Size evolution

The reaction engineering model links the penetration theory to a population balance that includes particle formation and growth with the aim of predicting the average particle size. The model was then applied to the precipitation of CaC03 via CO2 absorption into Ca(OH)2aq in a draft tube bubble column and draws insight into the phenomena underlying the crystal size evolution. 

Hansen, S., and Ottino, J. M., Aggregation and cluster size evolution in nonhomogeneous flows. ]. Colloid Interface Sci. 179, 89-103 (1996b). 

Volume conservation provides a relation between the diameter d(t) and the number of droplets N(t) at time t. As a consequence, the differential equation governing the size evolution is ... 

Because particles of different sizes are distributed throughout the bulk randomly, developing an exact model that couples diffusion to particle size evolution is daunting. However, a mean-field approximation is reasonable because diffusion near a spherical sink (see Section 13.4.2) has a short transient and a steady state characterized by steep concentration gradients near the surface. The particles act as independent sinks in contact with a mean-field as in Fig. 15.2. 

Galen C., Zimmer K. A. and Newport M. E. (1987) Pollination in floral scent morphs of Polemonium viscosum a mechanism for disruptive selection on flower size. Evolution 41, 599-606. 

Turbidity measurements are simple, fast and reproducible. Specific turbidity can successfully follow the particle size evolution during the course of emulsion polymerization and can be translated into weight average diameters. A combination of an on-line spectrophotometer with an on-line densitometer (to obtain concentration) would provide the potential to estimate Dw on-line, as well. An on-line determination of PSD s, for small particles however, would seem quite difficult due to the high correlation of their parameters. One should bear in mind that the above conclusions have been validated only for poly(vinyl acetate) latexes the analysis is currently being extened to other systems, such as polystyrene and poly(methyl-methacrylate). 

Fig. 7.6. (b) pore size evolution versus sintering temperature from Ref. [16]. 

The predictions of chemical evolution models can be tested in a cosmological context to study the galaxy surface brightness and size evolution as a function of redshift. Roche et al. (1998) have already done that and suggested that a size and luminosity evolution, as suggested by the inside-out scenario fits better the observations. 

---