Original Research Paper
Numerical analysis of mixing of particles in drum mixers using DEM

https://doi.org/10.1016/j.apt.2016.01.016Get rights and content

Highlights

  • DEM simulation studies for dead-zone formation in drum mixer with filling greater than 50%.

  • Mixing index proposed for quantifying degree of mixing.

  • Explanation of dead-zone formation on the basis of energy transfer pattern.

  • Elimination of dead-zone by incorporating baffles in the mixer.

Abstract

Mixing of particles in a rotating drum mixer with filling level greater than 50% has been analysed using Discrete Element Method (DEM). An attempt has been made to understand the mechanism of the dead zone formation and the degree of mixing by varying the mixing parameters. These include the size and packing of particles, speed and shape of the mixer, etc. While the formation of the dead zone is qualitatively analysed, the degree of mixing has been quantified with a suitable mixing index (ψ). It is found that packing arrangement and particle size significantly affect the formation of the dead zone, whereas, the drum speed and geometry has a relatively lesser effect. The effect of various parameters on the dead zone formation is explained on the basis of variation in energy distribution pattern from the wall towards the centre of the mixer. It has been found that the energy required for agitating the particles is transferred from the outer wall to the centre of the mixer. In the process of transfer, a significant amount of energy is expended before reaching the centre, which allows a compacted dead zone to form around the centre. A preliminary attempt has been also made to study mixing in a drum with baffles. The baffles act as the medium of efficient energy transfer by imparting their energy to the particles that come in contact with them thereby resulting in better mixing.

Introduction

Mixing and blending of particles is an important process in many industries, such as chemical, pharmaceutical, ceramic, plastic, fertilisers and minerals [1], [2]. The primary objective of mixing is to obtain a highly homogenised product, which often becomes difficult due to selective segregation of individual components. Although, different designs of drum mixers with lifters, blades or baffles have been attempted to avoid segregation, the improvements are not satisfactory. It is because of the design considerations that are often made without a fundamental understanding of the factors affecting mixing and segregation.

Rotating drum mixer shows different characteristics of charge motion depending on the mixer speed. The dynamic profile of the granular motion changes from slipping to centrifuging with increasing angle of repose as the speed of drum mixer increases [3]. The angle between the top surface of the rolling bed and the horizontal plane is called the angle of repose. The angle of repose increases with increase in speed of the drum [4], and decreases with the increase in particle size [5]. The transverse section of the rolling bed can be divided into active (also referred as rapid flow layer) and passive layers [6]. Boateng and Barr [6] defined a yield line or an interface surface that separates these two layers. Based on the initial filling pattern and filling level, various patterns are observed during the progress of mixing which also includes the avalanche effect [7]. The rapid flow of particles in the top layer along the slope is identified as the avalanche effect in mixers. Depending on the mixer design and operating conditions, the formation of the dead zone may also take place [7], [8]. Metcalfe et al. [7] and McCarthy et al. [8] primarily attribute this observation to static and dynamic angles of friction and to other geometrical variables.

The mixing rate varies in the axial and radial direction of the drum mixer. Convective mixing dominates in the radial direction, and slow diffusive mixing in the axial direction, and, therefore, statistical assessment of mixing based on sampling has been a challenge [9], [10]. The degree of mixing at various locations is an important parameter that describes the quality of mixing. Different type of mixing or segregation index based experimental [2], [11], [12], [13], [14], [15] and numerical studies [16], [17], [18] have been proposed by various authors to estimate the homogeneity of mixing. The use of thief probes is limited as they affect the mixing in surroundings of the insertion region [11]. The degree of mixing has been characterised by the methods such as optical imaging [12], online electrical capacitance measurement [13], near-infrared imaging [14], and other image analysis techniques [2], [15]. Cleary et al. [16] have proposed a model to describe mixing on the basis of local average of desired properties such as colour, mass or density. Moakher et al. [17] have quantified the degree of mixing by dividing the mixer into a number of vertical strips and tracking the axial coordinates of the particles present in each strip. Hill et al. [18] have used the tracer particles to determine the degree of mixing and segregation based on normalised standard deviation.

