Coagulation rapid

For a more complete understanding of colloid stability, we need to address the kinetics of aggregation. The theory discussed here was developed to describe coagulation of charged colloids, but it does apply to other cases as well. First, we consider the case of so-called rapid coagulation, which means that two particles will aggregate as soon as they meet (at high salt concentration, for instance). This was considered by von Smoluchowski 1561 here we follow [39, 57]. 

Table C2.6.5 Rapid coagulation half-life time for particles in water at 7 =300 K (equation (C2.6.16)).

As two particles approach in a liquid their charge fields may interact and form two minima as depicted in Figure 6.8. If the particles approach to a distance Li, known as the primary minimum they aggregate to form a configuration with minimum energy - and rapid coagulation is said to take place. On the other hand, if the particles remain separated at a distance L2, the secondary minimum, loose clusters form which do not touch. This is known as slow coagulation and is the more easily reversed. 

Thus, there is a size threshold that must be reached before a cluster of atoms becomes big enough to be detected and turns into a "condensation nuclei". Recent work by Madelaine and coworkers (Perrin, et al, 1978 Madelaine, et al., 1980) have extended the size of measurable ultrafine particles to the order of 0.003 ym. They find rapid coagulation of this ultrafine aerosol to a larger average diameter one that is easily observable. 

In a number of recent publications (1, 2) microcrystailine cellulose dispersions (MCC) have been used as models to study different aspects of the papermaking process, especially with regard to its stability. One of the central points in the well established DLVO theory of colloidal stability is the critical coagulation concentration (CCC). In practice, it represents the minimum salt concentration that causes rapid coagulation of a dispersion and is an intimate part of the theoretical framework of the DLVO theory (3). Kratohvil et al (A) have studied this aspect of the DLVO theory with MCC and given values for the CCC for many salts, cationic... 

A probabilistic kinetic model describing the rapid coagulation or aggregation of small spheres that make contact with each other as a consequence of Brownian motion. Smoluchowski recognized that the likelihood of a particle (radius = ri) hitting another particle (radius = T2 concentration = C2) within a time interval (dt) equals the diffusional flux (dC2ldp)p=R into a sphere of radius i i2, equal to (ri + r2). The effective diffusion coefficient Di2 was taken to be the sum of the diffusion coefficients... 

Calculate the critical value of the surface potential of the colloid which will just give the rapid coagulation case illustrated in Figure 7.15. Assume that the aqueous solution contains lOmM monovalent electrolyte at 25 °C. Also assume that the Hamaker constant for this case has a value of 5 x 10 J. 

Figure 7.15 Rapid coagulation condition for the interaction between two colloids.

EXAMPLE 13.2 Variation of Particle Concentration Due to Rapid Coagulation. An aqueous dispersion initially contains 109 particles cm -3. Assuming rapid coagulation, calculate the time required for the concentration of the dispersed units to drop to 90% of the initial value. The viscosity of water is 0.010 P at 20°C, which may be used for the temperature of the experiment. 

Attractive interparticle forces can enhance collision rates (although only moderately) and can cause more rapid coagulation however, in most practical cases of interest we are concerned with the reduction in collision rates (and the consequent increase in stability) caused by... 

What is meant by rapid coagulation What is the basic principle behind the Smoluchowski theory of rapid coagulation What is the rate coefficient for rapid coagulation How is it defined, and what properties of the dispersion determine its magnitude What are the limitations of this theory as presented in the text ... 

Figure 11.16 Relationship between sorbed and dissolved amphi-phile concentrations (upper isotherm plot). These different parts of the isotherm reflect changes in the solid surface as sorption proceeds, possibly explainable by the following in portion (I) with low dissolved concentrations, sorption occurs via ion exchange and related mechanisms. At some point, sufficient near-surface concentration enhancement occurs that micelles form there (Ha) and rapid coagulation between oppositely charged micelles and the surface follows (lib). When the surface becomes fLilly coated with such micelles, additional sorption is stopped (III). In portion III, the solid surface charge is converted from one sign to the other, implying sorbates must become physically associated with the particle surface, as opposed to simply being present in the diffuse double layer or the vicinal water layer.

Figure 5.2 Diagram of a water treatment process using rapid coagulation.

Rapid coagulation is, in fact, not quite as simple as this, because the last part of the approach of two particles is (a) slowed down because it is difficult for liquid to flow away from the narrow gap between the particles, and (b) accelerated by the van de Waals attraction between the particles. Lichtenbelt and co-workers205 have measured rapid coagulation rates by a stopped-flow method and found them, typically, to be about half the rate predicted according to equation (8.18). 

---