CRYSTALLIZATION AND PRECIPITATION ENGINEERING .6. 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

This paper deals with the numerical simulation of the nucleation and c rystal growth processes involved in the batch precipitation of photogr aphic emulsions by the simultaneous addition of solutions of silver ni trate and sodium bromide to an aqueous solution of sodium bromide and gelatin. These processes have been successfully modelled in a previous paper (Muhr et at, 1995, Chem. Engng Sci. 50, 345-355). Two methods u sed to solve the population balance equation in order to follow the cr ystal size distribution are described. The partial differential equati on which represents the dynamics of the particle size density function psi is transformed into a series of ordinary differential equations b y means of the method of classes or by the direct discretization of ps i. After a comparison of both methods, the second option was selected for the calculations. To this series of equations ale added balances f or 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. R esults from example simulations are reported; the total number of crys tals, the average crystal size, the standard deviation of the crystal size, and the crystal size density function are calculated. Special em phasis is set on the problems of grid spacing and representation of th e primary nucleation process.