Modelling of strongly coupled particle growth and aggregation
| Autor: | Frédéric Gruy, Eric Touboul |
|---|---|
| Přispěvatelé: | Laboratoire des Procédés en Milieux Granulaires (LPMG-EMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Centre Sciences des Processus Industriels et Naturels (SPIN-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département PROcédés Poudres, Interfaces, Cristallisation et Ecoulements (PROPICE-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-SPIN, Institut Henri Fayol (FAYOL-ENSMSE), Laboratoire Georges Friedel (LGF-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Lillouch, Fatima |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
History
[SPI.GPROC] Engineering Sciences [physics]/Chemical and Process Engineering growth Monte Carlo method particle growth Population balance equation 02 engineering and technology 010402 general chemistry 01 natural sciences Education Monte Carlo simulations bivariate population balance equation modelling symbols.namesake Initial value problem [SPI.GPROC]Engineering Sciences [physics]/Chemical and Process Engineering Statistical physics Mathematics Smoluchowski coagulation equation particle suspension aggregation Function (mathematics) 021001 nanoscience & nanotechnology 0104 chemical sciences Computer Science Applications symbols bivariate PBE Particle 0210 nano-technology Constant (mathematics) Event (particle physics) |
| Zdroj: | International Conference on Mathematical Modeling in Physical Sciences International Conference on Mathematical Modeling in Physical Sciences, Sep 2012, Budapest, Hungary. 410 (1), pp.012086, 2013 Journal of Physics: Conference Series Journal of Physics: Conference Series, IOP Publishing, 2013, 410 (1), pp.012086. ⟨10.1088/1742-6596/410/1/012086⟩ Journal of Physics: Conference Series (JPCS) International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE-2012 International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE-2012, Sep 2012, Budapest, Hungary. 410 (1), 2013 |
| ISSN: | 1742-6588 1742-6596 |
| DOI: | 10.1088/1742-6596/410/1/012086⟩ |
| Popis: | International audience; The mathematical modelling of the dynamics of particle suspension is based on the population balance equation (PBE). PBE is an integro-differential equation for the population density that is a function of time t, space coordinates and internal parameters. Usually, the particle is characterized by a unique parameter, e.g. the matter volume v. PBE consists of several terms: for instance, the growth rate and the aggregation rate. So, the growth rate is a function of v and t. In classical modelling, the growth and the aggregation are independently considered, i.e. they are not coupled. However, current applications occur where the growth and the aggregation are coupled, i.e. the change of the particle volume with time is depending on its initial value v0, that in turn is related to an aggregation event. As a consequence, the dynamics of the suspension does not obey the classical Von Smoluchowski equation. This paper revisits this problem by proposing a new modelling by using a bivariate PBE (with two internal variables: v and v0) and by solving the PBE by means of a numerical method and Monte Carlo simulations. This is applied to a physicochemical system with a simple growth law and a constant aggregation kernel. |
| Databáze: | OpenAIRE |
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