An experimental method and a Markov chain model to describe axial and radial mixing in a hoop mixer

Aoun-Habbache, M; Aoun, Mohamed; Berthiaux, Henri; Mizonov, Vadim E.

doi:10.1016/s0032-5910(02)00193-6

Cited by 29 publications

(16 citation statements)

References 6 publications

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“…Matrix P has the properties that the summation of the elements over each column vector is unity and the value of each element is always between zero and one [9,18,19]. The distributions of kinetic and impact energy of particulate systems modeled using Markov chains is written as…”

Section: Markov Chains Modelingmentioning

confidence: 99%

Modeling of time-dependent distributions of impact and kinetic energies of particulate systems

Tjakra¹,

Hudon²,

Bao³

et al. 2013

AIP Conference Proceedings

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Abstract. This work develops an approach to modeling and analyzing the kinetic and impact energy distributions of particulate systems based on Markov chains. Markov chain operators represent the dynamics of kinetic and impact energy distributions. It can be used to estimate the evolution of energy distribution with respect to time. The obtained results lead to a good approximation when compared to that from Discrete Element Method simulation. In addition, a measure based on collective dynamic analysis is developed to relate particle impact energy (which is unmeasurable during operation) and particle kinetic energy (which can be estimated during operation) is developed. This measure opens a new pathway to measure particle impact energy from particle velocity which can be used for online monitoring, control and optimization.

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Section: Markov Chains Modelingmentioning

confidence: 99%

Modeling of time-dependent distributions of impact and kinetic energies of particulate systems

Tjakra¹,

Hudon²,

Bao³

et al. 2013

AIP Conference Proceedings

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“…In the past, Markovian models have been applied to various powder mixers. One can refer to the following works: Chen et al [10], Lai and Fan [11], Wang and Fan [12,13], Fan and Shin [14], Aoun-Habbache et al [15], Berthiaux et al [16], Ponomarev et al [17]. As all these papers described the process under steady conditions, only homogeneous Markov chains have ever been considered for mixing.…”

Section: A Simple Markov Chain Representation Of Continuous Mixingmentioning

confidence: 99%

Predicting bulk powder flow dynamics in a continuous mixer operating in transitory regimes

Ammarcha

Gatumel

Dirion

et al. 2012

Advanced Powder Technology

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 9970 a b s t r a c tOver recent years there has been increasing interest in continuous powder mixing processes, due mainly to the development of on-line measurement techniques. However, our understanding of these processes remains limited, particularly with regard to their flow and mixing dynamics. In the present work, we study the behaviour of a pilot-scale continuous mixer during transitory regimes, in terms of hold-up weight and outflow changes. We present and discuss experimental results concerning the start-up dynamics of a Gericke GCM 500 mixer, for which a specific experimental protocol has been developed to determine the evolution of the hold-up in the mixer and the real outflow. Empirical relationships are derived so as to link hold-up weight variations with operating conditions. A simple stochastic approach, based on a non-homogeneous Markov chain, is developed to simulate the bulk particle flow and transport in the continuous mixer at a macroscopic level. Although this simple model is only based on the start-up behaviour, it provides a full description of the mixer dynamics in response to strong perturbations on the flow rate or on the rotational speed of the stirring device, such as negative or positive steps. This model is validated experimentally for a wide range of operating conditions, and constitutes a first approach to process control.

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“…The same basic ideas can be used to describe chemical reaction kinetics or residence time distribution, as discussed by Tamir [13]. In powder technology, Markov chains have been specifically applied to model mixing and particulate flow [14][15][16][17][18].…”

Section: General Concepts and Toolsmentioning

confidence: 99%

Markov-chain modelling and experimental investigation of powder-mixing kinetics in static revolving mixers

Ponomarev¹,

Mizonov²,

Gatumel³

et al. 2009

Chemical Engineering and Processing: Process Intensification

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chain modelling and experimental investigation of powder-mixing kinetics in static revolving mixers. Keywords: Static mixer Mixing Markov chains Model Mixture quality a b s t r a c tThis study aims to develop a general model that is able to describe powder flow and mixing in static mixers, regardless of the type of mixer or the mixing configurations. The process model is based on a homogeneous Markov chain describing the flow of each component through the mixing zone by a series of interconnected cells. It accounts for the number of mixing elements and their disposition in the mixer, as well as particle segregation via different transition probabilities. Some simulations are given to emphasize this particular aspect. Other outcomes of the model include the number of passages to reach a required mixture quality, as well as the asymptotic distribution of components. A laboratory static mixer of revolving type was designed specially for this study. It comprises up to 10 mixing sections, and its high internal voidage favours free flow of the powder. Segregating and non-segregating mixtures have been used to test the model and adjust unknown parameters. The model gives very satisfying results. In particular, it is able to account for the oscillating character of mixing kinetics due to particle segregation. It is also suggested that these parameters could be linked separately to powder flowability and mixing element characterization.

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An experimental method and a Markov chain model to describe axial and radial mixing in a hoop mixer

Cited by 29 publications

References 6 publications

Modeling of time-dependent distributions of impact and kinetic energies of particulate systems

Modeling of time-dependent distributions of impact and kinetic energies of particulate systems

Predicting bulk powder flow dynamics in a continuous mixer operating in transitory regimes

Markov-chain modelling and experimental investigation of powder-mixing kinetics in static revolving mixers

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