Liquid Transport Rates during Binary Collisions of Unequally-sized Particles

In this paper, we study the liquid transport between particles of different sizes, as well as build a dynamic liquid bridge model to predict liquid transport between these two particles. Specifically, the drainage process of liquid adhering to two unequally-sized, non-porous wet particles is simulated using direct numerical simulations (DNS). Same as in our previous work (Wu et al., AIChE Journal, 2016, 62:1877–1897), we first provide an analytical solution of a proposed dynamic liquid bridge model. We find that such an analytical solution also describes liquid transport during collisions of unequally-sized particles very well. Finally, we show that our proposed model structure is sufficient to collapse all our direct numerical simulation data. Our model is hence able to predict liquid transport rates in size-polydisperse systems for a wide range of parameter

Laboratory studies of aeolian sediment transport processes on planetary surfaces

International audienceWe review selected experimental saltation studies performed in laboratory wind tunnels and collision experiments performed in (splash-) laboratory facilities that allow detailed observations between impinging particles on a stationary bed.We also discuss progress in understanding aeolian transport in nonterrestrial environments. Saltation studies in terrestrial wind tunnels can be divided into two groups. The first group comprises studies using a short test bed, typically 1–4m long, and focuses on the transitional behavior near the upwind roughness discontinuity where saltation starts. The other group focuses on studies using long test beds — typically 6 m or more — where the saturated saltation takes place under equilibrium conditions between wind flow and the underlying rough bed. Splash studies using upscaled model experiments allow collision simulations with large spherical particles to be recorded with a high speed video camera. The findings indicate that the number of ejected particles per impact scales linearlywith the impact velocity of the saltating particles. Studies of saturated saltation in several facilities using predominantly Particle Tracking Velocimetry or Laser Doppler Velocimetry indicate that the velocity of the (few) particles having high trajectories increases with increasing friction velocity. However, the speed of the majority of particles that do not reachmuch higher than Bagnold's focal point is virtually independent of Shields parameter—at least for lowor intermediate u⁎-values. In this case mass flux depends on friction velocity squared and not cubed as originally suggested by Bagnold. Over short beds particle velocity shows stronger dependence on friction velocity and profiles of particle velocity deviate from those obtained over long beds. Measurements using horizontally segmented traps give average saltation jump-lengths near 60–70 mm and appear to be only weakly dependent on friction velocity, which is in agreement with some, but not all, older or recent wind tunnel observations. Similarly some measurements performed with uniform sand samples having grain diameters of the order of 0.25–0.40mmindicate that ripple spacing depends on friction velocity in a similar way as particle jump length. The observations are thus in agreementwith a recent ripple model that link the typical jump length to ripple spacing. A possible explanation for contradictory observations in some experiments may be that long observation sequences are required in order to assure that equilibrium exists between ripple geometry and wind flow.Quantitative understanding of saltation characteristics onMars still lacks important elements. Based upon image analysis and numerical predictions, aeolian ripples have been thought to consist of relatively large grains (diameter N 0.6mm) and that saltation occurs at high wind speeds (N26 m/s) involving trajectories that are significantly longer than those on Earth (by a factor of 10–100). However, this is not supported by recent observations from the surface of Mars, which shows that active ripples in their geometry and composition have characteristics compatible with those of terrestrial ripples (Sullivan et al., 2008). Also the highest average wind speeds on Mars have been measured to be b20 m/s, with even turbulent gusts not exceeding 25 m/s. Electrification is seen as a dominant factor in the transport dynamics of dust onMars, affecting the structure, adhesive properties and detachment/entrainment mechanisms specifically through the formation of aggregates (Merrison et al., 2012). Conversely for terrestrial conditions electric fields typically observed are not intense enough to significantly affect sand transport rates while little is known in the case of extra-terrestrial environments

