Particle size correlations and the effects of limited mixing on agglomerating particulate systems
Abstract Population balance equations for particulate systems are derived based on two basic but tacit assumptions. The first is that a local volume of thorough particle mixing exists over which a more detailed balance equation may be averaged to obtain the population balance equation. The second is that there is a large enough population in the mixing volume that particle correlation effects do not become important. Both the foregoing assumptions are investigated for Brownian agglomeration. The volume of mixing is estimated by scaling arguments. Monte Carlo simulation techniques have been used to show that particle populations in the local mixing volume may be sufficiently small to cause correlation effects implying that the population balance predictions can be in error.
Modeling structure effects on aggregation kinetics in colloidal dispersions
The time evolution of the cluster-mass distribution (CMD) during colloidal aggregation can be modeled using population balance equations, given that the matrix of the aggregation rate constant (kernel) is known. Although numerous aggregation kernels have been proposed, their validity is still a major open problem, particularly when the role of the internal structure of the aggregates is referred to. A procedure is presented for the discrimination among possible kernel expressions including the structure effect. For aggregation processes in the submicron range, information about size and structure of aggregates can be obtained by dynamic and static light-scattering measurements, for example, in terms of the average hydrodynamic (Rh) and gyration (Rg) radii. These quantities can also be calculated from the cluster-mass distribution when accounting for the aggregate structure by the fractal concept and for the angular and rotational diffusion dependence of Rh. Since Rh and Rg represent different averages of the CMD, their simultaneous fitting is a severe test for a given kernel due to its inclusion of information on the average and width of the distribution. This procedure allows differentiation among several types of kernels proposed in the literature for DLCA and RLCA based on their ability to describe experimental data.
A theoretical study of the equilibrium particle size distribution of aerosols
Changes in the size distribution of small aerosol particles were computed for nineteen cases with various initial size distributions, patterns of particle generation, and mechanisms of particle aging. It was proven that, for the majority of the cases, the equilibrium size distribution for the larger particle sizes may be expressed as n (v) = Cv−β, and that the self-preserving function may also be expressed in the same form, [n (v) is the number concentration of particles of volume v.]