KONA Powder and Particle Journal No. 41 (2024) 151–171/https://doi.org/10.14356/kona.2024015

Review Paper

Current Progress of Experimental and Simulation Work of
Mixing Processes in Particulate Systems †Xin Jin and Yansong Shen *School of Chemical Engineering, University of New South Wales, Australia

Particle mixing is a fundamental process used in various industries to handle powders,
granules, and pellets. Understanding particle mixing is critical for optimizing industrial
processes involving particulate systems, making it an important scientific and practicalconsideration. In this review, the current research progress of experimental and simulation
works for widely used tumbler and convective mixers is reviewed, and research gaps are
summarized for future investigations. Finally, some new development points of modern
particle mixing technologies and topics are mentioned. This paper provides a comprehensive
review of the research work of mixers in particulate systems and sheds light on future
research in the field of particle mixing.
Keywords: particle mixing, mixture homogeneity, mixer, discrete element method

1. Introduction

Granular materials, powders, and bulk solids are ubiquitous in nature, including soil, sand, and grains as well as invarious process industries, such as detergent, paint, plastics, chemical, mineral processing, metallurgical, pharmaceutical, biotechnology, and chemical industries (Duran,
2012; Forterre and Pouliquen, 2008). According to relevant
statistical data, about half of industrial products andthree-quarters of the raw materials exist in the chemicalindustry and are treated in the form of particle state (Leeand Henthorn 2012; Rhodes, 2008). Currently, the fundamental theory of motion equations of individual particles
and the force analysis of their interaction with other particles are not enough to describe the bulk particles’ behavior
in a practical industrial process because a large number ofparticles makes it difficult to predict their complex interactions accurately. Meanwhile, particles naturally own different physical properties (such as size, density and shape)(Ghadiri et al., 2020), and the segregation phenomenon isfrequently encountered while the bulk particles are treatedduring the industries, further hindering the deep understanding of the granular system. Unfortunately, due to theopaque nature of granular materials, there are few reliablemeasuring methods available to date. Furthermore, in practical industrial applications, granular systems are often incompletely fluidised, resulting in a complex systemcomprising multiple coexisting granular flow states. This†*

Received 27 March 2023; Accepted 9 May 2023
J-STAGE Advance published online 31 August 2023
Corresponding author: Yansong Shen;
Add: Via Gate 2, High Street, UNSW Sydney, NSW 2052, Australia
E-mail: ys.shen@unsw.edu.au
TEL: +61-2-9385-4448

complexity poses challenges to researchers studying granular systems. Therefore, the fundamental study of the
granular system is still a great challenge for both industry
and academia at the current stage.
For powder, granular, or pellet products in different industrial processes, particle mixing is an essential unit operation, such as the drying and storage of grains, theprocessing and packaging of pharmaceuticals, and themining and processing of coal, etc. (Bridgwater, 2012;
Ottino and Khakhar, 2000). Most of these industrial processes require a well-mixed degree of mixture for the final
or middle products to confirm consistent product quality
and high production efficiency. The development of effective techniques and technologies for controlling particle
mixing and separation is of great importance, as it can leadto energy and cost savings in processing, as well as advancements in the field of particle mechanics. Achieving
rapid and homogeneous mixing is a crucial objective.
Therefore, it is of great significance to reveal the underlying fundamentals and promote the operating performanceof particle mixing processes for modern industries.
In this review, the current research progress of experimental and simulation works for widely used tumbler andconvective mixers is reviewed, and research gaps are summarized for future investigations. Finally, some new development points of modern particle mixing technologies andtopics are mentioned (Jin, 2022).

2. Research progress summary ofexperimental work

Over the past few decades, numerous experiments havebeen conducted to examine the mixing behavior of various
mixers. This section will present a concise summary of

Copyright © 2024 The Authors. Published by Hosokawa Powder Technology Foundation. This is an open
access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/).

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relevant experimental studies organised and reviewed
based on the categorisation of mixers.

2.1 Experimental work of tumbler mixers

Rotating drums, as versatile equipment, are extensively
employed in various industries, such as rotary kilns, dryers,
mixers, reactors, and granulators for processing granularmaterials. The rotating drum is a widely used apparatus inlaboratory studies of solid mixing phenomena due to its
simplicity in geometry and ease of operation control compared to other mixing equipment. Moreover, the rotating
drum can be designed to be transparent, closed, and relatively thin, making it suitable for observing particle motion
and studying fundamental phenomena of solid mixing. For
example, to investigate the movement of particles in athree-dimensional rotating drum at low to medium rotational speeds, Ding et al. (2001) employed a combinationof experimental and theoretical methods. The researchers
employed the non-invasive positron emission particle
tracking (PEPT) technique to monitor the trajectories andvelocities of particles. Additionally, they developed a mathematical model utilizing the thin-layer approximation tocharacterise the motion of solids within the active layer.
The experimental results were compared with the model,
and good agreement was found between the two. Santomaso
et al. (2004) conducted a study on the mixing of non-ideal
powders, specifically granular tetraacetylethylenediamine(TAED), in rotating batch cylinders that were operating in
the rolling regime. They characterised and quantified the
local mixture composition by utilizing a solidification technique in combination with computerised image analysis.
Observations showed the formation of a temporarily poorly
mixed core at low rotation speeds, and the role of convection in the mixing mechanism of non-ideal granular mate-

Review Paper

rial was identified through the identification of convective
fluxes resulting from the friction between the powder andend plates of the mixer. Zhang et al. (2018) conducted astudy utilizing the Magnetic Particle Tracking (MPT)
method to examine the particle motion in flighted rotating
drums. This was the first investigation of its kind to utilise
MPT. The study focused on the behavior of plastic balls
and soybeans in a rotating drum with a 5 % filling degree atvarious drum rotating speeds ranging from 10 to 40 rpm.
The study analysed the particle motion in a rotating drumby examining particle trajectories, distributions of translational and rotational velocity, falling time of the dilutephase, and instantaneous velocity of the dilute phase in theequatorial region. The analysis showed that the rotating
speed of the drum had a significant impact on the particle
motion, with only minor effects from particle size andshape within the studied range. The schematic of the experimental setup and the critical results can be seen in Fig. 1.
Li R. et al. (2021) conducted experiments to investigate thevelocity distribution of rice particles in a rotating drum. As
illustrated in Fig. 2, the results revealed that the flow of riceparticles often displayed multiple velocity peaks. At low
rotation speeds of 1–3 rpm, the particle flow within the rotating drum transforms into an avalanche mode. This is dueto the slope of the accumulation surface exceeding the angle of repose, causing particles to slide and cover the entire
particle bed. As a widely used apparatus in solid mixing
studies, rotating drum experiments have yielded important
insights in the past three years, as summarized in Table 1.
In contrast to the rotating drum, there exists a relatively
limited amount of experimental work on other types oftumbler mixers. The following section provides a review ofsome important experimental studies.
Brone and Muzzio (2000) performed a comparison ofFig. 1 Schematic of the experimental setup and critical experimental results, reprinted with permission from Ref. (Zhang et al., 2018). Copyright:(2018) Elsevier B.V.

