Experimental investigation into segregation behavior of spherical/non-spherical granular mixtures in a thin rotating drum

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RESEARCH ARTICLE

FEBRUARY 22 2024

Experimental investigation into segregation behavior of

spherical/non-spherical granular mixtures in a thin rotating

drum



Yun-Chi Chung (

鍾雲吉

)

;

Melany L. Hunt

;

Jia-Non Huang (

黃嘉農

)

;

Chun-Chung Liao (

廖俊忠

)



Physics of Fluids

36, 023342 (2024)

https://doi.org/10.1063/5.0190892

26 February 2024 18:29:15

Experimental investigation into segregation

behavior of spherical/non-spherical granular

mixtures in a thin rotating drum

Cite as: Phys. Fluids

, 023342 (2024);

doi: 10.1063/5.0190892

Submitted: 9 December 2023

Accepted: 30 January 2024

Published Online: 22 February 2024

Yun-Chi

Chung (

鍾

雲

吉

Melany L.

Hunt,

Jia-Non

Huang (

黃

嘉

農

and Chun-Chung

Liao (

廖

俊

忠

)

2,3,a)

AFFILIATIONS

Department of Mechanical Engineering, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City 320317,

Taiwan

Department of Mechanical and Civil Engineering, California Institute of Technology, 1200 E California Blvd. MC 104-44, Pasadena,

California 91125, USA

Department of Mold and Die Engineering, National Kaohsiung University of Science and Technology, No. 415, Jiangong Rd., Sanmin

Dist., Kaohsiung City 807618, Taiwan

Author to whom correspondence should be addressed:

liao0910@nkust.edu.tw

Tel.:

886-7-3814526.

Fax:

886-7-3830674

ABSTRACT

This paper uses physical experiments to investigate the segregation behavior of binary granular mixtures in a quasi-two-dimensional rotating

drum. Spherical polyformaldehyde (POM) beads and cylindrical red beans constitute the granular mixtures. The effects of particle size,

particle density, and particle shape interplay during the segregation process in the spherical/non-spherical particulate system. A long-axis

ratio (LAR), the ratio of the spherical POM beads

’

diameter to the red beans

’

primary dimension, was defined to explore the particle shape

effect. The experimental results show that the long-axis ratio and the rotation speed play substantial roles in the granular segregation behav-

ior. As the long-axis ratio increases, the steady-state segregation intensity decreases. An increase in the rotation speed enhances the segrega-

tion of the binary granular mixtures for each long-axis ratio studied here. In addition, the average velocity and granular temperature of

spherical POM beads increase as the long-axis ratio increases. Both properties also increase as the rotation speed increases. The dynamic

angle of repose for the binary mixtures increases with the increase in the long-axis ratio. Most interestingly, reverse granular segregation does

occur at a long-axis ratio of 0.70 with the cylindrical red beans in the core and the spherical POM beads at the periphery for each rotation

speed studied here. This reverse segregation has not been observed in previous studies. This highlights the substantial impact of particle shape

on the granular segregation in binary granular mixtures.

Published under an exclusive license by AIP Publishing.

https://doi.org/10.1063/5.0190892

I. INTRODUCTION

Granular materials are essential in industrial processes, such as

powder metallurgy, foodstuff processing, additive manufacturing,

pharmaceutical engineering, powder injection molding, energy pro-

duction, and chemical manufacturing. Rotating drums have widely

been used in chemical reactions, milling, mixing, granulation, drying,

and calcification.

–

Due to their capacity to efficiently generate

straightforward flow regimes for granular materials, these rotating

drums are always employed to study granular assemblies

’

flow charac-

teristics and mixing/segregation phenomena.

–

As a result, under-

standing the kinematics and kinetics of granular materials in rotating

drums is of fundamental physical interest and crucial practical con-

cern. Shape-induced granular segregation is a phenomenon that occurs

when particles of different shapes in a granular mixture segregate from

each other due to differences in their shapes.

5,6,9

–

This segregation

can have essential implications in designing materials with specific

properties, understanding natural hazards such as landslides, and opti-

mizing industrial processes such as pharmaceutical manufacturing,

additive manufacturing food processing, mining and mineral process-

ing, and powder manufacturing.

Size and density segregation have been extensively studied in the

past decades,

–

but shape-induced segregation has only received

limited attention. Pollard and Henein

used rotating cylindrical tum-

bler tests to investigate the kinetics of radial segregation of irregularly

shaped particles with different sizes. The segregation core was found to

contain more large non-spherical particles than that for similar experi-

ments with spherical particles. They attributed this phenomenon to

the cause that the particles

’

irregular shape reduces their flowability.

Phys. Fluids

, 023342 (2024); doi: 10.1063/5.0190892

, 023342-1

Published under an exclusive license by AIP Publishing

Physics of Fluids

ARTICLE

pubs.aip.org/aip/pof

26 February 2024 18:29:15

Makse

et al.

performedheapexperimentsforbinarymixturesof

cubical and spherical particles in a Hele

–

Shaw cell. The segregation in

avalanching heaps was observed to exhibit spherical particles at the

bottom and cubical particles at the top. They proposed that shape-

induced segregation is driven by differing angles of repose in both

granular materials. Through experiments, Dube

et al.

employed the

radioactive particle tracking technique to measure the dynamics of

non-spherical particles in rotating drums. Their results revealed that

the non-spherical tablets exhibit a lower axial dispersion coefficient

than the spherical particles, and that particle shape can affect the segre-

gation/mixing of binary granular mixtures in a rotating drum. Hohner

et al.

investigated the flow behavior of polyhedral dice in rotating

drums, and the dynamic angle of repose increased with the particles

’

increasing angularity.

