Zeta potential Huckel 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 microelectrophoretic mobility (jUe) is related to zeta potential ( ) via one of two equations. When the diameter of the particle is small relative to the thickness of the electrical double layer, the Huckel equation applies ... 

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... 

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. 

As the deserved droplets had large radii compared with the Dehye Huckel parameter (1/X)> the zeta potentials were calculated from the following equation ... 

Instrumentation. A Rank Bros, micro-electrophoresis unit was used in those studies, with a specially made quartz cell having a 6 cm. path length of rectangular inside cross-section (l mm thick, 10 mm deep) in which the Komagata equation (25) predicts zero mobility of the liquid phase in planes located at 0.612 of the distance b from the center plane of the cell to the wall. In electrophoresis experiments 300 to 1200 volts were applied to the cell and mobilities measured in planes a distance h from the center plane. The results were graphed as observed velocity versus (h/b)z as proposed by van Gils (26J, and if the straight lines characteristic of perfect parabolic flow resulted, the electrophoretic mobilities (v ) observed at h/b=0.612 were considered acceptable for calculation of zeta-potential. Zeta-potentials were calculated by the Huckel equation (27) ... 

Debye-Huckel Approximation In some situations where the zeta potential is small (i.e., < 25 mV), the hyperbolic function in Eq. 16 can be approximated as sinh(ze //A b7 ze lk, T, which is called the Debye-Huckel approximation. Equation 16 then becomes... 

Thus, with the Debye-Huckel assumption, dh can be expressed as an explicit function of the channel height through the average velocity equation, such that if the average velocity is known, then the initial guess for the zeta potential can be determined as... 

The quantity 1/rc, which has the dimensions of length, can be regarded as the effective thickness d of the double layer, and is to be compared with the effective thickness of the ionic atmosphere in the Debye-Huckel theory (see Section 6.5). Equation (11.123) gives the potential at the distance of closest approach, with respect to the bulk of the solution. If we give this potential the symbol C (zeta) we have... 

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