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Fig. 2 System and particle setup: (a) the measuring system includes a
LED light source and a CCD camera; (b) the drum is half filled withthree types of particles, respectively: spherical particles, Rice particles
A with AR = 2 and Rice particles B with AR = 3, reprinted with permission from Ref. (Li R. et al., 2021). Copyright: (2021) Elsevier B.V.

the mixing performance between a conventional doublecone blender and a modified version incorporating a stationary deflector plate. The latter was designed to enhance
axial particle flow and was found to be highly effective inachieving improved mixing outcomes. The results showedthat the incline of the deflector plate relative to the mixer
plane resulted in the creation of a convective axial flow
across the centre of the blender, leading to an increase in
the mixing rate by a factor of 25. The images demonstrating the plate effect on mixing within the double cone can befound in Fig. 3. Volpato et al. (2018) examined the effectsof the unloading process on mixture quality in three distinct
types of tumbling mixers, namely symmetrical double
cones, asymmetrical double cones, and conic mixers. The
experiments utilised tetraacetylethylenediamine (TAED)
powder that was available in different size ranges and differentiated by colour, either white or blue. The results
showed that tumblers capable of unloading the material in
the mass flow regime performed better than those operatingin funnel flow. Specifically, the best mixing performance
was obtained using an asymmetrical double-cone mixer.
An intrusive investigation of mixing characteristics in a
double-cone mixer utilizing discrete pocket samplers was
conducted by Cho et al. (2012). Millimetre-sized glass
beads were used in the study. The results indicated that axial mixing was improved by 70–90 % with the implementation of dual-axis rotation, compared to single-axis rotation.
It was observed that particles of smaller size (art sand) exhibited faster mixing compared to larger particles (glass
beads) due to the presence of mild cohesive effects. Fig. 4
provides visual representations, obtained through experiments, of the mixing characteristics of glass beads ofvarying sizes during single-axis and dual-axis rotations.
Alexander et al. (2004) conducted experimental studies
to examine the stable segregation patterns in V-blenders

Review Paper

under varying vessel capacities, fill levels, and rotation
speeds. The findings indicated that the magnitudes of particle velocities determined the pattern formation. However,
the relationship between the formation of segregation patterns and the fill level of the blender could not be established due to the intricate flow patterns in the V-blender.
The photographs related to this study are depicted in Fig. 5.
Kuo et al. (2005) utilised the PEPT technique to investigate
the movement of 3 mm glass beads within a V-mixer. The
results of their experimentation exhibited a linear correlation between the axial dispersion coefficient of the particles
and the rotational speed of the V-mixer, with an increase
observed in the coefficient from 15 rpm to 60 rpm. Crouterand Briens (2015) conducted a study exploring the feasibility of utilizing passive acoustic emission monitoring as atool for monitoring the mixing process in a V-blender. The
acoustic emissions acquired during the tumbling of the
V-shell were subjected to a wavelet filter to remove the associated vibrational noise. This enabled a concentration of
information pertaining to particle movement and interactions within the V-shell. The study conducted by Crouterand Briens demonstrates that passive acoustic emissions
can be employed as a monitoring method to gain insight
into the movement and interactions of particles in a
V-blender. By analysing the measured vibrations, valuable
information about particle behavior can be obtained. As
such, the study highlights the potential of this approach formonitoring V-blender operations.

2.2 Experimental work of convective mixers

In contrast to tumbler mixers, convective mixers incorporate rotating components to increase the mixing rate andimprove mixing performance (Rahmanian N. et al., 2008).
Some typical types of ribbon mixer can be found in ourprevious work, as shown in Fig. 6. MArczuk et al. (2017)
conducted experimental studies on a horizontal ribbon
mixer in a livestock farming mechanization laboratory,
employing a personal computer, measurement and control
devices, and instruments in accordance with GOST 15.10198. The results indicated that the mixing time significantly
affected the amount of mixing components, the uniformity
coefficient of the mix, the capacity, and the specific energy
consumption. Yeow et al. (2011) conducted an experimental investigation to examine the effects of various operating
parameters and feed preparation characteristics on the homogeneity of mixing in a batch ribbon mixer. Lactose
100 M, Lactose 200 M, Ascorbic Acid, and Zinc Oxide
powders were utilised as the testing materials for the study.
The physical geometry of the batch ribbon mixer is depicted in Fig. 6. The findings indicated that improved
mixing homogeneity could be achieved by increasing therotational speed and duration of mixing, as well as throughpre-blending and using smaller feed particle sizes, whichenabled the attainment of the desired homogeneity in a

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154

StructureD = 50 mm
L = 50 mm
Plexiglass

D = 400 mm
L = 400 mm
Plexiglass

D = 290 mm
L = 50 mm
Plexiglass

D = 122 mm
L = 75 mm
Plexiglass

D = 220 mm
L = 320 mm
Plexiglass

D = 160 mm
L = 10 mm
Plexiglass

D1 = 287 mm
D2 = 209 mm
D3 = 162 mm
L = 100 m

D = 400 mm
L = 400 mm
Plexiglass

Reference(Nijssen et al., 2022)(Miao et al., 2022)(Kumar et al., 2022)(Kato et al., 2022)(Jadidi et al., 2022)(Li R. et al., 2021)(Jiang et al., 2021)(Huang et al., 2021)
Glass beads
22 mm and 12 mm
2500 kg/m3

Acrylonitrile butadienestyrene (ABS)15, 10, 6, and 3 mm
1100 kg/m3

Glass beads 2 mm
2500 kg/m3
Rice length = 4 mm
aspect ratio 21020 kg/m3

Glass beads
5 mm2500 kg/m3

Plastic particles
6 mm
1800 kg/m3

Sphere, oblate, prolate
and elongated-needle
1–6 mm2500 kg/m3

6 and 12 mm
2500 kg/m3

Cork particles
6.3 mm152 kg/m3

Solid properties

20 %–50 % filllevel
10 rpm

30 % fill level
0–200 rpm

50 % fill level
3–5 rpm

40 %10, 40 and 70 rpm

2000 white2000 black
30, 50 and 70 rpm

60 % fill level
5 rpm

10 % and 20 % filllevel
±40 rpm

35 % and 45 % filllevel
20, 40, 60 and80 rpmImage recognition
method using
stacked images

PhantomV10
high-speed camera

PIV algorithm
using the images

Digital camera

Digital camera

Digital camera(NIKON D5300)

Multi-camera
acquisition system

Magnetic particle
tracking (MPT)

Operating condition Measuring method

The segregation indices, radial for short drums and axial for longdrums, can be utilised to quantify the overall level of segregation inrotating drums.

・The movement trajectories of individual and multiple particles inrotating drums were found to conform to the established similarity
criteria.

・The flow of rice particles frequently exhibits a distribution withmultiple velocity peaks.
・When the rotating drum’s speed is lowered to 1–3 rotations per
minute, the flow of rice particles transforms into an avalanche mode.

・The mixing performance was significantly impacted by both the
impeller speed and the initial loading pattern.

・A novel approach for determining the mixing curve of particles wasestablished through the use of discrete element method (DEM) simulation, which involved the examination of particle behaviour over alimited time.

・The mixing behaviour is influenced by the shape of both coarse andfine particles.
・The extent of radial segregation for coarse particles demonstrates adecreasing trend: sphere>oblate>prolate>elongated-needle. For the fineparticle, the trend follows as sphere>cube>prolate.

・The formation of alternating axial segregation bands can be observedin adjacent axial segments with similar velocity directions, while
improved overall mixing is observed under conditions where thevelocity direction is opposite.

・The presence of water leads to significant alterations in the particlewall and particle-particle interactions, resulting in significant changes
in the behaviour of the bed.

