Processes involving particles, are known to exhibit extremely unpredictable behaviour, mainly due to the mesoscopic nature of granular media. Understanding particulate processes, not only for intellectual satisfaction, but also for process design and operation, basically requires a systems approach in modelling. Because they combine simplicity and flexibility, the stochastic models based on the Markov chain theory are very valuable mathematical tools to this respect. However, they are still largely ignored by the whole core of chemical engineering researchers. This motivates the existence of this review paper, in which we examine the three traditional issues: mixing and transport, separation and transformation.
Continuous powder mixers offer a viable alternative to batch processes, but have received very little attention in scientific literature and in the industrial world. Mixer design is still very empirical and is not based on assessed methodologies. In this paper, we report experiments that aimed to compare two very different types of stirrers for a pilot-scale continuous powder mixer, and for two types of mixtures: a model mixture and a real pharmaceutical mixture. The first stirrer A is of the frame type with inclined paddles and internal transporting screw, the other stirrer B is of the shaft type with paddles mounted on it. Results are first presented from the viewpoint of bulk powder flow by holdup determination and correlation with operating conditions. General relationships are derived which show that the mobile B leads to higher holdups , which may be an important drawback. The study of mixture homogeneity globally confirms these findings, especially in a dense phase flow regime. In the fluidised regime, where the stirrer B can be used, attention is drawn to the negative effect of excessive rotational speeds on the quality of the mixtures.
This article demonstrates the efficiency of the application of the theory of Markov chains as a tool to model and simulate continuous powder mixing to aid in better design of such equipment. Markov chain models allow calculating practically all parameters of the process necessary for its characterization, and in particular those related to particle residence time distribution (RTD). Some numerical examples from the model, which are important for better understanding the process, are also included. It is shown that the main factor defining the efficiency of continuous mixing, through the variance reduction ratio (VRR), is the ratio of the mean residence time and the period of inflows fluctuation, rather than the variance of the RTD. Also, the influence of the dimensions of the mixer outlet on the mean residence time, and in turn on the VRR, is examined as another way of improving the design.
Cendrine Gatumel. A Markov chain model of mixing kinetics for ternary mixture of dissimilar particulate solids. Particuology , Elsevier, 2017, 31, p. a b s t r a c t This 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.
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