Protok granulisanog materijala u statičkoj mešalici, DEM/CFD pristup

The mixing process greatly influence the quality of the intermediate and/or the final product, moreover, the parameters of the mixing process and the design of used equipment have a strong impact on mixing efficiency, the quality and the price of the product. In this article, Discrete Element Method is used for modeling of granular flow in multiple static mixer applications (Komax and Ross configurations were utilized). Computational Fluid Dynamic method was chosen for fluid flow modeling, using Eulerian multiphase model. Coupling of these two methods provides reliable, sufficiently correct and adequate results of proposed model compared to experimental measurements. The aim of this article is to predict the behavior of granules in different mixer configuration and to optimize parameters of the mixing process taking into account the duration of the mixing process and the quality of mixture, as well as the price of final product.Proces mešanja veoma utiče na kvalitet krajnjeg poluproizvoda i/ili krajnjeg proizvoda, a parametri procesa mešanja i dizajn opreme veoma utiču na efikasnost mešanja, kvalitet proizvoda i cenu proizvoda. U ovom radu, prikazana je upotreba metode diskretnih elemenata (engl. Discrete Element Method - DEM) na modelovanje mešanja granula u različitim konfiguracijama statičkih mešača (korišćene su različite Komax i Ross konfiguracije za mešanje). Za modelovanje protoka fluida primenjena je metoda računske dinamike fluida (engl. Computational Fluid Dynamic - CFD), korišćenjem Ojlerovog višefaznog modela. Povezivanjem rezultata ove dve metode dobija se pouzdan, dovoljno tačan i adekvatan model koji daje rezultate koji odgovaraju eksperimentalnim merenjima. Praćene su i analizirane trajektorije, brzine i ubrzanja čestica, u cilju procene kvaliteta procesa mešanja. Dobro poznati kriterijum za kvalitet mešanja, pod nazivom relativna standardna devijacija (RSD) je korišćen za ovu svrhu. Optimizacija dimenzija i parametara mešanja u statičkoj mešalici je izvedena korišćenjem matematičkog modeliranja. Cilj ovog rada je bio da se predvidi ponašanje granulamog materijala u različitim konfiguracijama mešalica i da optimizuje parametre procesa uzimajući u obzir trajanje procesa mešanja, kvalitet mešavine i cenu finalnog proizvoda mešanja. U istraživanju je primećeno da su Komax elementi primenljiviji, u poređenju sa Ross elementima, posebno kada je visina instalacije mala. Međutim, upotreba Ross je finansijski prihvatljivija, zbog njegove jednostavnije geometrije. Dodatna pregrada sa kvadratnim otvorima, koja se postavlja na izlazu iz statičke mešalice, koristi se da bi se umirilo kretanje granula na obodu cevi, kao i da smanji segregaciju granula

Jigging : a review of fundamentals and future directions

For centuries, jigging has been a workhorse of the mineral processing industry. Recently, it has also found its way into the recycling industry, and the increasing concerns related to water usage has led to a renewed interest in dry jigging. However, the current scenario of increasing ore complexity and the advent of smart sensor technologies, such as sensor-based sorting (SBS), has established increasingly challenging levels for traditional concentration methods, such as jigging. Against this background, the current review attempts to summarize and refresh the key aspects and concepts about jigging available in the literature. The configuration, operational features, applications, types, and theoretical models of jigging are comprehensively reviewed. Three promising paths for future research are presented: (1) using and adapting concepts from granular physics in fundamental studies about the stratification phenomena in jigs; (2) implementing advanced control functions by using machine vision and multivariate data analysis and; (3) further studies to unlock the potential of dry jigs. Pursuing these and other innovations are becoming increasingly essential to keep the role of jigging as a valuable tool in future industry

Numerical Investigation of Particles Breakage and Growth in Gas-Solid Processes: Spiral Jet Milling and Polyolefin Polymerization in Fluidized Bed Reactors

L'abstract è presente nell'allegato / the abstract is in the attachmen

MULTI-SCALE MODELING OF HIGH-SHEAR GRANULATION

High shear wet granulation is a particle design process used to increase the size of a primary powder material through the addition of liquid binder. This thesis focuses on the multi-scale nature of high-shear granulation in order to understand behavior changes due to coupled consolidation and coalescence as well as operational changes that occur during the scale up of horizontal ploughshare mixer granulators. The methodology relied on a micro-scale model for coalescence, a meso-scale model to describe flow within the granulator and a macro-scale population balance to describe the whole system

