Smoluchowski’s formula

V. Smoluchowski s formula has been tested both by an examina-, tion of the rate of decrease of the primary particles present in gold suspension undergoing coagulation and also by counting the... 

The anomalous surface conduction was studied extensively by O Brien and by Hunter, and they could show that the Stem layer conduction is about thirty times larger than the diffuse layer conduction at low salt concentration. This explains substantial discrepancies between the electrophoresis and the conductance estimates of zeta potential. For thin double-layer systems such as this, the zeta potential is usually calculated from the electrophoretic mobility using Smoluchowski s formula, which in O Brien s case corresponds to a zeta potential of 50 mV [8]. Complex conductivity measurements result in f = —160 mV. 

We measured the electrophoretic mobilities of crude oil droplets in alkaline solution using a Zeta Meter (20). Since the droplet sizes were larger than one micron, the zeta potentials were calculated from electrophoretic mobilities using Smoluchowski s formula. 

It was shown by Dukhin (1983) that under the conditions of strong retardation the effect of an equilibrium DL is dominant for any surface activity of the surfactant. Therefore, Smoluchowski s formula is valid at any degree of surface activity. 

A noticeable deviation of sedimentation potentials from Smoluchowski s formula takes place at large siuface concentration variation along the bubble surface. Before considering experimental data, it has to be pointed out that the validity of Smoluchowski s formula for the description of the Dorn effect at large Peclet numbers applies only to solid spherical particles. In particular, the correctness of conclusions of some papers (Dukhin, 1964 Dukhin Buikov, 1965 Derjaguin Dukhin, 1967, 1971) is experimentally confirmed by Usui et al. (1980). Sedimentation potential for four sizes of glass balls appears to be the same. Since the radii of the particles under consideration are approximately 50, 150, 250, and 350 pm, the absence of any effect of Peclet and Reynolds numbers on the sedimentation potential could be demonstrated. 

The value of 1/2, which is the reciprocal of the friction parameter 2, decreases as the drag exerted by the hydrogel layer on the liquid flow increases. In the limit of 1/2—> 0, Eq. (21.55) tends to the well-known Smoluchowski s mobility formula for hard particles. In other words, as 1/2 increases, the hydrogel layer on the particle becomes softer. That is, the parameter 1/2 can be considered to characterize the softness of the hydrogel layer on the particle. The observed reduction of the softness parameter 1/2 (1.2 nm at 30°C to 0.9 nm at 35°C) implies that the hydrogel layer becomes harder, which is in accordance with the observed shrinkage of the hydrogel. 

In 1916 Smoluchowski gave an extension of Einstein s formula for the case when the (undeformable) particles bear a capillary electric charge ... 

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