Zeta potential Smoluchowski equation

In order to describe the effects of the double layer on the particle motion, the Poisson equation is used. The Poisson equation relates the electrostatic potential field to the charge density in the double layer, and this gives rise to the concepts of zeta-potential and surface of shear. Using extensions of the double-layer theory, Debye and Huckel, Smoluchowski,... 

The electrophoretic mobility, /jl, can be converted to a zeta potential by using the Smoluchowski equation,... 

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. 

In this result, the condition of small particles means that the actual size of the particles (which is often difficult to obtain) is not required. For reasons to be discussed later, we will call the potential obtained by this method the zeta potential (Q rather than the surface potential. In the following section we consider the alternative case of large colloidal particles, which leads to the Smoluchowski equation. 

This important result is called the Smoluchowski equation and, as before, the zeta potential is directly related to the mobility and does not depend on either the size of the particle or the electrolyte concentration. 

We have now reached the position of having two expressions —Equations (27) and (39) —to describe the relationship between the mobility of a particle (an experimental quantity) and the zeta potential (a quantity of considerable theoretical interest). The situation may be summarized by noting that both the Huckel and the Helmholtz-Smoluchowski equations may be written as... 

FIG. 12.8 Plot of rju/e versus f/0, that is, the zeta potential according to the Helmholtz-Smoluchowski equation, Equation (39), versus the potential at the inner limit of the diffuse part of the double layer. Curves are drawn for various concentrations of 1 1 electrolyte with / = 10 15 V-2 m2. (Redrawn with permission from J. Lyklema and J. Th. G. Overbeek, J. Colloid Sci., 16, 501 (1961).)... 

Criticize or defend the following proposition Zeta potentials for three different polystyrene latex preparations were calculated by the Helmholtz-Smoluchowski equation from electrophoresis measurements made in different concentrations of KCl.f... 

These zeta potentials are inaccurate because the range of kRs values exceeds the range of validity for the Helmholtz-Smoluchowski equation. The nature of the error is such as to make the estimated values of f too low. 

Substituting a for 7 uE/e (i.e a is the apparent zeta potential calculated from the Smoluchowski equation) gives... 

Besides there is uncertainty in hydrodynamics inside adsorbed layer, which can be (or not) permeable for flux. Hydrodynamic profile can deviate from parabolic Pois-seuille profile, that s why in this case the Helmholtz-Smoluchowski equation does not correctly transform the streaming potential into the zeta-potential values. So we indicate calculated f potential as apparent zeta-potential ( ). 

Electrophoresis of nonconducting colloidal particles has been reviewed in this chapter. One important parameter determining the electrophoretic velocity of a particle is the ratio of the double layer thickness to the particle dimension. This leads to Smoluchowski s equation and Huckel s prediction for the particle mobility at the two extrema of the ratio when deformation of the double layer is negligible. Distortion of the ion cloud arising from application of the external electric field becomes significant for high zeta potential. An opposite electric field is therefore induced in the deformed double layer so as to retard the particle s migration. 

Microelectrophoresis is used to measure the electrophoretic mobility or, in other words, the movement of liposomes under the influence of an electric field. From the electrophoretic mobility the electrical potential at the plane of shear or (zeta) potential can be determined (by the Helmoholtz-Smoluchowski equation). From the zeta potential values the surface charge density (o) can be calculated. 

Various equations have been derived for relating EM, u, to the zeta potential, f. Traditionally, the Smoluchowski equation,... 

In the limits of small Ka (ku electrophoretic mobility, 17, to zeta potential. These are the Hiickel and Smoluchowski equations, respectively. They may be expressed by... 

The most common method for determining the zeta-potential is the microelectrophoretic procedure in which the movements of individual particles under the influence of a known electric field are followed microscopically. The zeta potential can be calculated from the electrophoretic velocity of the particles using the Helmholtz-Smoluchowski equation. 

Enter the protocol zeta potential measurements with an initial pH point taken at the pH of the solution, in this case, pH 8.25, and points taken every 0.5 pH change until pH 3.7 is reached. Stir between each measure to insure the solution is homogeneous. Electrophoretic mobility is converted automatically to the potential, according to the Smoluchowski equation, by the system. 

In foams with charged gas/liquid interface, various electrokinetic parameters can be obtained, such as streaming potential and zeta-potential. For example, the relationship between the volumetric flow of a liquid flowing through a capillary or membrane and the zeta-potential can be given by the Smoluchowski equation. 

It should be emphasized that EOD is most attractive when the water is trapped between fine clay particles (i.e., small pores or water transport chaimels) and caimot be further removed efficiently by the application of pressure or vacuum, etc. If the ionic concentration of the trapped water is low, the thickness of the electrochemical double layerio i can become comparable to or even exceed the pore size, thus requiring corrections to the zeta potential approach based on the simple Helmholtz-Smoluchowski equation such corrections cannot, however, be carried out accurately despite many attempts. " ... 

The emulsions for electrophoresis measurements were prepared by adding one drop of dodecane to about 20 cm3 of a DMS solution and by subjecting the mixture to ultrasonic treatment for 30 sec. The emulsion was then aged overnight and remixed by shaking just prior to use. This procedure produced drops approximately 1—2//in. Zeta potentials (f) were calculated from the Smoluchowski equation,... 

Henry Equation A relation expressing the proportionality between electrophoretic mobility and zeta potential for different values of the Debye length and size of the species. See also Electrophoresis, Hiickel Equation, Smoluchowski Equation. 

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