Particle electrophoretic mobilities

Here, p is defined as the electrophoretic mobility (particle velocity/ applied electric field) of a particle of radius a. C is the zeta potential, and q is the viscosity of the suspending solution./(A ), a) is Henry s function and depends on the Debye length (see Section 5.5.2). This variable represents the thickness of the electric double layer. 

There are a number of complications in the experimental measurement of the electrophoretic mobility of colloidal particles and its interpretation see Section V-6F. TTie experiment itself may involve a moving boundary type of apparatus, direct microscopic observation of the velocity of a particle in an applied field (the zeta-meter), or measurement of the conductivity of a colloidal suspension. 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

Electroultrafiltration (EUF) combines forced-flow electrophoresis (see Electroseparations,electrophoresis) with ultrafiltration to control or eliminate the gel-polarization layer (45—47). Suspended colloidal particles have electrophoretic mobilities measured by a zeta potential (see Colloids Elotation). Most naturally occurring suspensoids (eg, clay, PVC latex, and biological systems), emulsions, and protein solutes are negatively charged. Placing an electric field across an ultrafiltration membrane faciUtates transport of retained species away from the membrane surface. Thus, the retention of partially rejected solutes can be dramatically improved (see Electrodialysis). 

Table 13. Electrophoretic mobility (U) and surface charge density (a) of particles, Im Hb in various media...

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

Gorin has extended this analysis to include (1) the effects of the finite size of the counterions in the double layer of spherical particles [137], and (2) the effects of geometry, i.e. for cylindrical particles [2]. The former is known as the Debye-Huckel-Henry-Gorin (DHHG) model. Stigter and coworkers [348,369-374] considered the electrophoretic mobility of polyelectrolytes with applications to the determination of the mobility of nucleic acids. 

O Brien, RW White, LR, Electrophoretic Mobility of a Spherical Colloidal Particle, Journal of the Chemical Society, Faraday Transactions 74, 1607, 1978. 

Ohshima, H Kondo, T, Electrophoretic Mobility and Donnan Potential of a Large Colloidal Particle with a Surface Charge Layer, Journal of Colloid and Interface Science 116, 305, 1987. O Neil, GA Torkelson, JM, Modeling Insight into the Diffusion-Limited Cause of the Gel Effect in Free Radical Polymerization, Macromolecules 32,411, 1999. 

The properties of the filter-cake formed by macroscopic particles can be significantly influenced by certain organic additives. The overall mechanism of water-soluble fluid loss additives has been studied by determining the electrophoretic mobility of filter-cake fines. Water-soluble fluid loss additives are... 

The velocity of particle migration, v, across the field is a function of the surface charge or zeta potential and is observed visually by means of an ultramicroscope equipped with a calibrated eyepiece and a scale. The movement is measured by timing the individual particles over a certain distance, and the results of approximately 10-15 timing measurements are then averaged. From the measured particle velocity, the electrophoretic mobility (defined as v/E, where E is the potential gradient) can be calculated. 

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 relation between electrophoretic mobility y and the surface properties of the particle (usually modeled as an ionic double layer for aqueous systems) is a classical problem in colloid science. 

A second possibility is that the Au particles scavenge electrons from the reaction electrodes, walls and solvent. This is the explanation we favor at the present time since we have been able to effect changes in electrophoretic mobilities by supplying electrical potential to the colloid solution as the particles form,( l ) and the fact that such charging has been reported before, for example with oil droplets in water.(43)... 

It is interesting to compare these results with the electrophoretic measurements made under identical electrolyte concentrations. Figure 8 shows that the variation of electrophoretic mobility with sodium chloride concentration is different for the bare and the PVA-covered particles. For the bare particles, the mobility remains constant up to a certain salt concentration, then increases to a maximum and decreases sharply, finally approaching zero. The maximum in electrophoretic mobility-electrolyte concentration curve with bare particles has been explained earlier (21) by postulating the adsorption of chloride ions on hydrophobic polystyrene particles. In contrast, for the PVA-covered particles, the mobility decreases with increasing electrolyte concentration until it approaches zero at high salt concentration. 

Figure 8. Electrophoretic mobility versus electrolyte concentration (NaCl) for different-size particles (o) 190nm particles (A) 400nm particles open points for bare particles and closed points for particles covered with Vinol-107 at saturation.

Initial studies were made with the Rank Bros, electrophoresis unit, using the dilute supernatant suspension over a dispersion of 3.33g of carbon black per liter of dodecane equilibrated for 24 hours with the added 0L0A-1200. The electrophoretic mobility (u) of 1-3 pm clumps of particles was observed at a field of 100 volts per centimeter. The zeta-potentials ( ) were calculated... 

As the redispersion region may be the result of a charge reversal, the electrophoretic mobilities of the MCC sols as a function of NaCl concentration were determined. No charge reversal was detected and the mobility of the particles decreased from 3.5 to 2.6 mobility units in a linear manner with increasing salt concentration indicating that the redispersion region was not caused by charge reversal. 

Ohshima, H. and Kondo, T. (1987). Electrophoretic mobility and Donnan potential of a large colloidal particle with a surface-charge layer, J. Coll. Interf. Sci., 116, 305-311. 

Carrique F, Arroyo FJ, Jimenez ML, Delgado Av. Influence of double-layer overlap on the electrophoretic mobility and DC conductivity of a concentrated suspension of spherical particles. J. Phys. Chem. B 2003 107 3199-3206. 

Microelectrophoresis (electrophoretic mobility) . This involves the measurement of particle charge in an applied field. For paper furnishes, the supernatant solution—which contains finely divided colloidal matter, is usually removed and used to conduct the measurement. It must be questioned therefore as to how reflective this is of the charge characteristics of the larger particles and fibres which settle. However, as it is the colloidal fraction which requires to be flocculated to assist retention during drainage, it is still a useful measurement. 

Figure 7.17 Effect of pH on the electrophoretic mobility of AKD emulsion particles and of a bleached Kraft pulp.

The zeta potential can be measured by electrophoresis, which determines the velocity of particles in an electric field of known strength [144]. This particle velocity, v, can then be related to the electrical field strength, E, as the electrophoretic mobility, fi. This is shown by... 

Electrophoretic mobility measurements can be performed by laser Doppler anemometry (LDA). LDA is fast and capable of high resolution of particle velocities [144]. It measures particle velocity, which is measured in the stationary... 

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