Electroosmosis

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 

An interesting biological application of electroosmosis is in the analysis of flow in renal tubules [70]. 

Another secondary effect in electrophoretic techniques is electroosmosis, sometimes called electroendosmosis. 

In a fused silica capillary, the surface is negatively charged when the pH is 3. The positive counterions dose to the surface are tightly bound, while the more loosely bound cations in the diffuse part of the double layer can move under the influence of an applied electric field. Because these cations are solvated, and the solvent molecules can hydrogen bond to other solvent molecules, the solvent is pulled toward the cathode. It should be mentioned that this effect occurs only in surface-charged capillaries with a rather narrow inner diameter (ID). 

With a negatively charged surface, the osmotic flow goes toward the cathode. If the surface is positiveiy charged, the osmotic flow is reversed, now toward the anode. 

In electrophoretic separation techniques, as opposed to the chromatographic techniques, there is no mobile phase or stationary phase. In zone electrophoresis (a kinetic process), the migration length (L = u-t) is proportional to the applied voltage (u=ju E) and time, and separation of analytes with different charge/size ratio (q/tj is obtained. 

Electrophoretic separation can also be carried out using techniques called moving boundary, isotachophoresis (both are kinetic processes), and isoelectric focusing (lEF) (equilibrium process). Zone electrophoresis and isoelectric focusing are the techniques mostly used for analytical separations. 

Besides electrophoretic migration, analytes in CE move by a process called electroosmosis (or electroendoosmosis). This phenomenon, occurring also in slab gel electrophoresis, produces electroosmotic flow, the electrically driven flow of the liquid within the capillary. However, while in slab gel electrophoresis the gel matrix reduces EOF to an annoyance, in CE this liquid flow can have a significant effect on the separation process. 

When electrophoresis begins, the voltage difference set up in the capillary causes the migration of the mobile positive ions (cations) toward the cathode. This ionic movement in turn osmotically drags fluid, the water in the capillary, in the same direction. It is this movement of fluid that generates the EOF. The velocity of this flow is increased with the dielectric constant of the fluid and the magnitude of the zeta potential, and decreased by the solution s viscosity. 

With bare (uncoated) silica capillaries, osmotic flow is from the anodic to the cathodic end. However, if the capillary is coated with a positive surface, the osmotic flow would be reversed. Although extremely variable in dependence of experimental conditions, EOF is generally in the order of fractions of milliliters per minute it can be empirically measured by injecting a neutral marker (e.g., acetone). 

A peculiarity of EOF is that originating at the walls of the capillary, its flow profile is almost flat, without the parabolic shape typical of pressuregenerated laminar flow, as in HPLC (Fig. 3.3). It is of interest to note that in comparison to a parabolic profile, a flat profile limits the broadening of the zones during migration in the capillaries. 

The usual arrangement of a capillary electropherograph necessitates that injection take place at the anodic end, with detection occurring close to the cathodic end of the capillary. Considering also that EOF is generally oriented toward the cathode and that it is greater than the electrophoretic velocity of most analytes, it follows that cationic, neutral, and anionic analytes will reach the detector in that order. 

It may be appreciated that electrokinetic phenomena are determined by electric properties at the plane of shear rather than at the real surface. In the following sections of this chapter, the relation between the measured property and is further analyzed. This is done for electroosmosis, electrophoresis, streaming current, and streaming potential. The sedimentation potential will not be discussed any further, because in practice this phenomenon does not play an important role. The electrokinetic charge density may then be derived from using the theory for the diffuse electrical double layer. 

The situation is more complicated when the surface comprises a permeable zone containing fixed charged groups. This is, for instance, the case for surfeces coated by a layer of polyelectrolytes. Coatings of polyelectrolytes are often present at biological surfaces, such as bacterial cell walls. We pay attention to these systems in Section 10.3.3. 

2 DERIVATION OF THE ZETA POTENTIAL FROM ELECTROKINETIC PHENOMENA 

FIGURE 10.2 Electroosmosis (a) distribution of ions in a charged capillary, (b) forces acting on a volume element of liquid. 

