Helmholtz-Smoluchowski equation. See

Smoluchowski Equation (Electrophoresis) A relation expressing the proportionality between electrophoretic mobility and zeta potential for the limiting case of a species that can be considered to be large and having a thin electric double layer. Also termed Helmholtz—Smoluchowski Equation. See also Electrophoresis, Henry Equation, Hiickel Equation. 

Ill) slopes at the te.p. The slopes (du/3pH) p decrease with Increasing c. The mobility u may be converted into f, using the Helmholtz-Smoluchowski equation if xa is large enough (no double layer polarization and no influence of surface conduction close to the zero point). Then, at low electrol3rte concentration / 9pH may approach 59 mV per pH unit at 25 , as would be the case for ilf° If the Nernst equation applies. However, such a steep slope persists only close to the zero point mostly it is much lower. Let us assume absence of specific adsorption (zeroth-order Stem theory, see flg. 3.17a) then we may write... 

The action of external electric field on the free disperse system results in particle motion (electrophoresis). The electrophoretic velocity, vE, is not a function of ( -potential only, but also depends on the particle radius, r, and the type of electrolyte present in the system. However, it turns out (see fine print further down) that all of these factors can be simultaneously accounted for by the numerical coefficient, kt, introduced into the Helmholtz-Smoluchowski equation (V.26). If the particles are spherical, k, changes from 2/3 for particles smaller compared to the ionic atmosphere thickness (kt 1) to 1 for large particles ( kt 1). Consequently, the particle flux due to the applied electric... 

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. 

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