Constant crystal growth model

Constant Crystal Growth Model. In this instance, crystals have an inherent constant growth rate, but the rate from crystal-to-crystal varies. The modeling of this phenomenon must be accomplished by use of probability transform techniques due to the presence of a growth rate distribution. The complete solution for the population density yields a semilogarithmic population density plot that is concave upwards similar to size-dependent growth (Berglund and Larson 1984). Since it is relatively difficult to handle, a moment approximation was developed for an MSMPR crystallizer (Larson et al. 1985). 

These observations have been summarized in a statistical-mathematical equation called the Constant Crystal Growth (CCG) Model [. The CCG Model provides a generalized engineering approach to account for distribu-... 

Erdey-Gruz and Volmer (2) derived the current-potential relationship in 1930 using the Arrhenius equation (1889) for the reaction rate constant and introduced the transfer coefficient. They also formulated the nucleation model of electrochemical crystal growth. 

Reddy M.M., Plummer L.N. and Busenberg E. (1981) Crystal growth of calcite from calcium bicarbonate solutions at constant Pc02 and 25°C A test of the calcite dissolution model. Geochim. Cosmochim. Acta 45,1281-1291. 

Fig. 20 Crystal growth rate G of n-CiggTbgg calculated as a function of concentration at constant Tc using the model in Fig. 19. Parameters are those for C198H398 crystallization from phenyldecane at Tc = 98.0 °C, experimentally measured in [44], Compare with Fig. 12 (from [44] by permission of American Physical Society)...

Blaurock and Carothers (1990) and Blaurock and Wan (1990) described a simple way, valid for butteroil, of analyzing isothermal DSC data to characterize the kinetics of early crystallization in a supercooled oil. This approach yielded a single crystallization-temperature dependent combined nucleation/crystal growth constant (which they called NG). The temperature dependence of NG could be modeled with the Arrhenius equation. 

Hydrate crystal growth, unlike hydrate nucleation, is not a stochastic process. Hence, the intrinsic kinetics of hydrate growth can be studied experimentally and modeled. The intrinsic rate constant obtained for this process can be independent of the equipment used for its determination, if determined carefully with proper experimental design, and thus can be used for industrial or other applications. 

In the example shown in Figure 13.8, we can see that the preferential surface roughness occurs along the (x, v) plane. This type of periodical behavior can be modeled by a mathematical expression for crystal growth, G(x,y). On a first approximation, we can consider that along x the growth of the catalyst is constant so that... 

Fig. 16 is casted into a simple but quantitative lattice algorithm. The basic idea is that individual chains successively increase their internal order (characterized by the degree of chain folding) during the crystallization process. The more the chain is ordered (the fewer folds it has) the lower is the surface area needed for this chain. The ultimate degree of order is represented by the completely stretched chain which only occupies a surface area proportional to the cross-section of one stem ao (area of a crystalUne unit cell), see Fig. 16. Let Ao be the area of the corresponding liquid chain, flatly adsorbed onto the surface. Then, M = Aq/ao N > 1 chains can occupy the same area Ao in the crystalUne state. By contrast, in a simple growth model [27] the area per particle remains constant and it is the original dilution of particles which is responsible for the various diffusion-controlled patterns [28,55].

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