Hervé Muhr

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

Abstract 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.

Crystallization and precipitation engineering—V. Simulation of the precipitation of silver bromide octahedral crystals in a double-jet semi-batch reactor

Abstract In order to simulate the precipitation of silver bromide octahedral crystals, a model is developed, which encompasses the main kinetic and thermodynamic features of crystallization including primary nucleation, as well as equilibria in solution. The model is then validated during three steps (nucleation, ripening and growth) of experimental precipitations, which are supposed to be performed under well mixed conditions. The unknown kinetic parameters of the primary nucleation process are fitted to experimental data through the precipitation model. These investigations will contribute to a better understanding of the nucleation process, which is shown to be the most critical moment for the shape of the final crystal size distribution (CSD). Nevertheless, the duration of nucleation step is so short and the nuclei are so small that no quantitative results can be expected. Finally, mixing effects were observed and seemed to play a major role during the nucleation step.

The yield of a consecutive-competitive reaction in a double jet semi-batch reactor: comparison between experiments and a multizone mixing model

Abstract David and Villermaux (1987,1989) and Muhr (1990) have developed and applied a multizone mixing model (MZM) for semi-batch single jet mixing in stirred tanks. The aim of the present paper is to generalize the multizone model (MZM) to the case of a semi-batch stirred tank with two separate feedstreams, and to compare experimental data and model predictions. The model is applied to a consecutive-competitive reaction system (A+B→R; R+B→S) where the first reaction is instantaneous and the key reactant B is in defect. The model is based on both non perfect macromixing -depicted by the growth and movement of two mixing clouds issuing from by the feedstreams- and micromixing -depicted by engulfment processes within the clouds, passing across three zones of different turbulence intensity and followed by coalescence of the reaction clouds generated by the feedstreams. The model was able to predict satisfactorily the selectivity of the above reaction system without any parameter fitting for various stirring speeds and two couples of feed points.