Theory aggregate size

Although the proposed theory has been used effectively in several practical applications, no experimental proof has been given that the oil solubilization rate is a function of surfactant aggregate size. In view of the importance of solubilization and the existence of practical methods of measuring and controlling surfactant aggregate size, we decided to correlate the solubilization rate with micellar properties for some anionic and nonionic surfactants. 

More rigorous analytical approaches are based on the individual perturbation fields of the primary particles within the aggregate and the corresponding perturbation forces they cause on the other particles. The Kirkwood-Riseman theory uses simplified and averaged expressions for the velocity and force perturbations (Kirkwood and Riseman 1948 Bloomfield et al. 1967 Hess et al. 1986), and provides relatively simple expressions for the hydrodynamic aggregate size (Chen et al. 1984 Lattuada et al. 2004). Stokesian dynamics simulation, which originally aims at the dynamic behaviour of suspensions (Brady and Bossis 1988), provides a... 

The mode of action of plasticizers can be explained using the Gel theory [35 ]. According to this theory, the deformation resistance of amorphous polymers can be ascribed to the cross-links between active centres which are continuously formed and destroyed. The cross-links are constituted by micro-aggregates or crystallites of small size. When a plasticizer is added, its molecules also participate in the breaking down and re-forming of these cross-links. As a consequence, a proportion of the active centres of the polymer are solvated and do not become available for polymer-to-polymer links, the polymer structure being correspondingly loosened. 

Smoluehowski also presented a simple theory of aggregation kineties assuming eollisions of perfeet eolleetion effieieney to prediet spherieal partiele size distributions in a uniform liquid shear field of eonstant veloeity gradient. The aggregation kernel is then expressed as... 

The formation of the layers was also checked by optical absorption measurements and eUipsometry. After the reaction the absorption spectrum was blue-shifted with respect to the bulk spectrum of CdS, indicating the formation of very small particles. It was also possible to estimate their sizes using Rama Krishna and Friesner theory (Rama Krishna and Friesner 1991). After washing with chloroform, the blue shift became smaller (but still remained), indicating the aggregation of the particles in the layer (Facci et al. 1994a). 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

At the simplest level, the rate of flow-induced aggregation of compact spherical particles is described by Smoluchowski s theory [Eq. (32)]. Such expressions may then be incorporated into population balance equations to determine the evolution of the agglomerate size distribution with time. However with increase in agglomerate size, complex (fractal) structures may be generated that preclude analysis by simple methods as above. 

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