Aggregate number density

The rate at which the aggregate number density, Np, changes can be expressed as... 

Closer observation of the aggregation time scale shows that it is inversely proportional to the characteristic total aggregate number density Nt, which is related to the characteristic disperse-phase volume fraction 0p. When the system is dilute (i.e.

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Let us consider a simple solute association equilibrium between n monomers (M) and an aggregate (A) such that nM -> A, which is described by an equilibrium constant K = Pa/Pm Conformational equilibria can also be investigated by simply setting n = 1. A differential for changes in the equilibrium constant at constant T can then be obtained from Equation 1.43 applied to the monomer and aggregate number densities after application of the equilibrium condition nnlpM =... 

Thus, the source terms for each environment S(c) and Sk ((/)) will be closed. Of particular interest are the local nucleation rates /(c ). As discussed in Wang and Fox (2004), due to poor micromixing the local nucleation rates can be much larger than those predicted by the average concentrations /((c)). This results in a rapid increase in the local particle number density mo due to the creation of a very large number of nuclei. As discussed below, this will have significant consequences on the local rate of aggregation. 

In our Galaxy, as well as in others, populations of stars aggregate from place to place in the so-called globular clusters. There the local number density of stars is far bigger than in the rest of the Galaxy except perhaps in its core. 

Biological samples such as bacteria and viruses have been studied by SdFFF as well as FIFFF. These two techniques provided bacterial number, density, size, and mass distributions of bacterial cells of diverse shapes and sizes, molecular weights, sizes, densities, and diffusivities of viruses. SdFFF has been used to analyze protein particles, including casein derived from nonfat dry milk, albumin microspheres, and particles in cataractous lenses originating from the aggregation of lens proteins. 

Fig. 48 Surfactant aggregation numbers determined at various adsorption densities (average number at each adsorption density shown along the adsorption isotherm)...

These computer simulations permit the number density of primary particles within the aggregate to be evaluated, important information for relating the properties of the aggregate to its composition. As might be expected, however, it is difficult to know a priori what model to use for a particular system. However, this technique does allow some interesting a posteriori interpretations of known structures to be made. Another closely related problem that has been... 

It was shown by McClain et al. that a series of PS- -PFOA copolymers studied by SANS and SAXS form polydisperse spherical core-shell micelles, where PS forms the spherical core and PFOA forms the corona, or shell, swollen with C02 (Londono et al., 1997 McClain et al., 1996b). In most cases, the core radius was 25 A, the shell radius was 85 A, and the aggregation number was 7. With an increase in C02 density implemented by decreasing the temperature, the polydispersity increased, likely from breaking a collection of aggregates of low polydispersity into a collection of smaller aggregates of higher polydispersity. 

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