Mechanical dispersion of semi-solid binders in high-shear granulation

Granulation is an important industrial process used to produce many foods, medicines, consumer products, and industrial intermediate products. This thesis focuses on high shear wet granulation with the specific case study of detergent manufacture using a high shear pin mixer. The key rate process in detergent manufacturing was determined to be the mechanical dispersion of the semi-solid surfactant binder. The pin mixer and mechanical dispersion utilized experiments, population balance models, and discrete element method (DEM) models. The mechanical dispersion of the surfactant binder was studied using a lab scale 6 liter pin mixer. An experimental method was developed to isolate mechanical dispersion from the other rate processes of granulation. Experiments were conducted over a range of impeller speeds, mixing times, and surfactant injection temperatures. Two surfactants where used each with different yield stresses. The yield stresses of both surfactants were characterized using uniaxial compression tests and extrapolated to the impact speeds observed in the pin mixer. Using the yield stress to calculate the Stokes deformation number revealed that the breakage of surfactant would occur at all impact conditions in the pin mixer. The mechanical dispersion results demonstrated that the rate process could be modeled as a breakage process. The results determined that the key parameter governing the mechanical dispersion of paste was the number of revolutions of the impeller. This implies that impaction or sudden stress from the impeller is the mechanism that causes nuclei breakage. The results of the mechanical dispersion experiments were then used to develop a mechanistic semi-empirical model. Because the results indicated that breakage should occur for every impact with the impeller, the model was based on particle impact efficiency between the impeller and nuclei. The impact efficiency was described in a way similar to particle gas filtration where the Stokes number is the characteristic dimensionless group. The population balance model was breakage only and was able to accurately predict the full size distributions of the surfactant nuclei. The results showed that the model was able to accurately account for the effect of tip speed and number of revolutions. This was found by fitting the simulation to a single impeller speed and then predicting the size distributions by varying only the velocity input. Finally, a DEM unit shear cell was developed to understand the transmission of stress from a bulk material to a single large particle of interest similar to surfactant nuclei. The simulation examined the effect of both shear rate, placement of the large particle, and the material properties. The results determined that the material properties used in the simulation had a much greater effect on the shear profile and stress in the shear cell than the effect of the macroscopic shear rate. Using the von Mises yield criteria, the results demonstrated that the shear cell transmitted more stress to the large particle than the yield stress characterized experimentally from the surfactant. The results indicate that the surfactant should break in shear within the pin mixer. Mechanical dispersion has been successfully modeled for the case of detergent granulation in the pin mixer. The combined results demonstrate that mechanical dispersion of surfactant can be modeled as a breakage process. The number of impeller orations and the Stokes number are key parameters to accurately describe and model the simulation. The surfactant should break apart due to both impact and shear within the granulator

A compartmental CFD-PBM model of high shear wet granulation

The conventional, geometrically lumped description of the physical processes inside a high shear granulator is not reliable for process design and scale-up. In this study, a compartmental Population Balance Model (PBM) with spatial dependence is developed and validated in two lab-scale high shear granulation processes using a 1.9L MiPro granulator and 4L DIOSNA granulator. The compartmental structure is built using a heuristic approach based on computational fluid dynamics (CFD) analysis, which includes the overall flow pattern, velocity and solids concentration. The constant volume Monte Carlo approach is implemented to solve the multi-compartment population balance equations. Different spatial dependent mechanisms are included in the compartmental PBM to describe granule growth. It is concluded that for both cases (low and high liquid content), the adjustment of parameters (e.g. layering, coalescence and breakage rate) can provide a quantitative prediction of the granulation process

