Dynamical model of brushite precipitation

The objectives of this work are twofold. From academic point of view the aim is to build a dynamical macro model to fit the material balance and explain the main kinetic mechanisms that govern the transformation of the hydroxyapatite (HAP) into brushite and the growth of brushite, based on laboratory experiments and collected database. From practical point of view, the aim is to design a reliable process simulator that can be easily imbedded in industrial software for model driven monitoring, optimization and control purposes.Based upon a databank of laboratory measurements of the calcium concentration in solution (on-line) and the particle size distribution (off-line) a reliable dynamical model of the dual nature of brushite particle formation for a range of initial concentrations of the reagents was derived as a system of ordinary differential equations of time. The performance of the model is tested with respect to the predicted evolution of mass of calcium in solution and the average (in mass) particle size along time. Results obtained demonstrate a good agreement between the model time trajectories and the available experimental data for a number of different initial concentrations of reagents.