Helmholtz-Von Smoluchowski

The Helmholtz—Von Smoluchowski equation relates the electroosmotic velocity f eof to the zeta potential in the following way ... 

The dependence of the velocity of the EOF (Ve,) on the zeta potential is expressed by the Helmholtz-von Smoluchowski equation [13] ... 

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the EOF depends on the magnitude of the zeta potential, which is determined by various factors inhuencing the formation of the electric double layer, discussed above. Each of these factors depends on several variables, such as pH, specihc adsorption of ionic species in the compact region of the double layer, ionic strength, and temperature. 

Using the SI units, the velocity of the EOF is expressed in meters/second (m s ) and the electric held in volts/meter (V m ). Consequently, the electroosmotic mobility has the dimension of m V s. Since electroosmotic and electrophoretic mobility are converse manifestations of the same underlying phenomena, the Helmholtz-von Smoluchowski equation applies to electroosmosis, as well as to electrophoresis (see below). In fact, it describes the motion of a solution in contact with a charged surface or the motion of ions relative to a solution, both under the action of an electric held, in the case of electroosmosis and electrophoresis, respectively. 

It has been pointed out above that electroosmotic and electrophoretic mobilities are converse manifestations of the same underlying phenomena therefore the Helmholtz-von Smoluchowski equation based on the Debye-Huckel theory developed for electroosmosis applies to electrophoresis as well. In the case of electrophoresis, is the potential at the plane of share between a single ion and its counterions and the surrounding solution. 

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 ... 

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