Electrokinetic radius

Fig. 12.18. Dimensionless water permeability as functions of electrokinetic radius at different...

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... 

If the electric field E is applied to a system of colloidal particles in a closed cuvette where no streaming of the liquid can occur, the particles will move with velocity v. This phenomenon is termed electrophoresis. The force acting on a spherical colloidal particle with radius r in the electric field E is 4jrerE02 (for simplicity, the potential in the diffuse electric layer is identified with the electrokinetic potential). The resistance of the medium is given by the Stokes equation (2.6.2) and equals 6jtr]r. At a steady state of motion these two forces are equal and, to a first approximation, the electrophoretic mobility v/E is... 

The quantity in the ordinary theory of electrolytes which corresponds to the potential in electrokinetics, is the potential due to an ion, at a distance from its centre equal to its radius, i.e. half the distance of closest approach of two ions. In the case of moderately complex charged particles such as the ionic micelle of paraffin chain salts, soaps, etc., the potential is the potential in the water just outside the micelle with its adherent gegenions , the small ions of opposite sign which, according to G. S. Hartley, adhere to the micelle and very considerably affect its motion in an electric field.1... 

Electroklnetlc Injection In electrokinetic injection, the sample is introduced in the capillary by applying a voltage (in general, lower than that used for the separation), while the injection end is dipped in the sample (Fig. 3.6). Under these conditions, the analytes contained in the sample are injected by electromigration as well as by electroosmotic flow. The amount of sample loaded increases with the electrophoretic mobility of analyte, the electroosmotic flow mobility, the inner radius, the voltage, the sample concentration, and the injection time. The amount loaded will decrease with the capillary length. 

Electrophoresis The most familiar electrokinetic experiment consists of setting up an electric field, E, in a solution containing charged particles and determining their velocity. The particle velocity, V, is measured by direct microscopic observation at the stagnation point (i.e., zero velocity point for electro-osmosis at the radius 0.707i c) in a capillaiy as shown in Figure 9.19. The zeta potential is then computed... 

The two equations above indicate that the pressure drop increases and the average velocity decreases dramatically with decreasing channel radius. Thus, it is obvious, why electrokinetic pumping procedures find widespread application in fluid systems with micrometer dimensions. 

Capillary zone electrophoresis (CZE), micellar capillary electrokinetic chromatography (MECC), capillary gel electrophoresis (CGE), and affinity capillary electrophoresis (ACE) are CE modes using continuous electrolyte solution systems. In CZE, the velocity of migration is proportional to the electrophoretic mobilities of the analytes, which depends on their effective charge-to-hydrodynamic radius ratios. CZE appears to be the simplest and, probably, the most commonly employed mode of CE for the separation of amino acids, peptides, and proteins. Nevertheless, the molecular complexity of peptides and proteins and the multifunctional character of amino acids require particular attention in selecting the capillary tube and the composition of the electrolyte solution employed for the separations of these analytes by CZE. 

These results show that at high concentrations (above 7T0- mole/cm ), addition of surfactant increases the degree of retardation of the bubble surface. Thus, under the condition Xb > X th adsorption can considerably deviate from the mean value only in the vicinity of the leading pole of the bubble and the electrokinetic potential can be calculated from the equilibrium adsorption value. When the concentration of the surfactant decreases, retards to a lesser extent the motion of the surface. The condition Xb < Xo is realised when the removal of surfactant to the rear of the bubble is possible, and adsorption is much lower than the equilibrium value over almost the whole bubble surface. This statement needs a confirmation if values of adsorption less than 10 ° mole/cm are taken into account since then a deviation of the electrokinetic potential from Stem potential was observed (Sotskova et al. 1982). Substituting this value and the velocity of the buoyant bubble with a radius of 150 pm condition (8.98) is fulfilled. 

The treatment given above of the diffuse double layer is based on the assumption that the ions in the electrolyte are treated as point charges. The ions are, however, of finite size, and this limits the inner boundary of the diffuse part of the double layer, since the center of an ion can only approach the surface to within its hydrated radius without becoming specifically adsorbed (Fig. 6.4.2). To take this effect into account, we introduce an inner part of the double layer next to the surface, the outer boundary of which is approximately a hydrated ion radius from the surface. This inner layer is called the Stern layer, and the plane separating the inner layer and outer diffuse layer is called the Stern plane (Fig. 6.4.2). As indicated in Fig. 6.4.2, the potential at this plane is close to the electrokinetic potential or zeta ( ) potential, which is defined as the potential at the shear surface between the charge surface and the electrolyte solution. The shear surface itself is somewhat arbitrary but characterized as the plane at which the mobile portion of the diffuse layer can slip or flow past the charged surface. 

Brooks and coworkers [136,141] measured drop electrophoretic mobilities in ATPSs. They were surprised to discover that the sign of the droplet mobilities was opposite to that predicted from the phosphate partition and the Donnan potential. They also found mobility to be directly proportional to drop radius, which is a contradiction of standard colloid electrokinetic theory [144]. Levine [140] and Brooks et al. [141] hypothesized that a dipole potential at the phase boundary oriented in a way that reverses the potential gradient locally is responsible for the paradox of the sign of electrophoretic mobilities of ATPS droplets. 

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