Mobility expression charged particles

The proportionality factor u, is a transport property, like thermal conductivity or diffusivity, called the mobility because it measures how mobile the charged particles are in an electric field. The mobility may be interpreted as the average velocity of a charged particle in solution when acted upon by a force of 1 N mol . The units of mobility are therefore mol N ms or mol s kg . The concept of mobility is quite a general one, since it can be used for any force that determines the drift velocity of a particle (a magnetic force, centrifugal force, etc.). The flux relation can also be expressed in terms of mass by... 

If we were to forget that the flow of current is due to a random motion which was already present before the field was applied—if we were to disregard the random motion entirely and assume that each and every electron, in the uniform field X, moves with the same steady velocity, the distance traveled by each electron in unit time would be the distance v used in the construction of Fig. 16 this is the value which would lead to a current density j under these assumptions, since all electrons initially within a distance v of the plane AB on one side would cross AB in unit time, and no others would cross. Further, in a field of unit intensity, the uniform velocity ascribed to every electron would be the u of (34) this quantity is known as the mobility of the charged particle. (If the mobility is given in centimeters per second, the value will depend on whether electrostatic units or volts per centimeter are used for expressing the field strength.)... 

Ohshima, H. and Kondo, T. (1989). Approximate analytic-expression for the electrophoretic mobility of colloidal particles with surface-charge layers, J. Coll. Interf. Sci., 130, 281-282. 

The dimensionless retention parameter X of all FFF techniques, if operated on an absolute basis, is a function of the molecular characteristics of the compounds separated. These include the size of macromolecules and particles, molar mass, diffusion coefficient, thermal diffusion coefficient, electrophoretic mobility, electrical charge, and density (see Table 1, Sect. 1.4.1.) reflecting the wide variablity of the applicable forces [77]. For detailed theoretical descriptions see Sects. 1.4.1. and 2. For the majority of operation modes, X is influenced by the size of the retained macromolecules or particles, and FFF can be used to determine absolute particle sizes and their distributions. For an overview, the accessible quantities for the three main FFF techniques are given (for the analytical expressions see Table l,Sect. 1.4.1) ... 

For particles, the electrophoretic mobility pe is related to their surface charge density, which is best expressed in terms of the -potential. For moderately charged particles ( -potential < 25 mV), this relationship is given by Eq. (75), where the function f(KDdH) varies smoothly between 1.0 and 1.5 as kd varies between very small and very large values [264] ... 

Equation (21.62) shows that as k co, p tends to a nonzero limiting value p°°. This is a characteristic of the electrokinetic behavior of soft particles, in contrast to the case of the electrophoretic mobility of hard particles, which should reduces to zero due to the shielding effects, since the mobility expressions for rigid particles (Chapter 3) do not have p°°. The term p°° can be interpreted as resulting from the balance between the electric force acting on the fixed charges ZeN)E and the frictional force yu, namely. 

AC) Electrophoresis is the motion of electrically charged particles under the influence of an AC electric field. For thin electrical double layers a Ad 1), dynamic mobility of spherical particles can be expressed as [9]... 

Analytical formulas in closed forms for the diffusiophoretic mobility of a charged sphere [6] and circular cylinder [7] of radius a in symmetric electrolytes at low surface charge density <7 (valid for ( up to 50 mV) and arbitrary Ka have been obtained. The diffusiophoretic velocity of the charged particle can be expressed as an expansion in powers of ( ... 

Electrophoresis refers to the motion of a charged particle in a solution in response to an applied electric field. The electrophoresis technique has been widely used to characterize the electrokinetic properties of charged particle-liquid interfaces. In the electrophoresis method, fine particles (usually of 1 pm in diameter) are dispersed in a solution. Under an applied electric field, the particle electrophoresis mobility, vg, defined as the ratio of particle velocity to electric field strength, is measured using an appropriate microscopic technique. The particle -potential is determined from the measured electrophoresis mobility, ve, by using the Smoluchowski equation expressed as... 

The charge or zeta ( ) potential of the filler particle (i.e. the charge at the plane of shear between the particle s diffuse double layer and the bulk liquid phase) can be obtained by measuring its mobility in an applied electric field of known magnitude. The mobility is a function of the field gradient and is therefore expressed as a speed per unit potential gradient (/im/s/V/cm). Mobility and therefore zeta potential are both a function of pH (Figure 6.4). 

The mobility depends on both the particle properties (e.g., surface charge density and size) and solution properties (e.g., ionic strength, electric permittivity, and pH). For high ionic strengths, an approximate expression for the electrophoretic mobility, pc, is given by the Smoluchowski equation ... 

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 ... 

With increasing ionic strength, some charges of the protein particle are neutralized by buffer ions of the opposite sign, according to the theory of Debye and Hiickel, and mobility consequently decreases. Mathematical expression of this phenomenon may be given by the equation of Audubert (A8) ... 

Some writers have urged that the results of electrokinetic measurements should be expressed in terms similar to those usual with electrolytes containing small ions, i.e. of mobilities and valencies, and not as potentials. One difficulty here is that, although the mobility is measured, it is very seldom that the actual magnitude or density of the charge on a colloidal particle or surface is known. The charge on, or valency of, a colloidal particle must depend on its size, and may also depend on its shape. The potential probably depends but little on either. 

The transport of particles by an electrical field is called electrophoresis. The electrophoretic mobility (U), which is the ratio of velocity of moving particles (v) to the strength (potential) of the electrical field (E), is related to the number of charges (Z) and the magnitnde of the particle charge (e) by the expression ... 

The sum in Eq. 3.39 is over all charged species (with valence Z,) in the mobile liquid phase. Equations 3.37 and 3.39 are the principal electrophoretic expressions applied to soil clay particles. Clearly, Eq. 3.37 is. dependent on fewer assumptions concerning the structure of the interfacial region near a soil particle than is Eq. 3.39. However, the present consensus is that the use of DDL theory to derive Eq. 3.39 is a valid step for 1 1 < 0.1 V and electrolyte concentrations below about 10 mol m". ... 

---