Aggregation doublet formation

Doublet formation is the first step of aggregate or cluster formation. When salt or pH is used to destabilize a colloidal suspension it is referred to as coagulation. When a polymer or surfactant is used to destabilize a colloidal suspension it is referred to as flocculation. The kinetics of doublet formation for both these methods of destabilizing a colloidal suspension is discussed in this section. 

The singlet concentration decreases with time due to doublet formation, while the doublet concentration increases. As a result, the rates of aggregation and floe fragmentation will approach each other. Correspondingly, the change in the number of doublets [Pg.73]

The same type of kinetic equation as we have been using for doublet formation was put forward by von Smoluchowski in 1917 to describe the formation of any aggregate containing m particles. If is the number of m-particle aggregates per unit volume, their rate of formation is given by... 

Figure 5. Size distribution of aggregated latex sample. The 2 1 size ratio suggests the formation of doublets.

Capture efficiency, a, is defined as the fiaction of shear-induced collisiorrs between two platelets that result in doublets, i.e., the ratio of the rate of the measured initial aggregate formation for dilute suspensions (dN/dt) to the frequency of two-body coUisiorts in the suspension. 

This derivation takes into account formation of only doublets. In reality, primary particles can also aggregate with multiplets. Solution for all particle aggregates containing / particles is given as... 

However, most practical cases involve concentrated systems, in which multiple panicle interactions occur. Rotating doublets or triplets of panicles may form temporarily, and more energy is dissipated as compared to the same number of single particles. The formation of permanent temporary aggregates has an-... 

The difference in turbidity owing to the formation of doublets from single particles has been studied by Lichtenbelt, Ras, and Wiersema (234). Also, aggregation has been followed by flow ultramicroscopy (235). 

Aggregation starts with the formation of doublets which is a rather easily modelled process. In the subsequent aggregation, a multitude of irregular particles are formed and a conventional kinetic treatment then becomes more or less impossible. The structure of the particle aggregates is dependent on the interaction potentials. Some information can be obtained by computer simulations. We will start our consideration of the aggregation kinetics by a discussion of the Smoluchowski theory and its ramifications on more recent work. 

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