Kinetics, droplet aggregation

Flocculation kinetics can be described in different ways. Here we introduce a treatment first suggested by Smoluchowski [547], and described in Ref. [538], p. 417. The formalism can also be used to treat the aggregation of sols. A prerequisite for coalescence is that droplets encounter each other and collide. Smoluchowski calculated the rate of diffusional encounters between spherical droplets of radius R. The rate of diffusion-limited encounters is SttDRc2, where c is the concentration of droplets (number of droplets per unit volume). For the diffusion coefficient D we use the Stokes-Einstein relation D = kBT/finr/R. The rate of diffusion-limited encounters is, at the same time, the upper limit for the decrease in droplet concentration. Both rates are equal when each encounter leads to coalescence. Then the rate of encounters is given by... 

In aggregation the species retain their identity but lose their kinetic independence since the aggregate moves as a single unit. Aggregation of droplets may lead to coalescence and the formation of larger droplets until the phases become separated. In coalescence, on the other hand, the original species lose their identity and become part of a new species. Kinetic stability can thus have different meanings. An... 

Although most colloidal dispersions are not thermodynamically stable, a consequence of the small size and large surface area in colloids, and of the presence of an interfacial film on droplets, bubbles or particles, is that dispersions of these species, having reasonable kinetic stability, can be made. That is, suspended droplets or particles may not aggregate quickly nor settle or float out rapidly and droplets in an emulsion or bubbles in a foam may not coalesce quickly. Many food and personal care product emulsions and suspensions, for example, are formulated to remain stable for months to years. It is crucial that stability be understood in terms of a clearly defined process, and one must consider the degree of change and the time-scale in the definition of stability. 

In colloid science the term colloid stability means that a specified process that causes the colloid to become a macrophase, such as aggregation, does not proceed at a significant rate. Colloid stability is different from thermodynamic stability (see Ref. [978]). The term colloid stability must be used with reference to a specific and clearly defined process, for example, a colloidally metastable emulsion may signify a system in which the droplets do not participate in aggregation, coalescence, or creaming at a significant rate. See also Kinetic Stability, Thermodynamic Stability. 

Although DLS is most often used to size solid colloidal particles, the technique has also been applied to characterize aerosols [78,86,87], emulsion droplets [88,89], amphiphilic systems [90-92], and macromolecular solutions [12,16,93]. Another common application is the study of the fractal structure and kinetics of colloidal aggregation [94-102], More information about dynamic light scattering and its applications can be found in Refs. 23. 103 (104), and 105, in reviews, Refs. 11, 13, 36, 37, 49, 50, and 106, and in collections of papers Refs. 12. 14. 16. 93 (107), 105, and 108-114. 

Agglomeration, droplet, first step in demulsification, 44 Aggregation definition, 6-7, 386 droplet, kinetics and methods of preventing, 36... 

Flocculation and Coalescence. Flocculation being the primary process, the droplets of the dispersed phase come together to form aggregates. In this process, the droplets have not entirely lost their identity and the process can be reversible. Since the droplets are surrounded by the double layer, they experience the repulsive effect of the double layer. Kinetically, flocculation is a second order reaction since it depends in the first instance on the collision of two droplets and is expressed in the form (31)... 

Coalescence being the secondary process, the number of distinct droplets decreases leading to a stage of irreversibility and finally complete demulsification takes place. Coalescence rate very likely depends primarily on the film-film repulsion, film drainage and on the degree of kinetics of desorption. Kinetically, coalescence is a unimolecular process and the probability of merging of two droplets in an aggregate is assumed not to affect the stability at other point of contact (32). 

Classical emulsion polymerization is divided into three kinetic stages. At the start of the process, the unsaturated monomers are dispersed into small droplets, stabilized with surfactants. Additional surfactant aggregates into micelles. These micelles are very small ( 10nm) relative to monomer droplets ( 1-10 pm). During stage 1 the initial formation of polymer... 

There is limited evidence for the applicability of the pseudophase kinetic model to microemulsions. Amines can act as cosurfactants and stabilize o/w microemulsions, and these amines are effective nucleophiles towards 2,4-dinitrochlorobenzene, and the rate constants in the microemulsion droplets are not very different from those in water [156]. Reactions in which bromide ion acts as a nucleophile also have similar second-order rate constants in a microemulsion aggregate as in a micelle, suggesting that it should be possible to apply an ion exchange model to microemulsions [157]. However, Mackay and coworkers have treated ion binding in microemulsions in terms of the surface potential of the aggregates [153,154], following an approach which has been applied to ionic micelles in water [158]. 

The next section describes measurements of interfacial tension and surfactant adsorption. The sections on w/c and o/c microemulsions discuss phase behavior, spectroscopic and scattering studies of polarity, pH, aggregation, droplet size, and protein solubilization. The formation of w/c microemulsions, which has been achieved only recently [19, 20], offers new opportunities in protein and polymer chemistry, separation science, reaction engineering, environmental science for waste minimization and treatment, and materials science. Recently, kinetically stable w/c emulsions have been formed for water volume percentages from 10 to 75, as described below. Stabilization and flocculation of w/c and o/c emulsions are characterized as a function of the surfactant adsorption and the solvation of the C02-philic group of the surfactant. The last two sections describe phase transfer reactions between lipophiles and hydrophiles in w/c microemulsions and emulsions and in situ mechanistic studies of dispersion polymerization. 

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