Influence of breakage on crystal size distribution in a continuous cooling crystallizer

A detailed two-dimensional population balance model of continuous cooling crystallization, involving nucleation, growth of the two characteristic crystal facets and binary breakage along the length of needle-shape crystals is presented and analysed. The population balance equation is reduced into a moment equation model of the joint moments of crystal size variables. The dynamic behaviour of the crystallizer and the effects of kinetic and process parameters on the characteristics of crystal size distribution are studied by simulation. The observations and analysis have revealed that there exist strong interactions between the breakage and the product properties

Modelling of heat exchange between drops in suspension polymerization of vinyl chloride

A population balance model is presented for suspension polymerization of vinyl chloride in a batch reactor to investigate the thermal properties of the system. Reactions are described using a simplified reaction model focusing on the heat generation of the highly exothermic polymerization reactions. The temperature of the continuous phase is assumed to be homogeneous over the reactor and the effects of some temperature rise of droplets due to the exothermic polymerization reactions and the possible heat exchange because of the coalescence/redispersion process are analysed. The population balance equation is solved applying a Monte Carlo method by coupling the deterministic polymerization reactions inside the droplets with the discrete event process induced by collisions of droplets. The results obtained by simulation show that rise in the temperature of droplets over the mean temperature of continuous phase lead to acceleration of the process. The possible size distribution of droplets and no smooth distribution of the initiator in those decrease the process efficiency

Modelling and Simulation of Particle Size Distribution of Precipitates in Continuous Tubular Crystallizers

This paper presents a population balance model for describing the temporal evolution of the particle size distribution of a precipitate produced in a laboratory scale tubular crystallizer, including nucleation, growth and agglomeration of crystals. The quadrature method of moments is used to calculate the moments of the crystal size distribution. The gamma probability density function with the sixth order Laguerre polynomials are used to reproduce the particle size distribution from moments. A sensitivity analyses is carried out by simulation that can be helpful when designing a crystallizer. Influence of the design and process parameters on the particle size distribution of product is analysed

Mathematical models fof simulation of continuous grinding process with recirculation

New mathematical and computer models and simulation programs were elaborated for studying processes of continuous grinding mills working with classification and partial recirculation of the product. The computer models were developed on the basis of the axial dispersion model taking into consideration also the effects of the mixing of the material to be ground. The effects of changes of parameters of both the mill and the material were studied. The stationary states of the continuous grinding mills working with and without classification and recirculation were compared to each other. The mathematical models and the computer programs developed are suitable for computing the processes of the grinding mills either with or without recirculation. They are usable for simulation based analysis and design of both continuous and batch grinding devices

Influence of cooling profile on the product properties in cooling crystallizers

Batch cooling crystallization process is investigated using different cooling procedures through mathematical modelling and computer simulation. The main element of the mathematical model is the population balance equation which contains both process and kinetic parameters. In the mathematical model of crystallizer the population balance equation is completed with the ordinary differential equations governing the mass balances of solute and solvent, as well as the heat balances of the crystalline suspension and the cooling medium. From the population balance model a set of differential equations was obtained for the first four moments of the size variable of crystals and the mass and heat balances, and the resulted equation system was solved in MATLAB environment. The dynamic properties and behaviour of the crystallizer depending on the cooling procedures was studied by numerical experimentation the results of which are presented and analysed

Quantification of the relative contribution of the different right ventricular wall motion components to right ventricular ejection fraction

Abstract Three major mechanisms contribute to right ventricular (RV) pump function: (i) shortening of the longitudinal axis with traction of the tricuspid annulus towards the apex; (ii) inward movement of the RV free wall; (iii) bulging of the interventricular septum into the RV and stretching the free wall over the septum. The relative contribution of the aforementioned mechanisms to RV pump function may change in different pathological conditions. Our aim was to develop a custom method to separately assess the extent of longitudinal, radial and anteroposterior displacement of the RV walls and to quantify their relative contribution to global RV ejection fraction using 3D data sets obtained by echocardiography. Accordingly, we decomposed the movement of the exported RV beutel wall in a vertex based manner. The volumes of the beutels accounting for the RV wall motion in only one direction (either longitudinal, radial, or anteroposterior) were calculated at each time frame using the signed tetrahedron method. Then, the relative contribution of the RV wall motion along the three different directions to global RV ejection fraction was calculated either as the ratio of the given direction’s ejection fraction to global ejection fraction and as the frame-by-frame RV volume change (∆V/∆t) along the three motion directions. The ReVISION (Right VentrIcular Separate wall motIon quantificatiON) method may contribute to a better understanding of the pathophysiology of RV mechanical adaptations to different loading conditions and diseases