Stability factor, Fuchs

This is an equation for a straight line, the slope of which is 2R /t, and describes the plots in Figure 8. From the experimental slopes one may calculate the half-life, T, and the Fuchs stability factor, W. These values are given in Table III. They confirm that coagulation is an important process in determining particle size and number from the outset. With no surfactant present the particles apparently have a net attraction for each other (W < 1), and disappear with a half-life on the order of four milliseconds. As surfactant concentration is increased it... 

Wf, W - Fuchs stability factors between radical and particle, and particle and particle —... 

W is the Fuchs Stability Factor, which dependes primarily on the surface charge of the particles and the ionic strength of the medium. 

This result collapses to that of Fuchs and Debye for diffusion in a field of force when is a constant. When K(/ ) = 0 for / > the Smoluchowski result of Eq. (1.2) is obtained. It is useful to denote deviations from Eq. (1.2) by a dimensionless stability factor 1F(0) so that... 

When there are energy barriers between the particles, for example, attractive and repulsive interaction energy beirriers like those discussed in the previous section, Fuchs [57] showed that the rate of coagulation, J, should be divided by a factor W, the colloid stability ratio, where W is given by [58,59]... 

The colhsion efficiency, Ey, in Equation 5.321 accounts for the interactions (of both hydrodynamic and intermolecular origin) between two colhding particles. The inverse of Ey is often caUed the stability ratio or the Fuchs factor and can be expressed in the following general form ... 

We now consider the kinetics of the flocculation of a system for which there is an energy barrier. The rate is a function of the probability of particles having sufficient energy to overcome this barrier. The problem is again one of diffusion and was first solved by Fuchs . His theory leads to a factor W by which the rapid rate (Smoiuchowski) is reduced by the presence of a repulsive force W is called the stability ratio and is related to the height of the potential energy barrier by... 

Smoluchowski neglected any kind of interaction between the particles, which means that the diffusion of a particle is not affected by the presence of other particles and that each event of collision leads to a stable aggregate bond. Yet, as Fuchs (1934) argued for the stability of charged aerosols, any attractive or repulsive interaction affects the diffusive approaching of two particles and Smoluchowski s aggregation rate is changed by a factor W ... 

The total energy of interaction between the double layers on adjacent solid particles is the sum of the attractive (and repulsive (contributions. It is this potential K which retards the process of rapid coagulation by a factor IF, the stability ratio of Fuchs [8], given by,... 

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