ТЕОРЕТИЧЕСКИЙ ПОИСК ОПТИМАЛЬНОЙ ЗАГРУЗКИ ПЕРИОДИЧЕСКОГО СМЕСИТЕЛЯ ДИСПЕРСНЫХ МАТЕРИАЛОВ

International audienceThe objective of the study is to investigate how the hold-up of particulate solids to be mixed in a batch mixer influences the mixture quality and mixer capacity. It is known that a small amount of components (i.e., a small hold-up) allows reaching better quality of a mixer but leads to small capacity of a mixer. It is particularly appreciably when it is necessary to mix the components, which have a strong tendency to segregate into each other. In this case the perfect mixture cannot be reached, and there exists the optimum mixing time, at which the mixture homogeneity reaches maximum. This optimum time increases with the hold-up increase. Thus, from the mixing as such viewpoint, it is better to mix components not in big portions one time but in small portions several times. However, the total time of a mixing process consists of the loading time, mixing time and discharge time. The loading time depends on many factors such as a dosage device design, feeders design, and others, while the discharge time is usually much smaller. Thus, the mixer capacity is determined not only by the mixing time but also by the loading time at least. In order to estimate the mixer capacity at a required mixture quality, a cell model based on the theory of Markov chains is used. It is shown that the optimum hold-up exists that provides the maximum mixer capacity, and tЦель настоящего исследования – выявить, как загрузка предназначенных для смешивания в периодическом смесителе дисперсных материалов влияет на качество смеси и производительность смесителя. Известно, что небольшие количества компонентов (то есть малая загрузка) позволяют обеспечить лучшее качество смеси, но приводят к меньшей производительности смесителя. Особенно это проявляется, когда необходимо смешать компоненты, склонные к значительной сегрегации друг в друге. В этом случае полностью однородная смесь вообще недостижима, и существует оптимальное время смешивания, при котором качество смеси достигает максимума. Это оптимальное время возрастает с ростом загрузки. Таким образом, с точки зрения собственно смешивания, предпочтительно смешивать компоненты не один раз большими порциями, а несколько раз малыми порциями. Однако, полное время процесса смешивания состоит из времени загрузки смесителя, времени собственно перемешивания и времени разгрузки. Таким образом, производительность смесителя определяется не только временем собственно перемешивания, но также, по меньшей мере, и временем загрузки. Для того, чтобы оценить производительность смесителя при заданном качестве смеси, использована ячеечная модель, основанная на теории цепей Маркова. Показано, что существует оптимальная загрузка, которая обеспечивает максимальную производительность смесителя, и эта оптимальная загрузка существенно зависит от времени загрузки компонентов

Extrapolation of DEM simulations to large time scale. Application to the mixing of powder in a conical screw mixer

International audienceThe paper proposes an original algorithm which allows a long time scale extrapolation of DEM results at a very low computational cost. This algorithm can be adapted to any periodic processes. In this study, it is applied to the mixing process of powders within a conical screw mixer. The results are then compared with long time DEM simulations. It appears that this method is able to predict the DEM results with a very good accuracy

A Markov chain model of mixing kinetics for ternary mixture of dissimilar particulate solids

International audienceThis paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells (those with the void space) according to the proposed algorithm. The degree of non-homogeneity in the mixture (the standard deviation) is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this ``common'' time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained.(C) 2016 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved

Intensification of vibration mixing of particulate solids by means of multi-layer loading of components

International audienceThe objective of the study is to show how initial distribution of dissimilar particulate components influences the mixing time and mixture quality. The dissimilar components have a tendency to segregate in one another, and it is impossible to achieve the perfect mixture of them in industrial settings. Nevertheless, the situation can be improved if the components are loaded as a sequence of several sandwiches, each of these sandwiches containing layers of components that are proportional to their share in the mixture. In this case, a sort of pre-mixing occurs while still at the loading stage – which allows reducing the optimum mixing time and increasing the homogeneity of the mixture. The theory of Markov chains was used to simulate the mixing kinetics. It is shown that the number of loaded sandwiches has a very strong influence on the process efficiency. A loading device that can effectively realize multi-layer loading is proposed. The mixing kinetics for ternary mixture of glass beads was investigated experimentally at a lab scale vibration mixer. A one-time loading and a two-sandwich loading were compared. It was shown that the optimum mixing time and non-homogeneity of the mixture were reduced by half in the latter case

CFD modelling of powder flow in a continuous horizontal mixer

This work presents a continuum model for simulating the flow of powders inside continuous horizontal mixers. The challenge is to adopt a reliable rheological model that allows simulating granular flows accurately. We selected the μ(I)-rheology model. First, we considered a set of granular collapse experiments, showing that the model can successfully reproduce these flows, and also using the experimental results to evaluate the material properties of the powders. Then, we investigated the complex powder flow in continuous horizontal mixers. Here computational cost is a challenge. We showed that the sliding mesh technique is accurate but expensive owing to the rotation of the boundaries, making this method impractical for industrial applications. Therefore, we also employed the multiple reference frame technique, showing that its results are accurate at far lower computational cost. The results section ends with a sensitivity analysis of the mixer solid mass loading to the powder material properties

Discrete element method modelling of complex granular motion in mixing vessels: evaluation and validation