Reported results

Table 1 Some essential experimental experiences for the mixing processes in the rotating drum in the last 3 years. (Continued on next page)

Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171
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Polyformaldehyde beads
3 mm and 4 mm

Polyformaldehyde
Particles
3 mm and 4 mm
1410 kg/m3
7 μm Al2O3 powders
Glass bead
6 mm
596 kg/m3

D = 280 mm
L = 20 mm
Glass

D = 280 mm
L = 20 mm
Glass

D = 194 mm
L = 150 mm
Acrylic glass

D = 280 mm
L = 20 mm
Glass

D = 300 mm
L = 15 mm
Glass

D = 140 mm
L = 200 mm
Plexiglass(L and Huang, 2021)(Chung et al., 2021)(Zhang et al., 2020)(Liao et al., 2020)(Lia and Tsai, 2020)(Chen et al., 2020)

50 % fill level2, 3, and 4 rpm

10 %–50 % filllevel
0.3 rpm

Glass beads
4–6 mm2500 kg/m3

50 % fill level
1, 2, 3, and 4 rpm

10, 15, and 20 %fill level10, 20, and 30 rpm

50 % fill level2, 3 and 4 rpm

50 % fill level2, 3 and 4 rpm

20 % fill level
20 rpmArea CCD camera(IDT Y7-S1)

Digital Video (DV)
camcorder (SONYHDR-PJ820)

Image-processing
technology and aparticle-tracking
methodParticle tracking
velocimetry (PTV)

Digital video
motion recorder/
analyzer(SONY
HDR-PJ820)

Image-processing
method andparticle-tracking
technology

Camera (1 fps,
HDR XR-520,
Sony, Japan)

Operating condition Measuring method

Polyformaldehyde
3 mm2480 kg/m3
1410 kg/m3
900 kg/m3

Polyformaldehyde
4 mm 1410 kg/m3
7 μm Al2O3

Glass beads
1.19 mm–1.41 mm
0.84 mm–1.00 mm
2500 kg/m3

D = 100 mm
L = 400 mm
Plexiglass(Huang et al., 2021b)

Solid properties

Structure

Reference

・The movement of particles resulting from an avalanche mode
induces the rearrangement of particles at the upstream region of the
granular bed.
・The magnitude of energy dissipation through particle rearrangement
increases with the degree of particle filling.

・In a binary granular mixture, the steady-state segregation index
increases proportionally with the density ratio.
・The final steady-state segregation index for multi-density granularmaterials is lower than that of binary granular mixtures.

・The inclusion of a minimal quantity of fine powder substantially
impacts the dynamic characteristics and segregation behaviour as
influenced by density.
・An increase in the fine powder content is found to result in a corresponding increase in both the average velocity and the average granulartemperature. This phenomenon is attributed to the presence of a lubrication effect between the particles.

・In relation to the rotating drum, an increase in the speed of rotation
corresponds to an increase in the holdup ratio and the discharge rangeof materials from the flight. The cascading rate of a single flight isfound to be more affected by the rotation speed during the initial andfinal discharging stages.

・The research has shown that the flow properties of granular mixtures
can be enhanced by the lubricating effect generated by an optimal
amount of fine powders.
・The degree of segregation, as measured by the segregation index, as
well as the rate of segregation, exhibit a positive correlation with thefraction of fine powder and the rotational speed of the drum.

・The state of liquid distribution significantly impacts the behaviour ofsize-based granular segregation.
・In this study, an examination of the relationship between the granulartemperature and segregation behaviour was conducted.

・When the IS ring pair is positioned outside the end wall shearing
zone, which is defined as an area with a radius of 10 particle diameters,
it was observed to have an independent impact on local mixing throughits ring shearing mechanism.
・In a drum with 40 % of the particles present, the critical width thatmust be present for an Inner-Shear (IS) ring pair to exist is roughly 30
particle diameters or 52 % of the transverse area of the bed.

Reported results

Table 1 Some essential experimental experiences for the mixing processes in the rotating drum in the last 3 years. (Continued from previous page)

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Fig. 3 Demonstration of the effect of the plate on mixing within the double cone. All experiments correspond to a filling level of 50 %. The standard
double cone shown at (a) the initial condition, (b) after one min and (c) after 10 min (160 revolutions). The enhanced double cone shown at (d) the
initial condition, (e) after 1 min and (f) after 10 min (160 revolutions), reprinted with permission from Ref. (Brone and Muzzio, 2000). Copyright:(2000) Elsevier B.V.

Fig. 4 Snapshots from the experiment with glass beads of different sizes for single and dual axes rotations. (a) 1 mm glass beads: corresponds to X
rotational speed = 10 rpm; no rotation about the Y axis (i.e. 0 rpm); (b) 1 mm glass beads: corresponds to X rotational speed = 10 rpm; the Y rotational
speed = 10 rpm; (c) 3 mm glass beads: corresponds to X rotational speed = 10 rpm; no rotation about the Y axis (i.e. 0 rpm); and (d) 3 mm glass beads:
corresponds to X rotational speed = 10 rpm; the Y axis rotational speed = 30 rpm. Dual rotation enhances mixing. Reprinted with permission from Ref.
(Cho et al., 2012). Copyright: (2012) Elsevier B.V.

shorter period at a lower rotational speed. Muzzio et al.
(2008) conducted a study to evaluate the impact of processing and equipment parameters in a ribbon blender on thehomogeneity of magnesium stearate. The study was carriedout by analysing the properties of the blender using a coresampling technique, which involved collecting at least one
hundred samples from throughout the blender and characterizing the entire bed. The investigation took into accountseveral parameters, such as the loading technique for the
lubricant, fill level, blade design, and blade speed, to evaluate their influence on the homogeneity of mixing in abatch ribbon mixer. The outcomes of this research canserve as a valuable reference for devising suitable blending
processes and characterisation protocols for ribbon blend-

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ers, as presented in Fig. 7. Gijón-Arreortúa and Tecante(2015) conducted a study to evaluate the impact of helical
double-ribbon impeller parameters on the mixing time andpower consumption during the blending of normal corn
starch and icing sugar. Results indicated that the optimal
mixing performance was achieved with an impeller speedof 75 rpm and a load ratio of 0.33, resulting in the lowest
mixing time and the highest coefficient of mixing rate.
By summering the previous experimental studies of ribbon mixers, it can be observed that the mixing behavior of
ribbon mixers is influenced by various parameters, including the design and geometry of the mixer, rotational speed,
fill level, feed preparation characteristics, and loading
methods. The results of these studies suggest that an

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optimal combination of these parameters can result in efficient mixing and homogenisation of the material. Moreover, various sampling and characterisation techniques,
such as core sampling and PEPT, have allowed for a morecomprehensive understanding of the mixing behavior in

Fig. 5 The three segregation patterns found in the 1 quart V-blenderwhen run at 50 % of capacity. (a) At low rotation rates (<7.5 rpm), the‘small-out’ pattern forms; (b) intermediate speeds (7.9–19 rpm) produce‘stripes’; and (c) high rotation rates (>19.3 rpm) induce ‘left–right’ segregation, reprinted with permission from Ref. (Alexander et al., 2004).
Copyright: (2004) Elsevier B.V.

Review Paper

ribbon mixers. Despite the advancements in the understanding of mixing in ribbon mixers, there is still a need forfurther research to fully comprehend the mixing mechanisms in these mixers and optimise their design for specificindustrial applications. This is especially important for thepharmaceutical and food industries, where strict standards
are in place for homogeneity, particle size distribution andproduct quality. Furthermore, the limited number of studies
conducted in this area highlights the need for future research to bridge the gap and provide a more comprehensive
understanding of the fundamental aspects of ribbon mixer
design, performance, and optimization.
The paddle mixer is a significant type of convective
mixer that finds widespread application in industrial operations. Ebrahimi et al. (2018) conducted an experimental
study to investigate the influence of impeller design on the
mixing efficiency of mono-disperse, free-flowing sphericalparticles in a horizontal paddle mixer. Fig. 8 displays theexperimental setup. The study involved collecting 16 samples for each experiment, which can be utilised to verify
simulation results. Sixteen samples were gathered during
each experiment, which can be employed to verify the results of simulations. Shenoy et al. (2015) conducted a study
that involved the examination of binary powder mixing in
a 2 L prototype lab-scale paddle mixer using several typesof food powders with varying particle sizes and poured

Fig. 6 The geometry of ribbon impellers: (a) 2-bladed impeller spiralling in the same direction (i.e., Design I); (b) 2-bladed impeller spiralling in the opposite direction (i.e., Design II); (c) 4-bladed impeller (i.e.,
Design III), reprinted with permission from Ref. (Jin et al., 2022).
Copyright: (2022) Elsevier B.V.