The velocity profile according to Equation 10.6 is depicted in Eigure 10.3. Neglecting the deviations near the shear plane the electroosmotic volume flux is given by 

The same phenomenon takes place if the moving phase is the solution, rather than particles. Thus, if an electric field is applied to the interface between a solid phase and a solution (i.e. the solid phase is a motionless charged wall, rather than a disperse medium), the solution starts moving. This motion is known as electroosmosis. 

It is obvious that only the relative motion of phases matters, therefore both phenomena should have the same physical nature even though they manifest themselves differently. 

The flow of electrolyte solution along a wall gives rise to an effect known as the flow potential. This effect essentially does not differ from the appearance of sedimentation potential. 

Electroosmosis is used in many technical applications, for example, in removal of moisture from the ground during construction, in dehydration of industrial waste, in biological processes, etc. 

Consider electroosmotic motion in a porous medium. We can model this medium by a system of parallel cylindrical microcapillaries. Consider one of such capillaries and assume that its wall carries a charge. The motion of Uquid in the 

In all the sections of this chapter until now we have focused attention on electrophoresis. We have seen that the potential at the surface of shear can be measured from electrophoretic mobility measurements, provided the system complies with the assumptions of a manageable model. One feature that has been conspicuously lacking from our discussions is any comparison between electrophoretically determined values of f and potential values determined by another method. The reasons for this are twofold  

Other techniques for measuring f are contingent on the same set of assumptions associated with electrophoresis and therefore do not constitute an independent determination. 

Uncertainty as to the location within the double layer at which the shear surface is located makes it difficult to relate f to other double-layer potentials, such as p0 as determined from knowledge of the concentration of potential-determining ions (see Equation (11.1)). 

In this section we describe electroosmosis and in the following section the streaming potential. These two electrokinetic techniques also permit the evaluation of f, but are subject to objection 1. In Section 12.8 we examine in greater detail the location of the surface of shear, which is the essence of objection 2 above. 

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.) 

An external electric field E is applied parallel to the wall in the x direction, whereas the y direction, is counted positively perpendicular to the wall which is located at y = 0, 

The basic equation of motion is the Navier Stokes Equation + ov.gradv = pg — VP + nAv + f  

For low flow rates (low Reynolds numbers), and stationary flows the left-hand 

In a first approach we neglect the gravity and pressure effects and get 

The external electric field is applied along the x direction, as well as the resulting velocity of the solvent. 

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The situation in electroosmosis may be reversed when the solution is caused to flow down the tube, and an induced potential, the streaming potential, is measured. The derivation, again due to Smoluchowski [69], begins with the assumption of Poiseuille flow such that the velocity at a radius x from the center of the tube is... 

E. Interrelationships in Electrokinetic Phenomena In electroosmosis, the volumetric flow and current are related through... 

The electroosmotic flow profile is very different from that for a phase moving under forced pressure. Figure 12.40 compares the flow profile for electroosmosis with that for hydrodynamic pressure. The uniform, flat profile for electroosmosis helps to minimize band broadening in capillary electrophoresis, thus improving separation efficiency. 

Electron tubes Electron tunneling Electrooptic materials Electrooptics Electroosmosis... 

There is an additional pressure drop across the cake, developed by electroosmosis, which leads to increased flow rates through the cake and further dewatering at the end of the filtration cycle. The filtration theory proposed for electrofiltration assumes the simple superposition of electroosmotic pressure on the hydraulic pressure drop. 

The physical separation of charge represented allows externally apphed electric field forces to act on the solution in the diffuse layer. There are two phenomena associated with the electric double layer that are relevant electrophoresis when a particle is moved by an electric field relative to the bulk and electroosmosis, sometimes called electroendosmosis, when bulk fluid migrates with respect to an immobilized charged surface. 

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... 

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. 

Process Concept The application of a direct elecdric field of appropriate polarity when filtering should cause a net charged-particle migration relative to the filter medium (electrophoresis). The same direct electric field can also be used to cause a net fluid flow relative to the pores in a fixed filter cake or filter medium (electroosmosis). The exploitation of one or both of these phenomena form the basis of conventional electrofiltration. 

