Precipitates growth

Use the simple rate-constant type of formulation employed in Sections 13.4.2 and 15.1.1 to analyze source-limited precipitate growth and particle coarsening, respectively. 

Diffusion of the solute is necessary for precipitate growth. The diffusional flux depends on both the diffusivity and the concentration gradient, which is proportional to cQ — ca. At low amounts of supercooling, the term ca — ca is nearly... 

Precipitation involves two distinct processes, namely nucleation and growth. Nucleation requires that the system is far from equilibrium (high supersaturation, or, in the case of ionic species, a solubility product far exceeding the solubility constant of the solid to be precipitated). Growth of the new phase takes place in conditions which gradually approach the equilibrium state. 

Occlusion is not very important in flow turbidimetry because, although water trapped in the interior of the crystal may contain some interferents, precipitate growth is limited and the precipitate is not dried as in gravimetric analysis. 

This structural unit for polymeric material was suggested by Hsu and Bates (14). and was adopted in our earlier work (12). It also was used by Stol et al. (15) as a basis for explaining precipitate growth in hydrolyzing Al solutions. It is the basis for the representation of Alb as Al6(OH)i2 in the equation for conversion of Ala to Alb (equation 2). In effect, the rate constants determined here represent the rate of converting free or monomeric OH into bridging OH. 

In the initial stage of a MSMPR precipitator operation, both the solute concentration and the particle number per unit volume increase rapidly. However, due to the rapid growth of these initial nuclei a subsequent rapid desupersaturation occurs. A steady state is established after about 10 mean residence times. On the other hand, in a semi-batch crystallizer, the particle number per unit volume quickly reaches a constant value while the solute concentration continues to decline steadily throughout the feed period as the precipitate growth proceeds. 

Fig. 14 Grain boundary precipitate growth showing solute transport path during precipitate growth according to the collector-plate mechanism. Solute B is transported to the a-a grain boundary and then along the boundary to form the P precipitate. Diffusion-controlled precipitate growth results in solute depletion from the a phase along the homophase boundary due to fast boundary transport [44].

Stage II a period of precipitate growth at constant volume fraction with no change in rg,. 

Precipitate growth is sometimes favored over nucleation, resulting in the develop-... 

Y. Wang and A. G. Khachaturyan, Shape instabiliQ during precipitate growth in coherent solids, Acta metalf. mater.. 43,1837-1857(1995). 

By carefully controlling the precipitation reaction we can significantly increase a precipitate s average particle size. Precipitation consists of two distinct events nu-cleation, or the initial formation of smaller stable particles of precipitate, and the subsequent growth of these particles. Larger particles form when the rate of particle growth exceeds the rate of nucleation. 

An increase in the time required to form a visible precipitate under conditions of low RSS is a consequence of both a slow rate of nucleation and a steady decrease in RSS as the precipitate forms. One solution to the latter problem is to chemically generate the precipitant in solution as the product of a slow chemical reaction. This maintains the RSS at an effectively constant level. The precipitate initially forms under conditions of low RSS, leading to the nucleation of a limited number of particles. As additional precipitant is created, nucleation is eventually superseded by particle growth. This process is called homogeneous precipitation. ... 

Xanthan, although a gum, is derived from the pure culture fermentation of an organism, TCanthomonas campestris. The organism is filtered from the growth medium and the gum recovered by alcohoHc precipitation, followed by drying. It is composed primarily of D-glucose and D-mannose units. 

When initiator is first added the reaction medium remains clear while particles 10 to 20 nm in diameter are formed. As the reaction proceeds the particle size increases, giving the reaction medium a white milky appearance. When a thermal initiator, such as AIBN or benzoyl peroxide, is used the reaction is autocatalytic. This contrasts sharply with normal homogeneous polymerizations in which the rate of polymerization decreases monotonicaHy with time. Studies show that three propagation reactions occur simultaneously to account for the anomalous auto acceleration (17). These are chain growth in the continuous monomer phase chain growth of radicals that have precipitated from solution onto the particle surface and chain growth of radicals within the polymer particles (13,18). 

The softened seawater is fed with dry or slaked lime (dolime) to a reactor. After precipitation in the reactor, a flocculating agent is added and the slurry is pumped to a thickener where the precipitate settles. The spent seawater overflows the thickener and is returned to the sea. A portion of the thickener underflow is recirculated to the reactor to seed crystal growth and improve settling and filtering characteristics of the precipitate. The remainder of the thickener underflow is pumped to a countercurrent washing system. In this system the slurry is washed with freshwater to remove the soluble salts. The washed slurry is vacuum-filtered to produce a filter cake that contains about 50% Mg(OH)2. Typical dimensions for equipment used in the seawater process may be found in the Hterature (75). 

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