Fig. 8 The experimental setup, reprinted with permission from Ref.
(Ebrahimi et al., 2018). Copyright: (2018) Elsevier B.V.

Fig. 7 Blender and fill level designations, reprinted with permission
from Ref. (Muzzio et al., 2008). Copyright: (2008) Elsevier B.V.

Fig. 9 Image of the 2 L paddle mixer, reprinted with permission from
Ref. (Shenoy et al., 2015). Copyright: (2015) Elsevier B.V.

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bulk densities (Fig. 9). The results of the study conductedby Shenoy et al. showed that a particle size ratio of up to
4.45 resulted in a well-mixed powder mixture. However,for higher ratios, there was a decrease in mixture quality
without any visual observation of segregation. The study
found that bulk density had a greater impact on mixture
quality compared to particle size. When the bulk density
ratios were elevated, complete segregation was noted, andits manifestation was primarily attributed to the irregularshapes of thyme and oregano powder particles. Berntsson
et al. (2002) proposed a technique for quantifying thechemical composition of powder mixtures in situ usingnear-infrared spectroscopy (NIRS) and a fibre-optic diffuse
reflection probe. The probe was inserted into the powder ina Nauta mixer. The application of NIRS and a fibre-optic
diffuse reflection probe for in-situ quantitative measurement of the chemical composition of powder mixtures in a
Nauta mixer was examined, and the results demonstrated
its feasibility. The findings indicated that high-speed sampling is an effective method for evaluating both the mean
composition and the distribution of the mixture composition during processing. The empirical content-over-time
trajectories were found to be consistent with a theoreticalsimulation model of blending in Nauta mixers.
Despite some progress being made, the research andunderstanding of solid mixing processes remain relatively
limited in scope. This highlights the need for further experimental studies to be conducted in this field in order to gaina more comprehensive understanding of the underlying
principles and mechanisms involved in these processes.
Most experimental studies in the field of solid mixing werelimited to a paradigm where only a few samples were collected for characterisation. Recent experimental studies
have investigated the impact of various parameters, such as
fill level, blade speed, and the number of blades, on the
mixing performance of mixers. Advanced measurement
techniques, such as non-invasive near-infrared (NIR) spectroscopy, tomography, and PEPT, have been utilised inthese investigations (Cullen et al., 2017; Page et al., 2015).
However, the experimental analysis of mixers is impededby the opaqueness of the equipment and the intricacy of theflow within the mixer. As a result, obtaining particle-scaledetails, such as particle velocity, inter-particle contact
force, and particle dispersion, is challenging. The absenceof such data limits the prospects for improving mixer performance. Furthermore, due to the high cost of experiments, the optimal design of mixers, which necessitates
extensive experimentation, has not been fully explored.

3. Research progress summary of simulation
work

The progression of computer technology and parallel
computing has facilitated the utilisation of numerical simulation as a primary approach in the advancement of solid

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mixing technology. This approach can potentially reducethe cost of design, operating time, and technical risks and isincreasingly being utilised to optimise mixer performance.
Additionally, numerical simulation offers the advantage of
observing the mixing process in a virtual environment, allowing for in-depth analysis and understanding of themixing mechanisms. As a result, numerical simulation has
become an indispensable tool in the field of solid mixing
technology, providing valuable information and insightsthat are otherwise difficult to obtain through experimental
methods.
The current simulation approaches used in the field ofsolid mixing can be classified into two main categories: thetwo-fluid model (TFM) and the discrete element method(DEM). TFM is a commonly used simulation method forthe study of mixing processes in industry-scale simulations. In this approach, the gas and solid phases are treatedas interpenetrating continua, and the computational load is
manageable. As an Eulerian-Eulerian method, TFM employs the kinetic theory of granular flow (KTGF) to determine the solid pressure and viscosity, providing valuable
mathematical insights into the particulate material’s microscopic and macroscopic behavior (Brone et al., 1998). The
method employs the kinetic theory of non-uniform dense
phases to model particle-particle collisions. However, themodel’s accuracy is constrained as it relies on simplified
and estimated empirical relationships for the physical properties of the solid particles, including their shape and size.
Another approach is DEM approach. In DEM, individual
particles are considered within the mixer, and the forces
acting on each particle are calculated through the specification of contact with all other particles. This approach allows for the calculation of the resulting acceleration ofeach particle through the application of the equation of
motion. The trajectory of each individual particle is determined by applying Newton’s equation of motion, which is
calculated by considering the forces acting on the particle
and its acceleration. Nonetheless, it is worth noting that theLagrangian approach for simulating solid mixing systems
demands a vast amount of computational resources (CPUand memory). Due to the importance of particle-particle
interaction details in solid mixing processes, DEM is
widely utilised for investigating such processes. Therefore,
this section will focus on a literature review of the DEM
approach.
DEM has been utilised extensively to examine the processes of particle mixing and segregation within a varietyof mixer configurations (Marigo M. and Stitt E.H., 2015;
Sakai M., 2016; Sakai M. et al., 2020). This section will
present a review of relevant DEM studies, which will besummarized based on the classification of mixers.

3.1 Simulation work of tumbler mixers

Considerable DEM simulations have been carried out toXin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171

examine the intricate particle mixing behaviors and theimpact of different parameters on the mixing efficiency inthe rotating drum. For example, (Yang et al., 2016) employed DEM to conduct a three-dimensional simulation of
the motion of solid particles in a laboratory-scale rotating
drum. The validity of the simulation results was confirmed
through comparison with experimental data. Subsequently,
the active-passive interface was identified, and particlescale information was obtained for both of these regions, as
shown in Fig. 10, utilizing DEM to perform a threedimensional simulation of the solid motion in a laboratoryscale rotating drum. The active-passive interface was
identified upon validation of the simulation results withavailable experimental data, and particle-scale information
were obtained for both regions. The investigation exploredthe influence of fill level and rotating velocity on the solid
motion. The study results revealed a higher concentrationof particles in the passive region compared to the active
region, with a more significant collision force observed in
the active region, particularly in the y-direction, comparedto the x and z directions. Yamamoto et al. (2016) investigated the mixing behavior of particles in a rotating drum
mixer (RDM) by means of DEM simulation to examine theimpact of particle density. DEM results of the study revealed the effects of fill level and rotating velocity on the
mixing behavior of stainless steel and alumina particles
within a rotating drum. The results indicated that the lowerdensity particles had greater mobility compared to higherdensity particles, leading to segregation. However, the use

Review Paperof lifters was found to control the behavior of both high andlow-density particles and improve the mixing of particles.
The mixing degree of the alumina and stainless-steel particles was evaluated, and the results were in good agreementwith the DEM simulation. Yazdani and Hashemabadi(2019) examined the effects of cohesive forces and rotating
speed on the segregation and mixing of cohesive particles
in a horizontal rotating drum. The simulation results indicated that both cohesion and rotation speed significantly
impacted the behavior of highly cohesive particles in thedrum, as illustrated in Fig. 11. Ma and Zhao (2017) conducted an investigation on the flow of granular materials
comprising ellipsoidal particles in a horizontal rotating
drum by using DEM. The study focused on examining theinfluence of the aspect ratio and rotation speed of the drumon transverse mixing, as shown in Fig. 12. The simulation
demonstrated that cohesive particles’ cohesion and rotation
speed in a horizontal rotating drum significantly impact
their behavior. The results showed that particles with lower
sphericity had a higher consistency in their orientation andthat better coating could be achieved at lower rotation
speeds in the rolling/cascading regime.
Currently, numerous DEM investigations of the rotating
drum have been conducted. Given a large number of rotating drum simulation studies, Table 2 presents a summaryof some representative recent DEM works regarding themixing processes in the rotating drum.
A limited number of simulations can be found for othertypes of tumbler mixers. Hence, the following discussion

Fig. 10 Schematic representation of the apparatus showing the instantaneous velocity distribution of the solid phase in the rotating drum, reprinted
with permission from Ref. (Yang et al., 2016). Copyright: (2016) Wiley Online Library.

