Precipitation, theory

There is considerable metallographic and electrochemical evidence in support of each theory and it is of interest to note that two of the most authoritative works on corrosion appear to support opposite views — Uhlig favours the selective dissolution of zinc theory, whereas Fontana and Greene favour the dissolution-precipitation theory. 

Solution-precipitation theory cannot be used to justify creep asymmetry or high tensile stress exponents for ceramic matrix composites. The theory suggests that creep is symmetric in stress and that the stress exponent is equal to 1. Justification of creep asymmetry by solution-precipitation would require other parameters in Eqn. (4) to depend on the sign of the applied stress. A nonlinear dependence on stress would be required. Diffusion and devitrification may play a role in this regard however, the data needed to support this possibility have yet to be obtained. 

Three main theories exist concerning stone formation in the urinary tract, namely, the precipitation theory, the theory of the lack of inhibitors, and the matrix theory. 

According to the precipitation theory, the urine becomes supersaturated with salts, which finally results in the precipitation of crystals that grow and form stones in the urinary tract (Fig. 2). The urinary pH may play an important role in this process. For example, normal urine specimens are supersaturated with uric acid at a pH below 5.5-5.7 (S5). At higher pH values, the solubility increases remarkably. At a pH of approximately 7, the solubility would increase about 10 times. However, a low pH cannot be the sole explanation for uric acid lithiasis, because comparably low urinary pH values are found in healthy subjects (F2). This leads to the second theory on urolithiasis, namely, the theory of the lack of inhibitors. 

Oils for Asphalt Precipitation Theory, Practice, and the Selection of Inhibitors," SPE PF10, 55-61. 

While, in principle, a tricritical point is one where three phases simultaneously coalesce into one, that is not what would be observed in the laboratory if the temperature of a closed system is increased along a path that passes exactly tlirough a tricritical point. Although such a difficult experiment is yet to be perfomied, it is clear from theory (Kaufman and Griffiths 1982, Pegg et al 1990) and from experiments in the vicinity of tricritical points that below the tricritical temperature only two phases coexist and that the volume of one slirinks precipitously to zero at T. ... 

If a neutral chelate formed from a ligand such as acetylacetone is sufficiently soluble in water not to precipitate, it may stiH be extracted into an immiscible solvent and thus separated from the other constituents of the water phase. Metal recovery processes (see Mineral recovery and processing), such as from dilute leach dump Hquors, and analytical procedures are based on this phase-transfer process, as with precipitation. Solvent extraction theory and many separation systems have been reviewed (42). 

Mott played a major part, with his collaborator Frank Nabarro (b. 1917) and in consultation with Orowan, in working out the dynamics of dislocations in stressed crystals. A particularly important early paper was by Mott and Nabarro (1941), on the flow stress of a crystal hardened by solid solution or a coherent precipitate, followed by other key papers by Koehler (1941) and by Seitz and Read (1941). Nabarro has published a lively sequential account of their collaboration in the early days (Nabarro 1980). Nabarro originated many of the important concepts in dislocation theory, such as the idea that the contribution of grain boundaries to the flow stress is inversely proportional to the square root of the grain diameter, which was later experimentally confirmed by Norman Fetch and Eric Hall. 

It is shown that solute atoms differing in size from those of the solvent (carbon, in fact) can relieve hydrostatic stresses in a crystal and will thus migrate to the regions where they can relieve the most stress. As a result they will cluster round dislocations forming atmospheres similar to the ionic atmospheres of the Debye- Huckel theory ofeleeti oly tes. The conditions of formation and properties of these atmospheres are examined and the theory is applied to problems of precipitation, creep and the yield point."... 

Further details can be found in several texts including those on the theory of particulate processes (Randolph and Larson, 1988), crystallization (Van Hook, 1961 Bamforth, 1965 Nyvlt, 1970 Jancic and Grootscholten, 1984 Garside etal., 1991 Nyvlt, 1992 Tavare, 1995 Mersmann, 2001 Myerson, 2001 Mullin, 2001) and precipitation (Walton, 1967 Sohnel and Garside, 1992). 

Figure 6.12 Particle size distributions for agglomerative precipitation, (a) Theory according to equation 4.25, (h) Experimental results CaC03, o BaS04 Hostom.sky and Jones, 1993a,h)...

An alternative theory has been developed to model precipitation with agglomeration where, beside the overall particle size, an additional co-ordinate of crystal number within an agglomerate is introduced (Wachi and Jones, 1992). Figure 8.22 shows the concept of agglomeration and disruption respectively. 

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. 

S. Olive, U. Grafe, I. Steinbach. The modelling of Ostwald-ripening during non-isothermal heat treatments resulting in temperature dependent matrix solubihty of the precipitate forming elements a further development of the LSW-theory. Comput Mater Sci 7. 94, 1996. 

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