Modelling of strongly coupled particle growth and aggregation

Abstract : 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.
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Journal of Physics: Conference Series, IOP Publishing, 2013, 410 (1), pp.012086. 〈10.1088/1742-6596/410/1/012086〉
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Frédéric Gruy, Eric Touboul. Modelling of strongly coupled particle growth and aggregation. Journal of Physics: Conference Series, IOP Publishing, 2013, 410 (1), pp.012086. 〈10.1088/1742-6596/410/1/012086〉. 〈hal-00786825〉

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