Dynamique d'écoulement et pellétisation dans un granulateur à rotor

Cette thèse propose différentes approches permettant de quantifier l’évolution de la dynamique d’écoulement particulaire dans un procédé de granulation et évaluer son impact sur celui-ci. Plusieurs types d’équipement permettent d’effectuer la granulation. Pour ce travail, un granulateur à rotor a été sélectionné puisqu’il permet de produire un écoulement de particules relativement simple à caractériser. Le choix de ce granulateur a aussi été basé sur le fait qu’il a été très peu étudié par rapport aux mélangeurs à cisaillement élevé ou les lits fluidisés. Le sujet de cette thèse est approché selon trois angles différents : • La caractérisation et la quantification des patrons d’écoulement et de ségrégation particulaire dans un sphéroniseur modifié (granulateur à rotor); • Le développement d’une méthode originale qui permet de contrôler l’intensité des forces interparticulaires dans un écoulement de particules à l’intérieur d’un sphéroniseur modifié; • Le développement d’un modèle multi-échelle prenant en compte le mouvement des particules afin de prédire la distribution de taille granulaire dans un procédé de granulation à rotor. Dans un premier temps, l’étude d’un écoulement dense d’un mélange de particules de 2 et 4 mm dans un sphéroniseur est effectuée. Pour y arriver, l’emploi d’une méthode par éléments discrets (DEM), une méthode numérique basée sur la seconde loi de Newton, permet de caractériser le déplacement des particules à l’intérieur de l’équipement. Le mélange des particules est analysé à l’aide d’indices de mélange ayant été développés par Doucet et al. (2008) afin de caractériser la ségrégation se produisant dans le domaine de particules. Cette partie du travail permet de montrer que le niveau de remplissage ainsi que la vitesse du disque (rotor) ont un effet significatif sur le phénomène de ségrégation observé. Pour des vitesses de disque variant entre 20 et 100 rad/s, le lit de particules prend la forme d’un tore où deux zones distinctes de ségrégation sont apparentes. Au fur et à mesure que la vitesse du disque augmente, les petites particules ont tendance à migrer de la zone localisée au centre du domaine toroïdal vers la deuxième zone localisée à la paroi du sphéroniseur. Les coefficients de corrélation spatiale employés pour le calcul de l’indice de mélange corroborent cette migration des petites particules. De plus, l’importance de prendre en compte l’intensité du cisaillement pour expliquer ces patrons de ségrégation est aussi exposée. Les deux zones de ségrégation associées à une concentration élevée de petites particules correspondent à l’emplacement où les taux de cisaillement sont les plus faibles. D’un autre côté, une corrélation considérant le niveau de cisaillement est développée afin de prédire le profil des vitesses azimutales des particules dans le sphéroniseur. Cette corrélation permet d’améliorer sensiblement la prédiction des profils de vitesses lorsque l’intensité du cisaillement est élevée. La deuxième partie de cette thèse présente le développement d’une nouvelle approche qui permet de simplifier l’introduction et le contrôle des forces interparticulaires de manière homogène dans un lit de particules en mouvement. Cette approche utilise un copolymère de PEA/PMMA qui, lorsqu’il est soumis à une augmentation de température au-dessus de sa température de transition vitreuse, cause l’apparition de forces cohésives entre des particules qui en sont enrobées. La relation entre les forces interparticulaires induites par le copolymère et l’écoulement des particules enrobées est établie avec l’aide d’un appareil de mesure de surface, plus communément appelé surface force apparatus (SFA). Cet équipement met en évidence l’augmentation linéaire des forces interparticulaires entre 10°C et 50°C. Les forces interparticulaires induites par cette nouvelle approche, comparées avec d’autres types de forces fréquemment rencontrées dans les procédés de granulation, permet de mettre en valeur la large étendue d’intensité de cohésion pouvant être obtenues. Par la suite, l’écoulement de particules cohésives est étudié pour deux applications différentes. La première application considère un écoulement dense de particules normalement observé pendant la granulation humide à l’intérieur d’un sphéroniseur modifié. La deuxième application montre la possibilité de pouvoir reproduire l’écoulement des particules observées dans les lits fluidisés à haute température avec l’avantage de pouvoir les opérer près de la température ambiante. La troisième partie de cette thèse utilise spécifiquement la méthode d’introduction des forces interparticulaires précédemment proposée afin de caractériser les écoulements de particules cohésives dans un sphéroniseur modifié. En contrôlant le niveau d’intensité des forces interparticulaires, quatre différents états d’écoulement sont obtenus. Le premier état est caractérisé par un écoulement libre des particules, lequel est observé près de la température ambiante. Le deuxième état est associé à l’apparition d’agglomérats à la surface du lit de particules, lesquels augmentent de taille à mesure