Mixing and Nucleation

A new method involving separate nucleation and aging steps was reported by Zhao et al. [20]. The key features of this method are a very rapid mixing and nucleation process in a colloid mill followed by a separate aging process. The design of the colloid mill is schematically illustrated in Fig. 2. 

Fig. 3 TEM micrographs of Mg/Al - CO3 LDHs with different Mg /Al ratios prepared using the new method using rapid mixing and nucleation in a colloid mill followed by a separate aging step (a-c) and conventional coprecipitation at constant pH (d-f). The new method affords smaller crystallites with a much narrower range of length. Reprinted with permission from [20]. Copyright ACS Journal Archives...

It is helpful to visualize the relationship between mixing and nucleation rates through an analogy with the reaction Damkoehler number (Da). The Da number for reaction is defined as Da for reaction = mixing time/reaction time... 

It should always be kept in mind that mixing and nucleation time can be arbitrarily defined as the time required from the initial state to, for example, 95% of the final state. These values are also affected by other operating factors, such as the type of solvent, temperature, degree of supersaturation, flow ratios of two streams, and vessel geometry. 

As in scale-up of chemical reactions, it is important to consider the relative time constants of mixing and nucleation in order to estimate which part of the S-curve applies to a particular system. Although this determination is conceptual, the insight provided by such analysis can be helpful in establishing operational design criteria. 

The Kleber-Colombes rigid PVC foam (253,254) is produced by compression mol ding vinyl plastisol to react and gel the compound, followed by steam expansion. The process involves mixing, mol ding, and expansion. The formulation consists of PVC, isocyanate, vinyl monomers such as styrene, anhydrides such as maleic anhydride, polymerization initiators, FC-11, and nucleators. The ingredients are mixed in a Wemer-Pfleiderer or a Baker Perkins... 

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

When a process is continuous, nucleation frequently occurs in the presence of a seeded solution by the combined effec ts of mechanical stimulus and nucleation caused by supersaturation (heterogeneous nucleation). If such a system is completely and uniformly mixed (i.e., the product stream represents the typical magma circulated within the system) and if the system is operating at steady state, the particle-size distribution has definite hmits which can be predic ted mathematically with a high degree of accuracy, as will be shown later in this section. 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

Growth and nucleation interact in a crystalliser in which both contribute to the final crystal size distribution (CSD) of the product. The importance of the population balance(37) is widely acknowledged. This is most easily appreciated by reference to the simple, idealised case of a mixed-suspension, mixed-product removal (MSMPR) crystalliser operated continuously in the steady state, where no crystals are present in the feed stream, all crystals are of the same shape, no crystals break down by attrition, and crystal growth rate is independent of crystal size. The crystal size distribution for steady state operation in terms of crystal size d and population density // (number of crystals per unit size per unit volume of the system), derived directly from the population balance over the system(37) is ... 

Etherton studied the growth and nucleation kinetics of gypsum crystallization from simulated stack gas liquor using a one-liter seeded mininucleator with a Mixed Suspension Mixed Product Removal (MSMPR) configuration for the fines created by the retained parent seed. The effect of pH and chemical additives on crystallization kinetics of gypsum was measured. This early fundamental study has been the basis for later CSD studies. 

Typically, the precursor solutions (usually aqueous salt solutions) are mixed, and the desired salt is precipitated as a gel by adding an add/base or another reagent. Precipitation has three stages supersaturation, nucleation, and growth. The... 

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