Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach

We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators

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. 1

Numerical modeling of two-phase underexpanded reactive CO2_2-into-sodium jets in the frame ofSodium nuclear Fast Reactors

International audienceSupercritical CO$_2$ (sCO$_2$) Brayton cycles have gained interest in the frame of Sodium-cooled nuclear FastReactors (SFRs), as an alternative to the conventional water Rankine cycles. If CO$_2$ leaks inside the CO$_2$-Na heat exchanger, an underexpanded CO$_2$-into-liquid-sodium jet is formed. CO$_2$ leaks at sonic velocityand chemically reacts with sodium, through an exothermic reaction. The consequences of such a scenariomust be investigated, in order to predict the temperature increasing inside the heat exchanger and on thetube walls, due to the exothermic chemical reaction, as well as the reaction products distribution insidethe heat exchanger. This article presents a numerical approach for modeling such a two-phase reactive jet.A two-fluid multi-component CFD approach is employed, with a heterogeneous reaction between theCO$_2$-gas and the sodium-liquid phases. The model allows to predict the most relevant information, such astemperature distribution, the jet penetration length and the reaction products distribution downstream theCO$_2$ leakage. Some experimental studies on underexpanded gas-into-sodium reactive jets, available inliterature, have been compared to our numerical results. It is found that the numerical temperature profilesare consistent with the ones experimentally measured

Étude qualitative de la croissance cristalline de HLnP2_2O7_7·3H2_2O ; (Ln = La, Gd)

The effect of reagents concentration, pH, and temperature on the crystallization of HLnP$_2$O$_7$·3H$_2$O (Ln=La, Gd) has been determined separately. The results show that the crystallization is enhanced at ambient temperature, by reducing reagents concentrations and using an optimal value of pH. Monocrystals of HLaP$_2$O$_7$·3H$_2$O and HGdP$_2$O$_7$·3H$_2$O have been obtained respectively with a length of 150 µm and 700 µm. The observation of HGdP$_2$O$_7$·3H$_2$O crystal state at different times of synthesis using optical microcopy indicates that the growth follows a bi-dimensional nucleation mechanism.L’influence de la concentration des réactifs, du pH et de la température, ont été étudiées séparément pour déterminer les conditions d’obtention des cristaux HLnP$_2$O$_7$·3H$_2$O (Ln = La, Gd). Les résultats ont montré que la cristallisation est favorisée, à température ambiante, pour des concentrations de réactifs relativement basses et dans un mélange dont le pH est optimum. Des monocristaux de HLaP$_2$O$_7$·3H$_2$O et HGdP$_2$O$_7$·3H$_2$O ont été obtenus de longueur respectives 150 µm et 700 µm. L'observation de l’évolution de la croissance de l'hydrate au gadolinium, par microscopie optique, a permis de conclure qu’elle se fait selon le mécanisme de nucléation bidimensionnell