Calcium sulphate crystallisation in the presence of mesoporous silica particles: experiments and population balance modelling

A population balance model is used to investigate the effect of mesoporous silica particles on calcium sulphate crystallisation in a stirred batch crystalliser. The model accounts for nucleation, growth, agglomeration, breakage, and particle-assisted nucleation, and the model equations are solved numerically using the method of classes over a logarithmic, non-uniform mesh. The crystallisation process is characterized experimentally using electrical conductivity to track the ion concentration and laser diffraction to measure the steady-state crystal size distribution obtained at the end of the experiments. The experiments are carried out over a range of temperatures, initial supersaturations, particle pore diameters, and particle loadings. The model is first fitted to experimental data obtained in the absence of particles to determine kinetic parameters of the nucleation, growth, agglomeration, and breakage for pure calcium sulphate crystallisation. Varying pore diameter did not influence the catalytic effect of the particles, however, particle loading was found to significantly decrease the nucleation induction time. The model was extended to account for the presence of particles by fitting two additional mechanisms. The first proposed a particle-assisted nucleation where nuclei are produced via heterogeneous crystallisation, then detach by particle-particle collision that is second-order with respect to particle loading. The second proposed that the crystal breakage frequency increases linearly with particle loading. Good agreement with the experimental data is demonstrated over the range of conditions examined