Growth rate expressions

Table 15.4. Mean over-all crystal growth rates expressed as a linear velocity ...

A number of investigators developed empirical growth rate expressions that included a size dependence. These models were siunmarized by Randolph Q2> 341 who showed that they all produced a concave upward semi-log population density plot thus are useful for empirical fits of non-linear MSMPR CSD data, lliese models however, supply no information on what is actually happening to cause the non-linear CSD. 

These dimensionless numbers can also be combined. For example, the ratio DaR/DaD compares the dissolution rate to the reactor throughput while the product DurNnu compares the nucleation rate with the reactor throughput. The exact form of the dimensionless numbers would change as the reaction kinetics, the growth rate expressions, etc. change, but the meanings would remain the same. 

Integration of this growth-rate expression then yields the parabolic growth law... 

Glucose activation constant in specific growth rate expression (mM) Glutamine activation constant in specific growth rate expression (mM) Lactate inhibition constant in specific growth rate expression (mM) Ammonia inhibition constant in specific growth rate expression (mM) Lactate concentration (mM)... 

The result of the above investigation is the following growth rate expression. For the case of one limiting nutrient, N, with Michaelis constant Km, the growth expression for the rate in the fh segment is... 

If we were to assume that the two-dimensional nucleus does not spread at all when it forms, a layer would be formed by the formation of enough two-dimensional nuclei of the critical size to cover the layer. The growth rate expression would therefore be... 

Limiting, Non-Zero Growth Rate Behavior. One of the most generally applicable growth rate expressions, developed for either kink, step, or ledge adsorption, is given as (Bliznakov 1959, 1965)... 

Based on the Cabrera and Vermilyea adsorption model. Black and Davey (1988) developed the following growth rate expression... 

Table E9.3 Numerically Integrated Crack Growth Rate Expression Between Oq and...

Figure 6.32. Dissolution and growth rates (expressed as a mass increase or decrease, normalized with the initial seed crystal mass) of a single potassium sulphate crystal in the presence o/Fe(III) as trace impurity added as FeNH4(S04)2 2H2O. (After Kubota et al., 1999)...

Estrin, J., Sauter, W.A. and Karshina, G.W. (1969) On size dependent growth rate expressions. AIChEJ, 15, 289-290. 

Figure 5.65. Dynamic relationship between specific rate of product formation and specific growth rate for various rates of the exponential decrease of the specific growth rate expressed with the aid of varied values of the constant K dapt (see Equ. 5.226). The steady-state relationship is obtained at large K values. (From Harder and Roels, 1982.)...

---