In recent years, it has been recognised that a better understanding of processes involving particulate material is necessary to improve manufacturing capabilities and product quality. The use of Discrete Element Modeling (DEM) for more complicated particulate systems has increased concordantly with hardware and code developments, making this tool more accessible to industry. The principal aim of this project was to study DEM capabilities and limitations with the final goal of applying the technique to relevant Johnson Matthey operations. This work challenged the DEM numerical technique by modelling a mixer with a complex motion, the Turbula mixer. The simulations revealed an unexpected trend for rate of mixing with speed, initially decreasing between 23 rpm and 46 rpm, then increasing between 46 rpm and 69 rpm. The DEM results were qualitatively validated with measurements from Positron Emission Particle Tracking (PEPT), which revealed a similar pattern regarding the mixing behaviour for a similar system. The effect of particle size and speed on segregation were also shown, confirming comparable results observed in the literature. Overall, the findings illustrated that DEM could be an effective tool for modelling and improving processes related to particulate material

Process systems engineering of continuous pharmaceutical manufacturing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, February 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 290-299).Continuous manufacturing offers a number of operational and financial benefits to pharmaceutical companies. This research examines the critical blending step for continuous pharmaceutical manufacturing and the characteristics of continuous downstream pharmaceutical manufacturing systems. Discrete element method (DEM) simulations were used to develop novel insights into the mechanism of mixing for continuous blending of cohesive pharmaceutical powders and to examine the effects of particle properties, blender design and operating conditions on blend homogeneity. To place continuous blending into the context of pharmaceutical manufacturing, the scope of the analysis was expanded to process system models of continuous downstream pharmaceutical manufacturing. DEM simulations were used to study the mechanisms of mixing in the continuous blending of pharmaceutical powders. Diffusive mixing from the avalanching particles appears to be the dominant mechanism of mixing in both the axial and radial direction for the double helical ribbon blender. This result can guide the development of future continuous pharmaceutical powder blenders by optimizing the mixing elements to increase the amount of particles transported to a position where they can avalanche/flow and diffusively mix. A range of particle properties, blender designs and operating conditions were examined for their effects on flow behavior and blend homogeneity. Three particle properties were examined: particle size, polydispersity and cohesive force.(cont.) Particle size was observed to be positively correlated to both flow rates and blend homogeneity. Polydispersity had no effect on flow rate and was negatively correlated to homogeneity. Cohesive force was negatively correlated to flow rate and had little to no effect on homogeneity. Two modifications of blender design were analyzed: changes in blender size and changes in shaft design. Blender size was observed to be positively correlated to flow rate and negatively correlated to homogeneity. The paddle shaft designs created a more homogeneous powder blend than the double helical ribbon shaft. Two operating parameters were also studied: rotation rate and fill fraction. Rotation rate was positively correlated to both flow rate and homogeneity. Fill fraction had the interesting result of being positively correlated to the absolute flow rate, but negatively correlated to the fill mass normalized flow rate. In addition, fill fraction has a clear negative correlation to homogeneity above fill fractions of 0.55, but is inconsistent for fill fractions lower than this. This research on particle properties, blender designs and operating conditions will help to guide the operation of continuous pharmaceutical blenders and the design of continuous pharmaceutical manufacturing systems. Process simulations comparing model batch and continuous downstream pharmaceutical manufacturing systems have quantified some of the potential size, cost and performance benefits of continuous processes. The models showed significant reductions in process equipment sizes for continuous manufacturing particularly in the blending step.(cont.) This reduction in equipment size translates to capital cost (CAPEX) savings for both the continuous process equipment and manufacturing facilities. The steady state operation of continuous processing also reduces the labor requirements and gives the continuous processes an operating cost (OPEX) advantage over batch processes. This research has contributed to the understanding of continuous pharmaceutical powder blending and quantified some of the benefits of continuous downstream pharmaceutical manufacturing. This work is being continued by the Novartis-MIT Center for Continuous Manufacturing whose work is providing the foundation for future industrial scale pharmaceutical continuous manufacturing systems.by Matthew J. Abel.Ph.D

Self-assembly of granular particles

Granular particles are ubiquitous in nature and daily life, and have wide applications in various disciplines such as infrastructure engineering, architecture, agriculture, etc. Yet, their fundamentals have not been fully understood by scientists. This is mainly because the structure of granular particles, which determines their properties, is complicated and can experience critical changes from disorder to ordered state. In recent years, understanding the fundamentals of such critical structural transitions of granular materials has become a hot multidisciplinary research topic attracting both scientists and engineers. Generally the transition from disordered to ordered structure can be regarded as a self-assembly process, which happens at different scales. In the nucleation of crystals, atoms or molecules can self-assemble due to thermal energy. For such thermodynamics systems, the theory of self-assembly is well established and is dependent on the Gibbs free energy. However, granular particles are much bigger and can dissipate energy quickly with the collision between particles, so they are normally at athermal or low-thermal states. The granular packings are prone to be disordered in structure, whereas they can also self-assemble with the input of external energy via vibration or shear, which can densify the granular packings and hence improve their properties for different applications. This thesis is devoted to advancing the knowledge of the self-assembly of granular spheres, particularly in better understanding the effects of the energy input and the boundary shape. The thesis has revealed a rich and deep picture for the effect of various factors on the self-assembly of granular particles, including the vibration mode, the container shape, material properties, different wall motions and gravity. The obtained results can improve the current understanding of the structural evolution and phase transition of the granular packings with or without vibration. The findings of this study enhance the knowledge on the self-assembly of granular systems and help take a step forward toward stablishing the mechanism behind the phenomenon. Thorough comprehension of the structure of the granular particles are essential for controlling the behaviour and properties of the granular materials, which can be of paramount importance for both the science and technology and have sensible influence on the mankind’s life