Aggregate growth

Crystallization kinetics erystal nueleation, growth, aggregation and disruption kineties (Chapters 5 and 6). 

We now turn to the question of developing a CFD model for fine-particle production that includes nucleation, growth, aggregation, and breakage. Applying QMOM to Eq. (114) leads to a closed set of moment equations as follows ... 

The detailed mechanisms of nanoparticle formation (nucleation, growth, aggregation, and ripening) are understood only in qualitative detail so there are no reliable process models available... 

Rate of growth/aggregation experiments with SAXS... 

Because the accuracy of the quadrature approximation strongly depends on the application, let us discuss some of these issues in detail for specific examples. In the case of standard nucleation, (positive) growth, aggregation, and breakage, application of the QBMM to the source term in Eq. (7.96) yields... 

This misconception is particularly common in crystallization. The hypothesis of a perfectly mixed system is, for crystallization and precipitation processes, labeled as mixed-suspension, mixed-product removal (MSMPR). With diis model the crystalUzer is modeled with a spatially homogeneous NDF, generally called the crystal-size distribution (CSD). However, the fact that the CSD is constant through the vessel does not mean that the rates of crystal nucleation, molecular growth, aggregation, and breakage are constant. 

Fig. 5.1. Life cycle of D. discoideum amoebae showing the successive phases of growth, aggregation, and fruiting body formation (Newell, 1977).

The formation of hydroxyaluminosilicate species at near-neutral pH is unique. No interactions occur between silicic acid and Ca or Mg at less than pH 10, so that the transport and binding of these cations is unhindered. The interactions of Fe with silicic acid at near-neutral pH are very different from those of aluminum. Acidic solutions containing Fe (10 " M) with a threefold molar excess of silicic acid remain clear on neutralization no visible precipitate forms. Instead, Fe-0 polymers are formed as spherical hydrated ferric oxide particles 10-15 nm in diameter, stabilized against growth, aggregation, and precipitation by an adsorbed layer of silicic acid [23]. 

Apart from nucleation and crystal growth, aggregation is an important process. Aggregation leads to fewer and larger, but yet porous particles. 

Cheng J, Yang C, Mao Z-S, Zhao C (2009) CFD modeling of nucleation, growth, aggregation, and breakage in continuous precipitation of barium sulfate in a stirred tank. Ind Eng Chem... 

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