osmotic effect. In an unobstructed capillary, the shape of the electro-osmotic flow profile is piston like. The flow velocity is constant over most of the tube cross section and drops to zero only near the tube walls. This is fortunate, as the flat flow profile of electro-osmosis will add the same velocity component to all solutes, regardless of their radial position, and thus will not cause any significant dispersion of the zone. Electro-osmotic flow causes the above equations to be modified. The migration time becomes... 

There is an essential physical s>mimetry between electro-osmosis and the streaming potential in that, for both phenomena, an applied force causes the mobile portion of a liquid phase near a stationary, electrified interface to flow. In electro-osmosis, an applied electric force causes the mobile liquid phase to move with the velocity given in Eq. 3.41. The corresponding volume flow is O Ueo where A is as defined in Eq. 3.42a. After multiplying both sides of Eq. 3.41 by A and comparing... 

Electro osmosis This technique involves the movement of a liquid relative to a stationary charged surface (e.g. a capillary or porous plug) by the application of an electric field. Experimentally, zeta potentials may be measured by this method by means of an apparatus such as that shown in Figure 10.10. The potential is supplied by electrodes, as shown in the schematic, and the transport of liquid across the tube is observed through the motion of an air bubble in the capillary providing the return flow. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/s if the surface potential (xjro) is 100 mV. 

When the porous medium saturated with the electrolyte is embodied in an external electric field E, there appears a nonzero volumetric body force within the Debye layer, which sets the ions in that region into motion. Far from the particle surfaces, this volumetric force is zero, since the solute there is neutral. However, the electrolyte is brought into motion also in the latter region as a result of the solute s viscosity. These processes lead to the appearance of an interstitial flow velocity field u(R). This velocity field, when integrated over a representative volume of the porous medium, yields a nonzero seepage velocity U in the absence of any macroscopic pressure gradient applied to the porous medium. This process is called electro-osmosis, and the velocity U is called the electro-osmotic velocity. 

---