An Exponential‐Hyperbolic Crystal Growth Rate Model

Abstract

A new exponential-hyperbolic size-dependent crystal growth rate function G (L) = Gm(eaL -b)/ (eaL -c) is proposed. The model has been examined in detail for the direct determination of size-dependent crystal growth rates from the cumulative number oversize distribution of continuous Mixed-Suspension Mixed-Product Removal (MSMPR) crystallizers using both simulated and realistic data, both for systems that hold and that violate McCabe's AL law, respectively. It is show that direct fitting of cumulative number oversize distribution data using the proposed model gives an improved estimation of effective crystal growth rates over the whole size range during MSMPR crystallization compared with previous models tested.

Multidimensional Population Balance Modeling for Pathological Calcium Pyrophosphate Dihydrate Crystals in the Presence of Amino Acids

“…In literature, there are various expressions for the size‐dependent growth rate. Among these, the exponential‐hyperbolic model proposed by Mydlarz provides an advanced assessment to cover the entire size range in predicting growth rates at the steady state with respect to some others . In this study, the exponential‐hyperbolic correlation, similar to the M4 model but with the parameters having different meanings, was preferred to express the growth rates depending on the dimensions.…”

“…In this paper, the model used in our previous study was rearranged according to the growth and breakage in two directions . The growth was expressed in two directions depending on the particle sizes by an exponential‐hyperbolic function similar to the M4 model in literature . The breakage was stated in two directions, depending on the sizes as well.…”

Modelling of Growth Rate for MSMPR Crystallizer Data

“…JANCIC, GARSIDE; RANDOLPH, SIKDAR; WHITE et al ; GARSIDE, JANCIC). The effect of size-dependent growth on the CSD obtained in MSMPR crystallizers has been recently analyzed theoretically by MYDLARZ and JONES (1989,1990,1993), MYDLARZ andBRIEDIS (1992, 1993), and MYDLARZ (1995). The proposed models discussed in these references, the MJ-2, MJ-3, M-2, and M-4 are summarized in Table 8.…”

“…For such cases, methods of crystal growth rate estimation for MSMPR crystallizer d a t a have been recently discussed by MYDLARL a n d JONES (1989,1990,1993), MYDLARZ andBHIEDIS (1992, 1993) and MYDLARZ (1995). Several methods of growth rate dispersion modelling for both batch and MSMPR crystallizer data have been recently pro- It is well known that the rate of growth of a crystal in a supersaturated solution depends upon the supersaturations, the temperature, the concentration and nature of any impurities present, and also upon hydrodynamics which determine the boundary layer thickness and the mass transfer coefficient.…”