Growth of particles

At the crystallization stage, the rates of generation and growth of particles together with their residence times are all important for the formal accounting of particle numbers in each size range. Use of the mass and population balances facilitates calculation of the particle size distribution and its statistics i.e. mean particle size, etc. 

From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (—2.5—3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a—time plot obeyed the power law [eqn. (2)] with 6 temperature coefficients of these processes were used by Wischin [201]... 

At room temperature and in the presence of oxygen the colloidal dispersion stabilized by glucose is less stable than the PVA stabilized ones owing to the slow glucose aerobic oxidation growth of particles from 2.7 to 3.5 nm has been observed in a few hours. 

Figure. 3.36. Schematic of the various stages in the formation and the growth of particles from a monomer dispersion during sintering (after Satterfield, 1991).

A representative TEM image of the sonochemically formed Au particles in the absence of stabilizer is shown in Fig. 5.9 [33]. In this experiment, only 20 mM of 1-propanol is included as an organic additive. It can be seen that the size of Au particles is in the nanometer regime. The sizes of the sonochemically formed metal nanoparticles are dependent on the initial concentration of metal ions and the types of stabilizers [26] as same as the conventional methods smaller metal particles are formed in the presence of lower initial concentration of metal ions. In addition, if a suitable stabilizer were used, the growth of particles would be suppressed effectively by the stabilizer adsorption on the particle surface, resulting in the formation of smaller metal particles. 

Growth of particles by accumulation on existing particles can be classed as two broad processes. If the precursor is supersaturated, growth will occur at a rate limited by vapor diffusion, which depends on the supersaturation, the temperature, the particle size, and the accommodation coefficient at the surface. The proportionality of particle size changes with the ratio of particle diameter to mean free path of the suspending... 

In the case of organic constituent formation, growth of particles is governed by physical laws of condensation, provided that the precursors are formed in the gas phase. For a diffusion-limited condensation process, the rate of volume change in particles is... 

Smog chamber studies have documented similar aerosol growth mechanisms. For example, in the photochemical oxidation of dimethyl sulfide, the formation and growth of particles in an initially particle-free system was observed. However, if seed particles with 34-nm mean size were present, an oscillation in the... 

Computer simulations combined with experiments have also shown that one can deduce from the fractal dimension the nature of nucleation and growth of particles and what chemical and physical mechanisms control the formation of particle aggregates. We consider this briefly before proceeding to other topics. 

Flocculation, coagulation and growth of particles in dilute slurries, to assist in subsequent sedimentation and filtration. 

Cylinders, Ellipsoids, and Elliptical Paraboloids. The diffusion-limited growth of particles whose planar intercepts are conic sections can also be analyzed by the scaling method. For example, the scaling function appropriate for a cylinder is T] = r/y/t.4 The solution for the growth of a cylinder is obtained in Exercise 20.5. 

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