Some aspects of crystallization theory: Systems that violate McCabe's delta L law

Abstract

In a continuous crystallizer operating at steady state, it is generally believed that crystal growth takes place in three steps (7). First, the solute being crystallized must diffuse from the bulk of the solution to the solid-liquid interface of the crystal. Second, at the interface a surface reaction occurs during which the solute becomes a part of the crystal lattice and heat of crystallization is liberated. Finally, the liberated heat must diffuse back to the bulk of the solution. Very little attention in the literature has been given the third step, and its effects on the overall process of crystallization are probably small in most systems, exhibiting relatively low heats of crystallization. The relative order of the first two steps has an important effect on the overall crystal growth rate.In most crystallization systems the solute diffusion resistance is less than the resistance offered b the surface tion made is that McCabe's AL law holds ( 1 ) . This law states that geometrically similar crystals of the same material suspended in the same solution grow at the same linear rate. If crystallization is truly a surface area-dependent reaction, with all resistance concentrated at the surface, then McCabe's AL law can be deduced from the following physical assumptions: (1) growth rate is a function only of supersaturation, (2) solubility differences due to crystal size are negligible, and (3) crystals remain geometrically similar with Growth rate r is here de ned as the rate of increase in length L of geometrically corresponding distances on the crystals. Thus For many systems where crystallization from solution occurs (1 to 3 ) , McCabe's AL law has been found to fit the experimental laboratory data well. For these systems, the diffusion resistance is probably less than the resistance due to the surface reaction, so that the rate of integration of the solute molecules into the crystal lattice determines the overall crystal growth rate. Since the solute molecules are believed to be added to the lattice much like building blocks, the growth rate as defined above should logically be essentially constant with increasing crystal size. In many industrial crystallizers that are well mixed, that is, approach closely the back-mixed or the MSMPR' concept ( 4 ) , the AL law has been found to hold as well.In a number of systems it has been observed that reaction. For these systems a common simpli Y ying assumprwth. growth rate actually increases with increasing crystal size ( 5 to 7). Most of these systems that violate the AL law have been highly hydrated crystals such as CuS04.5H20, MgS04.7Hz0, and Na2S04.10HzO. A diffusion mechanism can be postulated to account for violation of the AL law in such heavily hydrated systems where both the water molecules and the solute ions must diffuse to the solid-liquid interface before being integrated in the crystal lattice. For these systems, diffusion resistance plays a large part in determining overall reaction rate. In a mixed suspension, as the crystals grow larger, the slip velo...

Estimation of crystallization kinetics for an organic fine chemical using a modified continuous cooling mixed suspension mixed product removal (MSMPR) crystallizer

“…The Huber Tango (2) automated heater/chiller unit maintained the crystallizer vessel at a constant operating temperature. The recycle pipeline (9) was lagged with cotton wool and aluminium foil and a heat tracer was included to maintain a constant temperature in the transfer lines and prevent nucleation occurring in the lines. The heat exchanger temperature in the product recycle loop was increased as required to ensure complete dissolution of the solid in suspension and to ensure a crystal free recycle feed solution.…”

“…(8) and (9). The lower limits of the integrals were chosen as 1 mm and the upper limits as the largest crystal size produced in the crystallization vessel.…”

“…SDG and GRD are the most likely cause of deviation as discussed by Garside et al [6] and Janse and de Jong [7]. SDG has been modelled by direct fitting methods to the population balance using empirical correlations [8][9][10][11][12]. Mydlarz and Jones [13] proposed an exponential model, which has been successful in modelling SDG rates as a function of an effective SDG rate and crystal size and also applies to systems that obey the McCabe law.…”

Reaction‐Crystallization of Struvite in a Continuous Liquid Jet‐Pump DTM MSMPR Crystallizer with Upward Circulation of Suspension in a Mixing Chamber – an SDG Kinetic Approach

“…The available empirical or semi-empirical G(L) equations, proposed by Bransom [28], Canning and Randolph [29], Abegg, Stevens and Larson (ASL model) [30], Rojkowski (exponential [31], hyperbolic [32] and hyperbolic II models [33]), Mydlarz and Jones [34], and Mydlarz [35] were analyzed theoretically [36]. It was concluded, that the equations that are the most compatible of all with theoretical, physically grounded predictions (confirmed experimentally) are three SDG models developed by Rojkowski [31][32][33].…”

Nucleation and Crystal Growth Rates of Struvite in DTM Type Crystallizer with a Jet-Pump of Descending Suspension Flow in a Mixing Chamber

“…Using statistical methods (nonlinear regression) an appropriate kinetic SDG model was thus selected (assumed criterion -a minimum value of sum of variances over all n(L) measurement series). Five SDG models were taken under consideration: Canning-Randolph [22] , ASL (Abegg-Stevens-Larson) [23] as well as Rojkowski exponential [24] , Rojkowski hyperbolic [25] and Rojkowski hyperbolic II [26] ones. The Rojkowski hyperbolic [25] model proved to be an optimal one in respect to quality of fitting to the own experimental data-set, providing the values of G 0 , G ∞ and n 0 , Eqs.…”