Fig. 11 Snapshots of mixing of binary cohesive mixture for segregated loading pattern in the rotating drum containing 6000 cohesive particles withk ii and k jj of 100 kJ/m3 and without interparticle cohesion (k ij = k ji = 0), reprinted with permission from Ref. (Yazdani and Hashemabadi, 2019). Copyright: (2019) Elsevier B.V.

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Review Paper

Fig. 12 Snapshots of the flow of particles coloured by their magnitude of the translational velocity (from blue (minimum) to red (maximum)), reprinted with permission from Ref. (Ma and Zhao, 2017). Copyright: (2017) Elsevier B.V.

presents a review of selected literature on other types ofmixers to provide a representative sample. Arratia et al.
(2006) utilised DEM to examine the flow dynamics ofspherical particles within a tumbling cone blender. The
simulation results showed that the radial convection rate
was more significant than the axial dispersive transport,
leading to decreased mixing performance within this geometry. The particle velocity profiles were analysed, revealing the presence of two distinct regions in the flow: ahigh-velocity layer cascading above and a region with anearly solid body rotation, as depicted in Fig. 13. Ren et al.
(2013) employed a GPU-based DEM software to investigate the mixing and flow dynamics of granular materials ina conical tote blender. A parametric study was performed toevaluate the impact of fill level and rotation rate on the
mixing rate, productivity, and energy consumption. The
study revealed that the optimal values for fill level and rotation rate could enhance mixing effectively. Moreover, thefindings indicate that the conventional horizontal configuration of the blender leads to inadequate axial mixing.
However, tilting the blender at a specific angle can considerably enhance the mixing efficiency. Tanabe et al. (2019)
utilised DEM to assess the impact of an increase in particle
size and a reduction in blender geometry on the uniformityof the blend. The study revealed that the variation in particle size among components resulted in the segregation of
the three blends, as evidenced by the diverse standard deviation of active ingredient content. The research also identified two crucial factors that impact blending performance,
namely, the ratio of the blender container to particle size
and the total number of particles and samples in theblender. Furthermore, the study demonstrated the processof quantitative prediction of the sample BU probability
density distribution using DEM simulation, which can befound in Fig. 14.
Tahvildarian et al. (2013) employed DEM to simulate
the behavior of monodisperse, non-cohesive particles in a
V-blender. The simulation accounted for both particle–
particle and particle–boundary interactions, as depicted inFig. 15. As the filling level increased from 20 % to 46 %,160

the circulation intensity decreased, and at a filling level of
34 %, it reached its minimum value for all rotational
speeds. No significant change in circulation intensity wasobserved for filling levels greater than 34 %. The results
also depict the particle velocity in the Y–X plane when the
V-blender rotates from 0° to 360° at a fill level of 20 % androtational speed of 30 rpm. Lemieux et al., (2008) employed DEM to predict the flow dynamics of multiple particles over extended periods, with a specific emphasis on
the mixing phenomena that necessitate a considerable
amount of time to develop in such systems. To this end, theresearchers performed several extensive numerical simulations using the DEM approach, investigating the flow ofmonodisperse and bidisperse blends consisting of up to
225,000 particles for 120 seconds in a V-blender. Quantities such as particle velocity, granular temperature, mixing
system torque, RSD curves, and mixing times are examplesof variables commonly used to characterise and analyse thebehavior of granular materials during mixing processes.

3.2 Simulation work of convective mixers

In contrast to the tumbler mixer, convective mixers employ stationary outer vessels with added moving components to improve solid mixing performance.
Sarkar and Wassgren (2015) conducted a study using
DEM to examine the impact of modelled particle size on
flow and mixing in a bladed granular mixer. The findings
revealed that the macroscopic advective flow was considerably influenced by particle size, particularly in areas withsparse flow. Yaraghi et al., (2018) utilised DEM to investigate the flow patterns and mixing kinetics of non-cohesive,
monodisperse, and spherical particles in a horizontal paddle blender. The authors found that the most significant
factor affecting mixing quality was the rotational speed of
the impeller, with the quadratic effect of the impeller rotational speed and the vessel fill level having a lesser impact.
Furthermore, the empirical data obtained on granular temperature demonstrated that an increase in impeller rotational speed, from 10 to 70 rpm, resulted in a corresponding
increase in the granular temperature values. In a study

Solid properties

Particle size:
3–6 mmParticle density
2500 kg/m3
Particle number:
88379, 10105, 113630.

Particle size:
5.0 × 2.5 × 2.5 mm
4.0 × 4.0 × 2.0 mm
Particle density
1150 kg/m3
Particle number:1000

Particle size:
1.09 mm
Particle density
2445 kg/m3
Particle number:
43,200, 54,000, and63,837

Particle diameter:
4.9–10 mm
Particle density
1200 kg/m3
Aspect ratio:
1.0–6.0
Particle number:
25,027–31,764

Particle diameter:
0.1–0.3 mm
Particle density
596 kg/m3
Particle number:
3474

Particle diameter:
0.71 mm–0.84 mm
0.50 mm–0.59 mm
Particle density
2492 kg/m3

Particle diameter:
1–10 mm
Particle density
3100 kg/m3
Particle number:
29623, 24241, 9846
9928

Reference(Yu et al., 2022)(Mori and Sakai, 2022)(Silveira et al., 2022)(Li M. et al., 2021)(Zhang et al., 2021)(Huang et al., 2021a)(Deng et al., 2021)

Identify the optimal configurationand layout of the vanes or blades toachieve maximum dispersion anddistribution of the particles in theactive zone.
Investigate the flow behavior andmixing process of sphero-cylinders
with varying shapes at a filling levelof 40.5 % in a rotating drum.

Influence of the number of flights on
the dilute phase ratio in flighted
rotating drums

Study size segregation of binary
mixture in a rotating drum with innerdiameter variations.

Fill level
10.1 %, 12.7 %, and15 %,Rotating speed
21.3 rpm
Fill level
40.5 %
Rotating speed
10–50 rpm

Fill level
15 %Rotating speed
10–30 rpm
Fill level
20 %Rotating speed
20 rpmThe effect of slag size distributions
on mixing and segregation

The powder mixing of non-sphericalparticles in an industrial rotating
drum mixer.

Rotating speed
20, 60 rpm

Fill level
30–33 %
Rotating speed
10 rpm・Polydisperse particles are characterised by a composite structure where
small particles serve as nuclei surrounded by larger particles.
・Monodisperse particles exhibit a relatively elevated velocity of theactive layer, whereas polydisperse particles tend to exhibit greater radial
segregation.

The flow behavior of polydisperse
particles in a rolling mode rotating
drum.

Fill level
30 %, 40 % 45 %Rotating speed
5.4, 8.5, 11.6 rpm

・Previous studies have highlighted the limitations of whole-process
mixing criteria in fully capturing the intricate nuances of subprocesses.
・The use of subprocess criteria, which combine the index of entry orderand the number of contacts, has been shown to be effective in accurately
evaluating the duration of mixing in granular beds.

