A population model for crystallization processes using two independent particle properties

Abstract In this contribution a population model for crystallization processes with two independent particle properties is developed. The driving force for this model development was the enduring discussion about the influence of inner lattice strain on crystal growth. Different theories including deformation energies, mosaic spread and inner lattice strain have been brought up in the last years. In this work a first attempt is made to incooperate these ideas into a mathematical population model using two internal particle properties. The considered particle properties are the crystal length and the internal lattice strain of the individual crystals. Different assumptions for the relaxation of the internal lattice strain are compared with classical hypotheses for the growth behavior of crystals. The presented simulation results show a strong dependence of the steady-state mass density function on the different assumptions for the relaxation of the internal lattice strain during crystal growth.

[1]  R. Ristic,et al.  Assessment of the strain in small sodium chlorate crystals and its relation to growth rate dispersion , 1988 .

[2]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization—II. A moving pivot technique , 1996 .

[3]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[4]  Alfons Mersmann,et al.  Calculation of interfacial tensions , 1990 .

[5]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[6]  Alfons Mersmann,et al.  General prediction of median crystal sizes , 1992 .

[7]  J. Rawlings,et al.  Model identification and control of solution crystallization processes: a review , 1993 .

[8]  Terry A. Ring,et al.  Fundamentals of crystallization: Kinetic effects on particle size distributions and morphology , 1991 .

[9]  A. Mersmann,et al.  Initial-size-dependent growth rate dispersion of attrition fragments and secondary nuclei , 1992 .

[10]  William E. Schiesser.  The numerical method of lines , 1991 .

[11]  Alfons Mersmann,et al.  Brittle fracture in crystallization processes Part A. Attrition and abrasion of brittle solids , 1999 .

[12]  A. Myerson.  Handbook of Industrial Crystallization , 2002 .

[13]  S.E. Mattsson,et al.  A new technique for solving high-index differential-algebraic equations using dummy derivatives , 1992, IEEE Symposium on Computer-Aided Control System Design.

[14]  Sjoerd Dijkstra,et al.  Dynamic modeling of suspension crystallizers, using experimental data , 1995 .

[15]  Wolfgang Marquardt,et al.  DIVA—an open architecture for dynamic simulation , 1990 .

[16]  D. Ramkrishna.  The Status of Population Balances , 1985 .

[17]  M. A. Larson,et al.  Transient and steady state size distributions in continuous mixed suspension crystallizers , 1962 .

[18]  A. Mersmann.  General prediction of statistically mean growth rates of a crystal collective , 1995 .