Electrophoretic mobility, velocity hydrodynamics

In a free solution, the electrophoretic mobility (i.e., peiec, the particle velocity per unit applied electric field) is a function of the net charge, the hydrodynamic drag on a molecule, and the properties of the solutions (viscosity present ions—their concentration and mobility). It can be expressed as the ratio of its electric charge Z (Z = q-e, with e the charge if an electron and q the valance) to its electrophoretic friction coefficient. Different predictive models have been demonstrated involving the size, flexibility, and permeability of the molecules or particles. Henry s theoretical model of pdcc for colloids (Henry, 1931) can be combined with the Debye-Hiickel theory predicting a linear relation between mobility and the charge Z ... 

Practical applications of electrophoresis usually associate with the migration of particles in the vicinity of solid boundaries subject to an external electric field. Several examples have been mentioned in the Introduction section. The electrostatic and hydrodynamic interactions between the particle and the boundary wall will affect the particle s electrophoretic mobility. In this section, boundary effects on the electrophoretic velocity will be presented and discussed. 

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. 

Some types of electrophoretic cells are stationary layer problem free , but in the other cells the electroosmotic flow can lead to erroneous results. The observed velocity of particles is a sum of the electroosmotic flow of the fluid and the velocity of particles with respect to the fluid. The latter is a function of the potential of the particles and the former is a function of the position in the cell cross section. Hydrodynamic calculations make it possible to find the stationary levels, i.e. the positions in the cell cross section where the electroosmotic flow equals zero. Certainly the position of stationary levels in commercial electrophoretic cells can be found in the user s manual, and there is no need to perform any calculations. The fastest method to determine the electrophoretic mobility is from the velocity at one stationary level, but such a procedure can lead to substantial errors. For example, when the cell position is adjusted at room temperature and then measurements taken... 

Reliable, though relative, information about the size of ions in aqueous media can be obtained from data on the electrophoretic mobility of these ions [160], as the velocity of their movement in an electric field is direcdy proportional to their charge and inversely proportional to their hydrodynamic radius. According to these estimations (Table 12.3), the size of hydrated cations and anions decreases according to the following series ... 

Trinh et al. [399] derived a number of similar expressions for mobility and diffusion coefficients in a similar unit cell. The cases considered by Trinh et al. were (1) electrophoretic transport with the same uniform electric field in the large pore and in the constriction, (2) hindered electrophoretic transport in the pore with uniform electric fields, (3) hydrodynamic flow in the pore, where the velocity in the second pore was related to the velocity in the first pore by the overall mass continuity equation, and (4) hindered hydrodynamic flow. All of these four cases were investigated with two different boundary condi-... 

---