・When the CR value equals 0.9, the percolation mechanism is improved,
and the contracting wall has a greater impact on smaller particles, leading
to their migration towards regions with larger inner diameters, resulting in
expanded dimensions. On the other hand, when the CR value is 0.5 or 0.3,
the contracting wall imposes additional shear forces on the bed and
impedes the migration of particles of both sizes.

・The number of flights varies depending on the holdup ratio and cascading rate of both single and active flights.
・The FRD exhibits a greater production of the dilute phase, which ismore stable, when configured with either 8 or 12 flights.

・Sphero-cylinders with different Ars can reach well-mixed states undersufficient rotation conditions.
・Both the macro- and microscopic properties change with the rotation
speed and AR; however, when AR > 3, its influence becomes less obvious.

・The experimental findings revealed that the flight configuration with aseparation distance of 15° resulted in a 24.6 % increase in the occupied
area by the particles in the active region, and a 38.5 % reduction in theheterogeneity of the solid dispersion compared to the configuration withaligned flights.

・The influence of a nonspherical shape on the progression of powder
mixing in a ribbon mixer has been demonstrated to be negligible.

Reported results

Operating condition Research Descriptions

Table 2 Summary of representative DEM work for the mixing processes in the rotating drum in recent years. (Continued on next page)

Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171
Review Paper

161

162

Solid properties

Particle density
2500 kg/m3
Aspect ratios
0.5 and 2.0

Particle density
2500 kg/m3
Aspect ratios
0.4–2.5
volume-equivalentdiameter: 3 mm
Particle number:
400000Particle diameter:
1.5 and 3 mm
Particle density
2500 kg/m3
Particle number:
2500 for 3 mm
20,000 for 1.5 mm

Particle diameter:
1.1 and 6.3 mm
Particle density
2455 and 1160 kg/m3
Particle number:
2500 for 3 mm
20,000 for 1.5 mm

Particle diameter:
3 mm
Particle density
2500 kg/m3
Particle number:
2000

Particle diameter:
1.5 and 2 mm
Particle density
1000 kg/m3
Particle number:
14,222 for 1.5 mm
6000 for 2.0 mm

Reference(Wang et al., 2021)(He et al., 2021)(Li D. et al., 2021)(Brandao et al., 2020)(Rong et al., 2020)(Yazdani and
Hashemabadi, 2019)

Investigate the mixing/segregation
behavior of particles in an unbaffledrotary drum

Investigate the effects of particle
contact parameters, sliding friction
coefficient (SFC), rolling friction
coefficient (RFC) and restitution
coefficient (RC) in a rotating drum.

Fill level
25 % and 50 %Rotating speed
0.59, 1.10 and
1.77 rad/s
Fill level
35 %Rotating speed
40 rpmSimulate the segregation and mixing
of cohesive particles in a horizontal
rotating drum

Forecast the flow characteristics of
two-sized particles, binary particle
systems, in a horizontal rotating
cylindrical drum and an ellipsoidal
drum, a numerical simulation
approach can be employed.

Fill level
20 %Rotating speed
40,150 and 200 rpm

Fill level
25 % and 55 %Rotating speed
6, 12 and 18 rpm

Report an interesting phenomenon
that for ellipsoid-sphere mixtures.

Fill level
38 %Rotating speed
40 rpm・When mixing cohesive and non-cohesive particles, the bed displayed atendency towards segregation, with cohesive particles gravitating towards
the outer layer of the rotating bed. Conversely, complete mixing was not
attained without interparticle cohesion between two types of cohesive
particles.
・The results indicated that the duration necessary to attain the final
mixed state increased in the case of highly cohesive particles.

・The sliding friction coefficient was identified as a crucial element indetermining both the mean power draw and mean collision energy. On theother hand, the restitution coefficient had the most pronounced impact on
the frequency of collisions.
・The influence of the sliding friction coefficient and restitution coefficient on both the collision frequency and mean collision energy wasobserved to vary across different rotational speeds.

・The simulations, utilising experimentally determined input parameters
obtained through the DEM, demonstrated the closest agreement with theexperimental responses, such as the repose angle and radial mixture.

・At elevated rotational speeds, the degree of mixing of binary-sizedparticles in the RED can be augmented.
・The resulting contact forces exhibit a gradual increase with the increment of rotational speed and flattening.

・The severity of axial segregation attains a peak at aspect ratios of 0.67
and 2.0.
・In the outer region, the migration of both ellipsoids and spheres
towards the central section of the transverse slice was observed, while in
the inner region, particles showed a propensity to migrate towards the end
walls.

・The distribution of small and large particles in the drum was found to
be concentrated in the centre and periphery, respectively, while mediumsized particles were evenly distributed throughout the system.
・As the granular system approaches a high-speed centrifugal state, thesmallest particles exhibit the highest radial velocity and tend to be locatednear the drum wall.

Rotating speed
7.5–130 rpm

The influences of particle shape,
standard deviation of the mixture,and rotating speed on the segregation
behaviors.

Reported results

Operating condition Research Descriptions

Table 2 Summary of representative DEM work for the mixing processes in the rotating drum in recent years. (Continued from previous page)

Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171
Review Paper

Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171

conducted by (Ebrahimi et al., 2018), the efficacy of mixing monodisperse spherical particles in a horizontal agitating paddle mixer was investigated using the DEM method.
The study involved simulating five different impeller
designs to determine their influence on mixing performance. The study evaluated five distinct impeller designs
through simulation. The findings demonstrated that impeller design significantly affected both the mixing performance and the granular behavior of the materials, as
demonstrated in Fig. 16. Additionally, the study analysed
(a)

(b)

Fig. 13 Example of velocity fields of a mono-disperse system at 40 %fill level. (a) Side view at 3/4 of a revolution. (b) Top view at 3/4 of arevolution, reprinted with permission from Ref. (Arratia et al., 2006).
Copyright: (2006) Elsevier B.V.

Review Paper

the effect of impeller configuration on the forces of contact
between the impeller and particles, and between the particles themselves.
Ribbon mixers are deemed appropriate for blending dry
powders and free-flowing granular materials. Literaturesuggests that a ribbon mixer can achieve improved uniformity in powder mixing due to the high shear stresses it
generates and its ability to handle a mixture of particles ofvarying sizes. Hence, the utilisation of DEM in analysing
the ribbon mixer offers valuable insights into its performance and potential optimization. Halidan et al. conducteda series of DEM studies investigating the mixing behaviors
in ribbon mixers. A survey was conducted by the researcher
to investigate the influence of impeller speed on the mixing
behavior of cohesive and non-cohesive particle mixtures ina ribbon mixer, which is characterised by a horizontal cylindrical vessel (Halidan et al., 2016; Musha et al., 2013).
The DEM simulations indicated that the mixing rate ofboth cohesive and non-cohesive mixtures in the ribbon
mixer increased as the impeller speed increased up to acertain threshold, after which a decrease was observed. For
non-cohesive particles, the mixture quality may deteriorate
at higher impeller speeds, but this was not the case for cohesive particles. Halidan et al. (2018) employed DEM to
examine the impact of impeller speed and fill level on theblending behaviors of particle mixtures with varying

Fig. 14 Quantitative prediction of the sample BU probability density distribution in reality using the DEM simulation, reprinted with permission
from Ref. (Tanabe et al., 2019). Copyright: (2019) Elsevier B.V.

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Review Paper

Fig. 15 Particle velocity in the Y-X plane when the V-blender rotated from 0° to 360° at 20 % fill level and 30 rpm, reprinted with permission from
Ref. (Tahvildarian et al., 2013). Copyright: (2013) Elsevier B.V.

