MULTI-SCALE APPROACH TO POPULATION BALANCE MODELLING OF DISPERSE SYSTEMS

A three-scale model is presented and analysed using the multi-scale methodology of complex systems. The micro-scale model is formulated as a set of stochastic differential equations for the individual disperse objects and it is shown that the population balance equation, containing also terms describing collision interchange of extensive quantities between the disperse elements is a meso-scale model of disperse systems. The macro-scale model is formulated by means of the moments of internal quantities. As an example a two-population model, governing the coupled behaviour of crystals and fluid elements is presented for describing micromixing in solution crystallization.