# MULTI-SCALE APPROACH TO POPULATION BALANCE MODELLING OF DISPERSE SYSTEMS

### Béla Lakatos

#### Abstract

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.

#### References

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#### Paper Citation

#### in Harvard Style

Lakatos B. (2011). **MULTI-SCALE APPROACH TO POPULATION BALANCE MODELLING OF DISPERSE SYSTEMS** . In *Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-8425-78-2, pages 186-191. DOI: 10.5220/0003620701860191

#### in Bibtex Style

@conference{simultech11,

author={Béla Lakatos},

title={MULTI-SCALE APPROACH TO POPULATION BALANCE MODELLING OF DISPERSE SYSTEMS},

booktitle={Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2011},

pages={186-191},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003620701860191},

isbn={978-989-8425-78-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - MULTI-SCALE APPROACH TO POPULATION BALANCE MODELLING OF DISPERSE SYSTEMS

SN - 978-989-8425-78-2

AU - Lakatos B.

PY - 2011

SP - 186

EP - 191

DO - 10.5220/0003620701860191