Fig. 16 A snapshot of particle mixing after 10 revolutions of mixing from the front view sliced at the centre of the mixer, reprinted with permission
from Ref. (Ebrahimi et al., 2018). Copyright: (2018) Elsevier B.V.

cohesion in both two-bladed and four-bladed ribbon mixers, each possessing a horizontal cylindrical vessel. Beyond
that, the mixing rate was observed to decline. In particular,
the mixing rate of cohesive particles was found to deteriorate
at higher impeller speeds in the 2-bladed mixer. The results
showed that with an increase in fill level, the flow behaviorof non-cohesive particles changed from sliding flow to recirculation flow and eventually to cascading flow. The
comparison results can be seen in Fig. 17. Chandratilleke
et al. conducted a numerical investigation of the impact of
blade-supporting spokes on the overall mixing performance in a ribbon mixer using DEM. This study analysed
the effect of several key variables, including the number of
spokes, the cohesiveness of particles, and the fill level on
the mixing performance. The results indicated that, in the164case of non-cohesive particles, increasing the number of
spokes was advantageous for improving the overall mixing
rate when the fill level was substantial. However, this improvement came with the cost of increased contact forces.
In contrast, the best overall mixing performance wasobserved with a no-spoke impeller for cohesive particles.
The critical findings are depicted in Fig. 18. Subsequently,
DEM was used to examine the impact of particle size anddensity on particle mixing in a laboratory-scale ribbon
mixer (Chandratilleke et al., 2021). The study conducted byBasinskas and Sakai (2016) employed numerical simulations to examine the impact of various factors on the degreeof mixing in a laboratory-scale ribbon mixer. The results
indicated that the mixing rate decreased as the particle size
was reduced with the fill level fixed, and the density effectXin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171

Review Paper

Fig. 17 Effect of fill level on the mixing performance of a 2-bladed mixer at different Bond numbers (shaft speed = 100 rpm), reprinted with permission from Ref. (Halidan et al., 2018). Copyright: (2018) Elsevier B.V.

was negligible for small particle sizes. An empirical equation was formulated to describe the particle-size effect,
which was also extrapolated to consider much smaller particles. The present investigation employed numericalmethods to assess the impact of powder quantity, blade
speed, and initial loading on the degree of mixing in a ribbon mixer (See Fig. 19). The degree of mixing in the axial
direction was found to be relatively less variable than thatin the perpendicular direction. The results indicated that theamount of powder and the blade speed positively influenced the mixing performance. However, the study foundthat only the initial loading and powder quantity had a significant impact on the quality of mixing in the ribbon
mixer, with only modest variations observed in the axial
direction compared to the perpendicular direction. Recently, several noteworthy DEM studies on the mixing
processes in convective mixers have been reviewed andsummarized in Table 3.

4. Current progress and future perspectives

The mixing of particles is a common practice in several
industries, including ceramics, pharmaceuticals, food, andchemicals, where a high-quality end product is crucial. The
quality of powder products, which are composed of particulate ingredients that must be thoroughly mixed, is heavily
influenced by the design of the mixer and its operating
conditions. Various types of mixers, such as rotating drums,
orbiting screw mixers, and ribbon mixers, are used for thispurpose. However, the mechanism of particle mixing inthese mixers is still not well understood due to the complex

nature of particle behavior in the mixing system. Understanding and controlling particle behavior during mixing
remains a significant challenge for improving the operationand optimization of mixers. Up to date, the design of solid
mixers is generally limited to first selecting qualitatively
the equipment that might be suitable and then arranging
tests with potential suppliers, where unified theory andcriteria are still not available due to insufficient knowledgeof the mixing mechanism. An extensive understanding ofparticle mixing is crucial both from a scientific perspective
and a practical standpoint to optimise industrial processes
related to it.
Despite the prevalence of powder mixing in various industries, there remains a lack of robust and systematic
methods for characterizing mixing quality and determining
the optimum mixing conditions. This has motivated researchers to focus on developing more advanced experimental techniques to better understand the underlying
physics and mechanics of particle mixing. By improving
our understanding of the mechanisms and principles thatgovern particle mixing, researchers aim to improve the efficiency and quality of powder processing. Therefore, there
is a growing need for improved experimental techniques
and advanced simulation methods to better understandparticle mixing behaviors and incorporate the particles’
microscopic properties into the models. This would lead toa more accurate prediction of mixing performance andcould aid in the design and optimization of industrial solid
mixing processes. Additionally, the integration of experimental data and simulation results can help to establish a

165

166

Solid properties

Particle size:
4.75–8 mm
Particle density
2837 kg/m3

Particle size:
3, 4, 5 and 6 mm
Particle density
2500 kg/m3
Particle number:
88379, 101005 and
113630Particle size:
3 mmParticle density
1414 kg/m3
Particle number:
20000, 30000, 35000
and 40000

Particle size:
6 and 12 mm
Particle density
2500 kg/m3
Particle number:
20000, 30000, 35000
and 40000

Particle size:
3 mmParticle density
2700 kg/m3
Particle number:
10000

Particle size:
3 mmParticle density
1358.8 kg/m3
Particle number:
37600

Particle size:
3 and 5 mm
Particle density
2500 kg/m3
Particle number:
153,780 for 3 mm,
38,446 for 5 mm

Particle size:
0.6 mmParticle density
2500 kg/m3
Particle number:
100,000, 200,000 and
300,000

Reference(Xiao et al., 2023)(Yu et al., 2022)(Xu et al., 2023)(Miao et al., 2022)(Liu et al., 2022)(Wu et al., 2022)(Ebrahimi et al., 2021)(Deng et al., 2021)

The effects of various operational parameterson the mixing performance.

The mixing of bi-disperse particles in ahorizontal paddle mixer.

Fill level
40 % and 60 %Rotating speed
40, 70 and 100 rpm

Rotating speed
20, 40 and 60 rpm

Prediction of particle mixing time in a rotary
drum by 2D DEM simulations and crosscorrelation.

Effect of baffles on mixing and heat transfer indrums is studied.

Particle mixing and segregation behaviors in
the rotating drums with adjacent axial
segmentations in different speed directions.

Effect of drum structure on particle mixing
behavior.

Fill level
20 %Rotating speed
15 rpmFill level
50 %Rotating speed
3 rpm

Fill level
20 %Rotating speed±40 rpm

Fill level
15 %, 23 %, 26 % and 31 %Rotating speed
5, 8, 10 and 15 rpm

The flow behavior of polydisperse particles ina rolling mode rotating drum.

Fill level
45 %Rotating speed
40 rpmFill level
35 %, 40 % and 45 %Rotating speed
5.4, 8.5 and 11.6 rpm

Research Descriptions
The mixing processes of gravel materials.

Operating condition

・Factors such as rotational speed, filling level, liquid viscosity, and paddle obliquity
can significantly impact the mixing performance.
The identification of various mixing mechanisms can be achieved through the utilization of the probability distribution function.

・rn had the most significant effect on the mixing performance.
The study’s results revealed that the mechanism of diffusion was predominant over thatof convection. Furthermore, when the values of the diffusion coefficients for 5 mm and
3 mm particles were found to be comparable, the optimal mixing performance wasachieved.

Compared to machine learning approaches, the cross-correlation method has theadvantage of interpretability, expandability, and relatively high accuracy for limited
data size.

・The optimal length-to-diameter ratio of central baffles varies between 0.4 and 0.7.
・The peripheral baffles perform best at a high length-to-radius ratio of 0.9.

・Alternating axial segregation bands can be formed in adjacent axial segmentations
with the same velocity direction, while the overall mixing degree is improved underconditions of the opposite velocity direction.

・The contact number between particles and wall is improved in LC and LLC compared to the cylinder drum.