que la température est haussée. Le troisième état fait référence à la formation d’une seconde couche de particules agglomérées dont le volume change de manière périodique en fonction du temps. Le quatrième état est caractérisé par un écoulement en masse produit par l’agglomération quasiment complète des particules. L’emploi d’un profileur laser permet de quantifier les différents états d’écoulement en mesurant la forme du tore obtenu ainsi que la variabilité de la position du profil de la surface du lit de particules. À la suite des résultats obtenus, un diagramme des états d’écoulement est construit. Ce diagramme montre le potentiel de cette approche pour imiter les écoulements cohésifs propres aux procédés de granulation humide. En conséquence, il est recommandé que la granulation humide soit opérée dans des conditions permettant d’obtenir le deuxième état d’écoulement décrit précédemment. Ceci est expliqué par le fait que les forces interparticulaires permettent d’induire la formation d’agglomérats sans toutefois nuire au mélange granulaire qui est essentiel pour obtenir un produit homogène. La quatrième partie de cette thèse utilise un modèle multi-échelle qui fait intervenir un bilan de population résolu à l’aide d’une méthode de Monte-Carlo commandée par événement. Ce bilan de population est utilisé pour simuler la granulation humide dans un sphéroniseur modifié. Il prend en compte l’échelle particulaire en considérant trois mécanismes de granulation qui sont le mouillage des particules, la coalescence et le bris. D’autre part, à l’échelle du granulateur, l’intégration du mouvement granulaire est prise en compte à l’aide d’une compartimentation du lit de particules. À l’aide d’une approche utilisant une chaîne de Markov à temps continu, les mouvements de particules entre les zones peuvent alors être considérés. La construction des propriétés de la chaine de Markov, soient le temps de séjour dans les zones et la matrice indiquant la probabilité de transition des particules entre celles-ci, est effectuée grâce aux résultats ayant été obtenus à l’aide de la DEM dans la première partie de cette thèse. Une fois le modèle multi-échelle mis en place, celui-ci est comparé à un modèle utilisant un bilan de population qui ne tient pas compte du déplacement des particules. Les résultats de simulation obtenus sont comparés aux expériences de granulation afin de voir les améliorations obtenues avec le modèle multi-échelle. Il apparaît que pour des conditions où le taux de mouillage est modéré, la considération du mouvement des particules permet d’améliorer les résultats de la modélisation. La distribution de taille des particules en fonction du temps correspond mieux à la tendance observée expérimentalement qu’avec un bilan de population conventionnel. Par contre, pour un taux de mouillage élevé, le modèle multi-échelle et le bilan de population conventionnel donnent sensiblement les mêmes résultats. ---------- This thesis proposes different approaches to quantify particle flow dynamics effects for granulation processes. Different types of granulation equipment exist. The rotor granulator has been selected for the simplicity of its design which produces easy to characterize particle flow patterns. The rotor granulator has also several advantages of the high shear mixers and fluid bed granulators but it has not been extensively covered in the literature compared to these granulators. The particle flow dynamics in the rotor granulator is investigated following three different points of view: • The characterization and quantification of the flow and segregation patterns in a modified spheronizer, which is similar to a rotor granulator; • The development of a new approach to control the intensity of the interparticle forces within the particle flow inside a modified spheronizer; • The development of a multiscale model which takes into account the motion of particles in order to predict the particle size distribution during granulation with a modified spheronizer. The first part of this thesis studies the dense granular flow of a 2 and 4 mm particle blend inside a spheronizer. The use of the discrete element method (DEM), a particulate model that can simulate the particle motion based on Newton’s second law of motion, allows characterizing the particle flow behavior inside the equipment. The particle mixedness state is assessed with the help of mixing indexes that have been developed by Doucet et al. (2008) in order to quantify the segregation occurring inside the particle bed. This study shows that the fill level and the disc rotational speed have a significant impact on the segregation phenomena observed. For a disc speed varying between 20 and 100 rad/s, the particle bed takes the form of a torus within which two distinct segregation zones are observed. As the disc speed increases, the small particles tend to migrate from a zone located at the center of the torus toward another zone which is observed near the spheronizer wall. This transfer of small particles is confirmed by the coefficients of correlation used by the mixing index, which relate the particle size and spatial coordinates. Moreover, the