The mechanism by which analytes are transported in a non-discriminate manner (i.e. via bulk flow) in an electrophoresis capillary is termed electroosmosis. Eigure 9.1 depicts the inside of a fused silica capillary and illustrates the source that supports electroosmotic flow. Adjacent to the negatively charged capillary wall are specifically adsorbed counterions, which make up the fairly immobile Stern layer. The excess ions just outside the Stern layer form the diffuse layer, which is mobile under the influence of an electric field. The substantial frictional forces between molecules in solution allow for the movement of the diffuse layer to pull the bulk... 

Electroosmosis is used in medicine for introducing into the body continuously or periodically liquid medications in rigorously defined quantities. 

Four different electrokinetic processes are known. Two of them, electroosmosis and electrophoresis, were described in 1809 by Ferdinand Friedrich Renss, a professor at the University of Moscow. The schematic of a cell appropriate for realizing and studying electroosmosis is shown in Fig. 31.1a. An electrolyte solution in a U-shaped cell is divided in two parts by a porous diaphragm. Auxiliary electrodes are placed in each of the half-cells to set up an electric held in the solution. Under the inhuence of this held, the solution starts to how through the diaphragm in the direction of one of the electrodes. The how continues until a hydrostahc pressure differential (height of liquid column) has been built up between the two cell parts which is such as to compensate the electroosmotic force. 

In 1861, Georg Hermann Quincke described a phenomenon that is the converse of electroosmosis When an electrolyte solution is forced through a porous diaphragm by means of an external hydrostatic pressure P (Fig. 31.1ft), a potential difference called the streaming potential arises between indicator electrodes placed on different sides of the diaphragm. Exactly in the same sense, in 1880, Friedrich Ernst Dorn described a phenomenon that is the converse of electrophoresis During... 

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). 

The electrokinetic processes can actually be observed only when one of the phases is highly disperse (i.e., with electrolyte in the fine capillaries of a porous solid in the cases of electroosmosis and streaming potentials), with finely divided particles in the cases of electrophoresis and sedimentation potentials (we are concerned here with degrees of dispersion where the particles retain the properties of an individual phase, not of particles molecularly dispersed, such as individual molecules or ions). These processes are of great importance in particular for colloidal systems. 

Auxiliary electrodes are placed into the solution to set up the electric field that is needed to produce electrophoresis or electroosmosis. Under these conditions an electric current passes through the solution and the external circuit its value depends on the applied voltage and on solution conductivity. The lower this conductivity, the higher will be the electric field strength E (or ohmic voltage drop) in the solution that can be realized at a given value of current. 

Like the velocity of electroosmosis, the value of the streaming potential is independent of geometric parameters of the porous sohd through which the liquid is forced. 

Electrophoresis The physical situation of relative motions of a solution and another (insulating) phase during electrophoresis is exactly the same as in electroosmosis. Hence, the linear velocity of a cylindrical particle (which is the equivalent of a cylindrical pore) is given by the value following from Eq. (31.4). With particles of dilferent shape, this velocity can be written as... 

Interrelations Between the Electrokinetic Processes Equation (31.4) for electroosmosis and Eq. (31.10) for the streaming potential, as well as the analogous equations for the other two electrokinetic processes, yield the relation... 

Electroosmosis is used to remove liquid (moisture) from different porous solids (e.g., in drying soil for building purposes, which improves the bond between the foundations and the soil). A combination of electrophoresis and electroosmosis is sometimes used to dry peat or clay. In this way, the water content of peat can be reduced from 90% to 55-60%. Unfortunately, the energy required for a further reduction of the water content is very high. 

Ishii, C. Y. and Boxer, S. G. (2006) Controlling two-dimensional tethered vesicle motion using an electric field interplay of electrophoresis and electroosmosis. Langmuir, 22, 2384—2391. 

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. 

E > Ec, increases in permeate flux rate are due only to electroosmosis in the filtration medium. 

Jorgenson, J. W. and Lukacs, K. D, High-resolution separations based on electrophoresis and electroosmosis, /. Chromatogr. 218, 209, (1981)... 

Ericson, C., Holm, J., Ericson, T., and Hjerten, S., Electroosmosis- and pressure-driven chromatography in chips using continuous beds, Anal. Chem. 72, 81,... 

Flow Capillary forces, gravitation, forced flow Electroosmosis... 

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