McCabe AL law

On the basis of the McCabe AL law, these results will be found ... 

Furthermore, the solution of a differential population balance requires that the relationship between growth rate and size of the growing crystals be known. When all crystals in the magma grow at a constant and identical rate, the crystal-solvent system is said to follow the McCabe AL law, while systems that do not are said to exhibit anomalous growth. 

The McCabe AL law (Ml) is probably the best known method for predicting product crystal size distribution. 

Crystal growth is a description of the linear velocity of a growing face, that is, the linear velocity perpendicular to that face. Growth velocity, in the classical view, is considered to be constant (size independent), according to the classical McCabe AL Law (McCabe 1929). 

If the system under consideration follows McCabes AL law, G G L), the result becomes... 

One of the first models for crystal growth is McCabe AL law and is given by the following size independent rate. 

Systems are said to follow McCabe s AL law (McCabe, 1929a,b) if they exhibit this behaviour, if not they are said to exhibit anomalous growth. 

A theoretical analysis of an idealized seeded batch crystallization by McCabe (1929a) lead to what is now known as the AL law . The analysis was based on the following assumptions (a) all crystals have the same shape (b) they grown invariantly, i.e. the growth rate is independent of crystal size (c) supersaturation is constant throughout the crystallizer (d) no nucleation occurs (e) no size classification occurs and (f) the relative velocity between crystals and liquor remains constant. 

Related Calculations. This method uses McCabe s AL law, which assumes total growth and no nucleation. For many industrial situations, these two assumptions seem reasonable. If significant nucleation is present, however, this method will overpredict product crystal size. 

McCabe s (1929a,b) AL law states that crystals of the same substance growing under the same conditions should grow at the same rate. Experimental evidence has shown that this law is frequently violated. The growth rate of a crystal face, for example, and the instantaneous velocity of steps spreading across the surface of a crystal have been shown to fluctuate with time, even though external conditions, e.g. temperature, supersaturation and hydrodynamics, remain constant. 

With the assumption that the growth rate G is not a function of the particle size (McCabe s AL-law), for a constant crystallizer volume and for a crystal-free inlet flow (no seeding) the population balance becomes... 

Let us now focus on an MSMPR crystallizer having a size-independent growth (McCabe s AL law). To determine the effect of t,es, we assume two situations where the suspension density Mp is identical but 4es/ G and n are different. From expression (6.4.18) for Mj and for two situations (identified by subscripts a and h) and from above,... 

If growth of the crystals does not follow McCabe s AZ law, then an underlining assumption of the derivation of the population distribution shown in Eq. (5.2) is not fulfilled. A generalized treatment of the curvature that can exist in the plot of In/i versus Z under such conditions is given by Abegg et al. (1968). 

Gulbransen and Andrew (1952), and McCabe et al. (1958) were treated separately by the third law then combined as shown in Table 42. The resulting linear equation,... 

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