Crystallization and precipitation engineering-VI. Solving population balance in the case of the precipitation of silver bromide crystals with high primary nucleation rates by using the first order upwind differentiation

• Published in: Chemical engineering science Vol. 51; no. 2; pp. 309 - 319
• Main Authors: Muhr, H, David, R, Villermaux, J, Jezequel, P.H
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1996; Elsevier
• Subjects: Applied sciences; Chemical engineering; Crystallization, leaching, miscellaneous separations; Exact sciences and technology; Crystal growth; Grain size; Chemical precipitation; Crystallization; Grain size distribution; Population balance; Batchwise; Photographic emulsion; Crystal nucleation; Numerical simulation; Silver Bromides; Kinetics; Semicontinuous
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/0009-2509(95)00257-X

This paper deals with the numerical simulation of the nucleation and crystal growth processes involved in the batch precipitation of photographic emulsions by the simultaneous addition of solutions of silver nitrate and sodium bromide to an aqueous solution of sodium bromide and gelatin. These processes have been successfully modelled in a previous paper (Muhr
et al., 1995,
Chem. Engng Sci.
50,345–355). Two methods used to solve the population balance equation in order to follow the crystal size distribution are described. The partial differential equation which represents the dynamics of the particle size density function ψ is transformed into a series of ordinary differential equations by means of the method of classes or by the direct discretization of ψ. After a comparison of both methods, the second option was selected for the calculations. To this series of equations are added balances for the total volume, moles of silver and moles of bromide. The aim of the present paper is to point out several details of the simulation. Results from example simulations are reported; the total number of crystals, the average crystal size, the standard deviation of the crystal size, and the crystal size density function are calculated. Special emphasis is set on the problems of grid spacing and representation of the primary nucleation process.