Aggregation regime

Figure 7.9 characterizes the effective attraction between vacancies with and without their aggregation. In the aggregation regime an additional short-range force arises (curve 2) which has many-particle nature and is caused by the non-linear term in the mean-force potentials, equations (5.1.45) to (5.1.47), at r < 1. 

Ruiz, R. et al.. Dynamic scaling, island size distribution, and morphology in the aggregation regime of submonolayer pentacene films, Phys. Rev. Lett. 91, 136102, 2003. Pratontep, S. et ah. Correlated growth in ultrathin pentacene films on silicon oxide Effect of deposition rate, Phys. Rev. B 69, 165201, 2004. 

Given that neither a pore blocking mechanism nor a reduced cake thickness due to aggregate back-transport can account for the obsen ed differences in flux for cakes formed from rapidly-formed compared to slowly-formed aggregates, we must conclude that the differences in permeation velocity arise from differences in permeability of the cakes formed under the different aggregation regimes. The order of magnitude difference in specific resistances of cakes developed at 20 mM and 100 mM KCl concentrations (approx. 1 10 tti.g versus approx. 0.1 10 respectively) supports the... 

The effect of different aggregation regimes (rapid versus slow) was discussed in detail in section 6.5. Here, the effect of aggregation under conditions much closer to surface waters (neutral pH and background solution) will be investigated. The experiments were carried out with the smallest colloids (40 nm, 75 nm). At pH 7-8 aggregation is expected in all cases. 

This study was divided into five major sections, (a) fractionation and rejection studies of natural organics under varied solution chemistries, (b) colloid and aggregate studies under controlled aggregation regimes, (c) filtration of calcium-organic aggregates, (d) particulate systems (SPO, OPS), and (e) ferric chloride floes combined with the above systems. 

Ferretti, R., Zhang, J. and Buffle, J. (1998). Flocculation of hematite with polyacrylic acid fractal structures in the reaction and diffusion-limited aggregation regimes. J. Colloid Interface ScL, 208, 509-517. 

Table 4.2 Fundamental aggregation regime for colloidal particles in a quiescent liquid (based on Femandez-Toledano et al. 2007)...

Initial aggregation Initial and medium aggregation Final aggregation regime... 

In the presence of repulsive interactions, the sticking probability becomes smaller than 1 and the so-called slow aggregation regime may be realized. The slow aggregation rate constant, F may be estimated as ... 

The exact analytical solutions of PBE for Brownian and ballistic kernels have not yet been obtained. In slow aggregation regime, these kernel may be estimated as ... 

Colloidal particles aggregate in concentrated electrolyte solutions by diffusion (fast aggregation regime). The onset of this process is controlled by the formation of particle dimers, as illustrated in the following scheme ... 

In order to distinguish between the fragmented and the aggregated regime, it is useful to introduce the order parameter [255]... 

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