Mobility, electro-osmotic

Thus the coefficient a2 describes the electro-osmotic flow velocity per unit of potential gradient, i.e., the electro-osmotic mobility. 

Fig. 6.138. A schematic diagram for the computation of the electro-osmotic mobility.

But v/X is the electro-osmotic velocity of the fluid per unit of electric field, i.e., the electro-osmotic mobility. It is interesting to note that both the electro-osmotic mobility v/X = a2 and the streaming-current coefficient j/AP = a3 have beat proved to be equal to each other and to ltfZ/4nr. This only means that the Onsager reciprocity relation has been shown to be consistent with a simple model of some electrokinetic phenomena. 

Electrokinetic phenomena depend on the relative motion of the phases constituting the double layer. In the treatment of electro-osmotic mobility, the electrolyte was considered to move within a stationary capillary—a moving cylinder of liquids within a static cylinder of solid. But the arguments only need relative motion the arguments would be equally valid if one considered a moving cylindrical solid within a stationary liquid. 

Another factor that controls the migration of the solute is the electro-osmotic mobility //EOS, which results in movement of the electrolyte or electro-osmotic flow. This flow is present in gel electrophoresis to a small extent and to a greater extent in capillary electrophoresis because of the internal wall of the capillary. 

The flow velocity is linearly dependent on the electric field strength applied (veo= peo , where peo denotes the electro osmotic mobility). In glass or fused silica, linear flow velocities of 100 pm/s to 1 mm/s can be achieved with field strengths in the order of several 100 V/cm. For a typical channel cross section of 10 5 cm2 (50 x 20 pm) this results in corresponding volume flowrates in the order of 100 pl/s to 1 nl/s. 

If the potential gradient V is unity, i.e., 1 e.s. unit of potential per cm., the uniform velocity, given the symbol Uo, is called the electro-osmotic mobility it is determined by the expression... 

The results of measurements by the microscopic method show that the electrophoretic mobility of the particles varies with the distance from the wall of the cell particles close to the wall move in a direction opposite to that in which those in the center migrate. In any event, the results show an increase in velocity from the walls to the center of the cell. The explanation of this fact lies in the electro-osmotic movement of the liquid a double layer is set up between the liquid and the walls of the cell and under the influence of the applied field the former exhibits electro-osmotic flow. For the purpose of obtaining the true electrophoretic velocity of the suspended particles it is neceasary to observe particles at about one-fifth the distance from one wall to the other. A more accurate procedure is to make a series of measurements at different distances from the side of the cell and to apply a correction for the electro-osmotic flow. The algebraic difference of the corrected electrophoretic velocity and the speed of the particles near the walls gives the electro-osmotic mobility of the liquid in the particular cell. If the solution contains a protein which is adsorbed on the surface of the walls of the vessel and on the particles, it is possible to compare the electrophoretic and electro-osmotic mobilities in one experiment reference to the significance of such a comparison was made on page 532. 

Using SI units, the velocity of the electro-osmotic flow is expressed in meters per second (m/s) and the electric field in volts per meter (V/m). Consequently, in analogy to the electrophoretic mobility, the electro-osmotic mobility has the dimension square meters per volt per second. Because electro-osmotic and electrophoretic mobilities are converse manifestations of the same underlying phenomenon, the Hehnholtz-von Smoluchowski equation applies to electro-osmosis as well as to electrophoresis. In fact, when an electric field is applied to an ion, this moves relative to the electrolyte solution, whereas in the case of electro-osmosis, it is the mobile diffuse layer that moves under an appUed electric field, carrying the electrolyte solution with it. 

In a capillary tube, the applied electric field E is expressed by the ratio VILj, where V is the potential difference in volts across the capillary tube of length Lj (in meters). The velocity of the electro-osmotic flow, Veo (in meters per second), can be evaluated from the migration time t of (in seconds) of an electrically neutral marker substance and the distance L, (in meters) from the end of the capillary where the samples are introduced to the detection windows (effective length of the capillary). This indicates that, experimentally, the electro-osmotic mobility can be easily calculated using the Helmholtz-von Smoluchowski equation in the following form ... 

Another model that accounts for the decrease of the electro-osmotic flow with increasing the electrolyte concentration relates the electro-osmotic mobility to the concentration of a monovalent counterion, introduced with the buffer, according to the following relationship [4] ... 

The dependence of the electro-osmotic flow on the specific adsorption of counterions in the electric double layer can be described by a model which correlates the electro-osmotic mobility to the charge density in the Stern part of the electric double layer (arising from the adsorption of counterions) and the charge density at the capillary wall (resulting from the ionization of silanol groups) [5]. According to this model, the dependence of the electro-osmotic mobihty on the concentration of the adsorbing ions (C) in the electrolyte solution is expressed as... 

The reversal of the direction of the electro-osmotic flow by the adsorption onto the capillary wall of alky-lammonium surfactants and polymeric ion-pair agents incorporated into the electrolyte solution is widely employed in capillary zone electrophoresis (CZE) of organic acids, amino acids, and metal ions. The dependence of the electro-osmotic mobility on the concentration of these additives has been interpreted on the basis of the model proposed by Fuerstenau [6] to explain the adsorption of alkylammonium salts on quartz. According to this model, the adsorption in the Stern layer as individual ions of surfactant molecules in dilute solution results from the electrostatic attraction between the head groups of the surfactant and the ionized silanol groups at the surface of the capillary wall. As the concentration of the surfactant in the solution is increased, the concentration of the adsorbed alkylammonium ions increases too and reaches a critical concentration at which the van der Waals attraction forces between the hydrocarbon chains of adsorbed and free-surfactant molecules in solution cause their association into hemimicelles (i.e., pairs of surfactant molecules with one cationic group directed toward the capillary wall and the other directed out into the solution). 

Neutral polymeric molecules, such as polysaccharides and synthetic polymers, may also adsorb onto the Stern layer, causing a variation of viscosity in the double layer with distance from the capillary wall, which affects the electro-osmotic mobility according to the following relationship [2] ... 

Electro-osmotic mobility - electro-osmotic flow (EOF)... 

Yin J, Finno RJ, Feldkamp JR. (1995). Electro-osmotic mobility measurement for kaolinite clay. Proceedings of the Specialty Conference on Geotechnical Practice in Waste Disposal, ASCE, Part 2 (of 2), New Orleans, LA. New York ASCE. February 24-26, pp. 1550-1563. 

The derivation shown below is adapted from that introduced earlier (122). The electro-osmotic velocity, ugo, is deflned at the product of the electro-osmotic mobility, pgo, and the applied electric field, E. For an applied voltage V and for a length of capillary L, we can write... 

This equation can be restated in terms of electrophoretic and electro-osmotic mobilities as follows ... 

Control of Micro-fluidics, Fig. 3 Control of a bead with significant surface charge along a figure 8. The bead has an approximate electrophoretic mobility of c = (-57.3 5.6) X 10 m V s . (By comparison, the electro-osmotic mobility of our PDMS devices is = (36.5... 

Oddy MH, Santiago JG (2(K)4) A method for determining electrophoretic and electro-osmotic mobilities using AC and DC electric field displacements. J Colloid Interface Sci 269 192-204... 

The ratio of the velocity of the EOF to the applied electric field, which expresses the velocity per unit field, is defined as electro-osmotic coefficient or, more properly, electro-osmotic mobility ([Xeo). 

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