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

Abstract

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.

Markov Chain Modeling the Mixing of Coal and Solid Heat Carriers in a Continuous Colliding Static Mixer

“…The results were different from those reported by some previous literature. 18,19 It indicated that the physical properties had little effect on the transition probability of particles in the continuous colliding static mixer, and the matrix of transition probability depended mainly on the type of mixing elements. The results showed that large different particles with a segregation potential could make good mixing in the continuous colliding static mixer.…”

“…The binary system is a kind of mixture easy to be separated because the ratio of particles size is close to 10. 18 3.3. Procedure.…”

Impact of process parameters on critical performance attributes of a continuous blender—A DEM‐based study

“…9 Several other types of mixing processes have been studied using computational techniques. 3,[9][10][11][12][13][14][15] These methods predominantly use discrete element modeling (DEM) to simulate flow and mixing, although other methods such as continuum modeling, [16][17][18] and Markov chain modeling, [19][20][21] data based methods, 22 and compartment modeling 23 have also been used in certain cases. DEM simulations have been shown to have good agreement with experimental studies of mixing using techniques such as Positron emission particle tracking 24,25 in batch mixers such as the V-blender 26 and simple rotating cylinder.…”

A 2D Markov chain for modelling powder mixing in alternately revolving static mixers of Sysmix® type

“…The matrix representation of the model allows state occupation to be calculated rapidly and also facilitates the derivation of macroscopic criteria of process efficiency, such as mixture homogeneity. Recently, we developed a Markov chain model to simulate the evolution of the axial non-homogeneity of binary mixtures in static mixers of "tube type", accounting for particle segregation during downward gravity flow [12]. In essence, it is a one-dimensional cell model which is not able to capture the crosswise mixing of particles during their flow through the tube.…”