Baffles or blades are used in drum mixers to improve mixing and to avoid the dead zone formation [19], [20]. Design consideration of baffles and level of filling are critical for the improvement in mixing and reduction in the size of dead zone [19]. Jiang et al. [20] have extensively studied the effect of baffles. It was reported that baffles placed at the centre of the drum mixer along the axis results in improved mixing when compared to the baffles placed near the periphery.

Coarse particle mixing can be studied by direct simulation using Discrete Element Method (DEM), but as particle size decreases DEM becomes cumbersome and computationally intensive. Compared to continuum models, DEM treats granular materials as an assembly of discrete particles, each governed by fundamental laws of classical mechanics [21]. Mishra and Rajamani [22] have pioneered the application of DEM for studying the media charge motion in tumbling mills. A review on the applications of DEM techniques has been given by Guo and Curtis [23]. Most of the DEM simulation studies on mixing in rotating drum mixers have been confined to less than half filled mixers [14], [15]. The dead zone formation in more than half filled drum mixers have been reported earlier [7], [8]. However, the effect of packing on mixing and dead zone formation was not considered by these authors. In a practical scenario, packing fraction which is the ratio of volume occupied by solid to the total cell volume (φ = Vs/V), depends on the manner of filling/pouring of particles, agitation, surface properties, and moisture content. To represent different packing fractions, packing arrangements namely random packing, body centred cubic packing (BCC) and hexagonal close packing (HCP) have been studied. The present work is a continuation of the preliminary work carried out by Mishra et al. [24] to study mixing and flow behaviour of particles in a drum mixer with filling levels greater than 50%. It is an attempt to investigate on the missing understanding of the physics behind the mixing process and dead zone formation. In this study, detailed 3D-DEM simulations and experiments have been carried out to elucidate the effect of packing arrangement, particle size, speed and shape of drum mixer on the degree of mixing and the size of dead zone. A new method to quantify degree of mixing has been suggested and implemented, which throws light on the formation of the dead zone and variation in mixing pattern.

Section snippets

Model development and mixing index

In the present study, soft sphere or time-driven linear contact model based on Hooke’s law is used in the DEM simulations to compute the forces between the colliding particles [25], [26]. The general force balance equation for colliding particles is given byF=(Fn-Fnd)+(Ft-Ftd)where Fn, Fnd, Ft and Ftd are normal, normal damping, tangential and tangential damping force components, respectively. The mathematical expressions for these forces are given below.Fn=1615ER15mVcn216RE1/5δnFn

Experimental method

A Plexiglas drum of length 140 mm and diameter 280 mm was used for the experimental study. Black and white spherical glass beads of 5, 7.5 and 10 mm diameter at a time were randomly packed. The effect of particle size and mixer rpm on the extent of mixing and dead zone formation were investigated and validated experimentally. Two types of particles in the present study had identical properties but could be differentiated by their different colours. A vertical splitter was placed in the mixer along

Numerical simulations

DEM simulations for mixing of two types of particles were carried out under the simulation conditions given in Table 1. In most instances, the mill was filled up to 75% filling level with 5 mm particles in a random arrangement and rotated at 4 rpm unless otherwise stated. Particle properties, particle–particle and particle–wall interaction properties used in the simulations are given in Table 2. The material properties given in the table are obtained from the literature [28], [29], [30], [31].

Results and discussion

In order to study the effect of filling level on the mixing efficiency, DEM simulations were carried out with 30%, 50% and 75% filling levels. Fig. 3a–c shows the mixing patterns after four revolutions with filling levels of 30%, 50% and 75%, respectively. A dead zone is clearly visible in the case of 75% filling level. Fig. 3d shows the variation in ψmixer for the three different filing levels. The ψmixer values are much higher for the lower filling levels, indicating good quality of mixing

Conclusions

DEM simulations and experimental studies have been carried out to understand the mixing behaviour in drum mixers, with different filling levels, especially greater than 50%. The dead zone which is defined as an unmixed compact core has been observed in cases of filling levels more than 50%. Effect of various parameters, such as packing arrangement, particle size, speed of mixer and shape of mixer have been studied. It is found that the packing arrangement, particle size and mixer shape have a

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