・The behaviour of particle flow in a drum was investigated through the examinationof particle velocity, duration of residence, mixing intensity, and axial dispersion invarious regions within the drum. The objective was to reveal the flow behaviour ofpolydisperse particles.
・Propositions are put forth to enhance the rotating drum’s efficiency in the rollingmode.
・The distinction in flow behaviour between polydisperse and monodisperse particles
is presented.

・The introduction of rods into a drum has been found to enhance the mixing degree ofparticles.
・The diameter of the cylindrical rods appears to have a minimal effect on the particle
mixing degree.
・The smaller the distance between the rods, the better the mixing degree.

Reported results

Table 3 Summary of representative DEM work for the mixing processes in the convective flow in recent years. (Continued on next page)

Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171
Review Paper

Solid properties

Particle size:
6, 10 and 20 mm
Particle density
7750 kg/m3
Particle number:
43,200, 54,000, and63,837

Particle diameter:
3 mm
Particle density
2500 kg/m3
Particle number:
120,000

Particle diameter:4.52 mm
Particle density
1000 kg/m3
Particle number:
60000

Particle diameter:
1.5 mm–12 mm
Particle density
1000 kg/m3
Particle number:
113,152

Particle diameter:
5–15 mm
Particle density
417–2500 kg/m3

Particle diameter:
4 mm
Particle density
2500 kg/m3
Particle number:
120,000 80,000

Particle density
3948 kg/m3
Particle diameter:
40, 50 and 60 mm
Particle number:
52348 and 104549

Particle diameter:
15 mm
Particle density
417 kg/m3
Particle number:
18000

Reference(Horváth et al., 2019)(Yaraghi et al., 2018)(Pasha et al., 2015)(Sarkar and Wassgren, 2015)(Chandratilleke et al., 2021)(Tsugeno et al., 2021)(Gao et al., 2019)(Halidan et al., 2016)
Rotating speed
100 rpm

Rotating speed
15, 25 and 35 rpm

The effect of interparticle cohesion on powder
mixing in a ribbon mixer was studied bymeans of the discrete element method.

The effects of the operational and geometricalparameters, including initial loading, particle
size, impeller rotational speed, and inner
blades on the mixing quality of particles witha double U-shaped vessel.

An effective parameter for better mixing in the
ribbon mixer using DEM.

The effects of the particle size and density on
particle mixing on a laboratory-scaleribbon mixer.

Fill level
40 %Rotating speed
100 rpm
Rotating speed
20 and 60 rpm

The influence of the modelled particle size on
flow and mixing in a bladed granular mixer.

Simulate PEPT
experiments for a paddle mixer using DEM.

NA

Fill level
30 %Rotating speed
30 rpmThe influence of impeller configuration on the
mixing performance of free-flowing monodisperse spherical particles in a horizontal
agitating paddle mixer.

Create a DEM model suitable for determining
the mixing power requirements of an agitateddrum dryer pilot plant, which can be applied
to the modeling of mixing granular materialsof various moisture content.

Fill level
10 %–25 %,Rotating speed
0.63; 0.95; 1.58 r/s

Fill level
40 %Rotating speed
40 rpmResearch Descriptions

Operating condition

・With increased cohesion, mixing rate and uniformity deteriorate. The coordination
number increases, indicating a loss in free-flowing motion ability, and many particles
have more vital tangential velocity for bulk angular motion.

・The initial loading and the rotational speed of the impeller have a significant impact
on the quality of particle mixing, while the effect of the other two parameters was
relatively small.
A numerical investigation on the ribbon mixer equipped with a double U-shaped vessel
indicates that better mixing performance is achieved under top–bottom and front–backinitial loadings, whereas inferior mixing performance is observed under side–side
initial loading.

・The blade width is identified as a critical aspect for optimizing mixing performance.
・The relationship between the swept volume and the mixing index remained consistent despite changes in the paddle design.

・When the fill level was kept constant, a reduction in particle size resulted in a slower
mixing rate at a given density. However, for particles with small sizes, the effect ofdensity on mixing was negligible. The particle size effect was described by an empiricalequation and was extrapolated for even smaller particle sizes.

The effect of particle size on the macroscopic advective flow was found to be significant, particularly in dilute flow regions. These findings indicate that particle size should
be taken into consideration when performing DEM mixing simulations with larger
particles.

・It takes 251 seconds for a tracer to traverse the entire active space of the system.
・The average velocity distribution remains unaffected by an increase in the number oftracers in the paddle mixer system.

・The alterations in impeller configurations had minimal effect on the particle-particle
contact forces.
・The simulation with the 0° angle paddle resulted in higher granular temperature
values than the rectangular one. This observation partially explains the improved
mixing performance obtained for the former impeller compared to the latter impeller.

・The results of the study showed that the moisture content of the material and therotational speed of the mixing unit have a significant impact on the mixing power
requirement. In addition, the mixing torque requirement was found to decrease as therotational speed increased.

Reported results

Table 3 Summary of representative DEM work for the mixing processes in the convective flow in recent years. (Continued from previous page)

Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171
Review Paper

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Xin Jin et al. / KONA Powder and Particle Journal No. 41 (2024) 151–171(a) Two-bladed impeller withno spokes

Review Paper(b) Two-bladed impeller with
6 spokes

Fig. 18 The effect of blade-supporting spokes of the impeller on overall mixing performance in a ribbon mixer, reprinted with permission from Ref.
(Chandratilleke et al., 2018). Copyright: (2018) Elsevier B.V.

Fig. 19 Mixing states at different times for different loading methods, reprinted with permission from Ref. (Basinskas and Sakai, 2016). Copyright:(2016) Elsevier B.V.

more comprehensive understanding of particle mixing,
which is crucial for the continuous improvement of thepowder processing industry. Additionally, developing moreadvanced computational models that consider the microscopic properties of particles will be critical to understanding and improving the efficiency of solid mixing processes
in the industry (Ghadiri, 2020). This, in turn, can lead tosignificant advances in the quality and consistency of awide range of powder products, as well as reduced energy
consumption, lower costs, and reduced environmental impact associated with the production of these products.
Moreover, the integration of Industry 4.0 technologies,
such as the Internet of Things (IoT) and artificial intelligence (AI), can further enhance the accuracy and efficiency

168

of measurement and control systems, thereby enabling
more effective and efficient solid mixing processes in the
future (Bowler et al., 2020). It is also worth focusing on the
recently developed soft sensors, expected to gain popularity as they provide a low-cost and simple-to-implement
method of predicting final product qualities.

Acknowledgments

We sincerely acknowledge the financial support from theAustralian Research Council (DP220100306 and
FT190100361).

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Authors’ Short Biographies
Xin Jin
Dr Jin is a Postdoctoral fellow in Prof. Yansong Shen’s lab in the Department of Chemical Engineering at the University of New South Wales. He received a PhD in Chemical Engineering in 2022
from the same university. His research interests include the numerical simulation and process optimisation of industrial mixing and segregation systems.

Yansong Shen
Yansong Shen is a full Professor (tenured) and ARC Future Fellow (A/Prof, 2019–2021, SeniorLecturer, 2016–2018, UNSW; Lecturer, 2014–2016, Monash). He is the director of a vibrant researchlab - Process Modelling and Optimisation of Reacting Flows “ProMO Lab” (www.promo.unsw.edu.
au), with applications to a range of complex reactive flow processes in traditional and emerging industries particularly resource and energy sectors, including process metallurgy, solid fuel preparation/utilisation, water treatment, recycling processes of e.g. solar panels, plastic, and renewableenergy processes e.g. solar cell/biomass/hydrogen. His research interests range from understanding
fundamentals to optimising & developing new, cleaner and more efficient technologies, powered byadvanced numerical and experimental approaches. He is a member of the editorial boards of “Advanced Powder Technology” and “Metallurgical and Materials Transactions B”.

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