distribution of the shear rate in the particle domain explains the appearance of the segregation patterns. The two zones characterized by a high concentration of the smallest particles are correlated with the areas of the particle bed associated to a low shear rate. On the other hand, a correlation which considers the shear rate was developed to predict the azimuthal speed of the particles inside the spheronizer. This correlation improves the velocity profile predictions when the particle flow is characterized by high shear rate values. The second part of this thesis develops a new approach to incorporate and control interparticle forces homogeneously in the context of particle flow applications. This approach uses particles coated with a PEA/PMMA copolymer. When submitted to an increase of temperature above the copolymer glass transition state, the interparticle forces increase. A relationship between the interparticle forces created by the copolymer and the flow of coated particles is characterized with a surface force apparatus (SFA). This equipment shows that the cohesion forces increase linearly when the temperature in incremented from 10°C to 50°C. The interparticle forces obtained are in the same range as other common forces encountered frequently in granulation processes such as the capillary and the van der Waals forces. The flow behavior of the cohesive coated particles is applied to two different applications. The first application considers a dense particle flow normally encountered during a wet granulation with a modified spheronizer. The second application shows the possibility to mimic the particle flow behavior that would be obtained in high temperature fluidized beds but with the advantage of operating them near ambient conditions. The third part of this work uses the polymer coating approach proposed in the second part of the thesis to characterize the flow behavior of cohesive particles inside a modified spheronizer. By controlling the level of intensity of interparticle forces with the increase of temperature, four different flow states are observed. The first state is characterized by a free-flowing behavior of the particles, which is observed near ambient temperature. The second flow state is associated with the appearance of agglomerates at the surface of the torus of particles. These agglomerates increase in size as the temperature is incremented within this state. The third flow state refers to the appearance of a secondary layer formed by agglomerated particles the volume of which changes periodically with respect to time. The fourth state is characterized by a solid mass motion of the particle bed which is produced following the complete agglomeration of the particles. The use of a laser profiler helps to quantify the particle flow behavior observed for the different flow states by measuring the torus shape obtained and the variability associated with the surface profile position. These results help to construct a flow map representing the different flow behaviors observed. The flow map shows the potential use of the polymer coating approach to mimic the interparticle forces observed in wet granulation applications. Based on this flow map, it is shown that it is preferable to operate the wet granulation processes within the second flow state. This is explained by the fact that interparticle forces in this flow state induce the formation of agglomerates without preventing a good particle mixedness state that ensures the production of a uniform product. The fourth part of this thesis develops of a multiscale model based on an event-driven Monte-Carlo based population balance. It is used to simulate wet granulation in a modified spheronizer. The model takes into account the particle scale with three different granulation mechanisms, which are the wetting, the coalescence and the breakage of the particles. On the other hand, the granulator scale integrates the particle motion with a compartmental approach which divides the particle bed into different zones, each of which is associated with a granulation mechanism. The use of a continuous-time Markov chain allows representing the motion of the particles between the different zones. The properties of the Markov chain, which are the residence time in the different zones and the matrix containing the probabilities of transition between the zones, are built with the DEM simulation results of the particle flow in the spheronizer presented in the first article. Once the multiscale model is defined, it is compared to a conventional population balance that does not take into account particle motion. These two population balance models are then tested against granulation experiments with the modified spheronizer. The results show that for a low spray rate, the multiscale model improves results obtained with the conventional population balance without motion. On the other hand, the multiscale model and the conventional population balance give similar results when the spray rate is high. In this case, the granulation mechanisms overcome the effect of the particle flow pattern and the advantage of the proposed multiscale model is less apparent