Saeed and Siraj

investigated the mixing of non-spherical par-

ticles in a cylindrical mixer using the discrete element method (DEM)

simulations. They reported that more complex or non-spherical shapes

exhibit more inter-particle contact forces, and complex shape particles

have lower mixing performance than spherical particles. Pereira and

Cleary

adopted the DEM to investigate the segregation of spherical

and cubical particles in a slowly rotating cylindrical tumbler where the

particles differ only in their shapes. They reported that more cubical

particles segregate to the core of the granular bed, while spherical par-

ticles migrate to the periphery of the drum. The primary mechanism

for this shape-induced segregation was reported to be the difference in

energy dissipation rates for different types of particle shapes when

avalanching down along the free surface. In their study, the cubical

particles dissipate energy much faster than the spherical particles. He

et al.

also used DEM simulations to explore the effect of particle

shape on the radial segregation of binary mixtures of ellipsoidal par-

ticles in a rotating drum. Their numerical results revealed that ellipsoid

particles could segregate either to the bed

’

scoreorperiphery,depend-

ing on the shape difference of the granular mixture. With the rotation

speed increasing from 5 to 40rpm, the segregation degree reduces for

all mixtures. In addition, granular mixtures with more considerable

shape differences lie in a cascading regime at the same rotation speed,

indicating that the shape difference could affect the flowing regime.

Since most granular mixtures differ in all three main intrinsic

properties (size, density, and shape), which are all known to cause seg-

regation, the underlying mechanisms that control shape-induced gran-

ular segregation are still not fully understood. Most importantly, few

studies have developed physical experiments to investigate the shape-

induced segregation of granular mixtures systematically. Given this,

the present study adopted a particle tracking method and an image

processing technology to study the non-spherical granular segregation

in rotating drums experimentally. To quantify the interlocking effect

resulting from particle shape, a long-axis ratio (LAR) was mainly intro-

duced. The effects of rotation speed and long-axis ratio on the shape-

induced segregation were systematically investigated. This study ana-

lyzed the transport properties, such as the segregation intensity, local

average velocity, granular temperature, and dynamic angle of repose.

II. EXPERIMENTAL SETUP FOR INVESTIGATING

SEGREGATION BEHAVIOR OF BINARY GRANULAR

MIXTURES IN A THIN (QUASI-2D) ROTATING DRUM

Figure 1(a)

shows a quasi-two-dimensional (quasi-2D) rotating

drum, which was established to investigate the segregation of spheri-

cal/non-spherical granular mixtures. In order to achieve a balance

between the wall friction and axial motion, the quasi-2D rotating

drum possessed a 28 cm diameter and a 2 cm axial length.

–

The

transparent glass was used for the front and rear face plates of the

rotating drum to facilitate optical observation. At the same time, an

Aluminum alloy was chosen for the annular sidewall to minimize elec-

trostatic interference. The binary granular mixtures comprised non-

spherical red beans and spherical polyformaldehyde (POM) beads.

The red beans exhibited a roughly cylindrical shape, with average mea-

surements of 8.5 mm in the primary direction and 5.5 mm in the

minordirection.ThesphericalPOMbeadscameinfourdiameters:3,

4, 5, and 6 mm, respectively.

Figure 1(b)

shows these single particles.

The density of the red beans is 1110 kg/m

, while that of the POM

beadsis1410kg/m

. The granular mixtures were composed of red

beans and POM beads of approximately the same volume for all

experiments. They were then filled into the drum by layer and layer

with a filling level of roughly 50%. The initial packing of a granular

mixture, where the cylindrical red beans were positioned on top of the

spherical POM beads, is shown in

Fig. 1(c)

Measuring the velocities of non-spherical particles through

experiments is still a challenge because of the limitations of modern

measurement technology. None of the existing particle tracking veloc-

imetry (PTV) technologies can be employed to measure the velocities

of non-spherical particles in rotating drums, even in quasi-2D models

with multiple layers of non-spherical particles. Given this limitation,

the granular mixtures comprising cylindrical red beans and spherical

POM beads were made. The white spherical POM beads were used as

tracer particles, allowing us to determine their trajectories using tradi-

tional PTV. To investigate the influence of particle shape, a long-axis

ratio (LAR) was introduced, which is defined as the ratio of the diame-

ter of the spherical POM beads (d

POM

) to the primary dimension of

the red beans (d

Bean

). Four LARs (0.35, 0.47, 0.58, and 0.70) were

selected in the study to investigate the non-spherical granular segrega-

tion. The mixing and segregation phenomena are believed to be influ-

enced by the interplay of shapes between the cylindrical red beans and

the spherical POM beads. Consequently, the size of the POM beads

was changed to control the relative shape effects.

The drum

’

s rotation speed also significantly affects the segrega-

tion of non-spherical granular assemblies.

6,13

The rotation speed was

varied in this study, and three different rotation speeds (i.e., 2, 3, and

4 rpm) were chosen to investigate the effect of rotation speed. With the

rotation speeds studied here, the motion of the granular assembly in

the rotating drum can be controlled in the rolling regime.

Figure 1(d)

provides a representative schematic of the rolling regime, characterized

by a dynamic angle of repose (

h

r), which exhibits both an active flow-

ing layer and a passive fixed layer. We observed the segregation pat-

terns of the granular mixture using a digital video motion recorder/

analyzer (SONY HDR-PJ820). Images with a resolution of 800

pixels

600 pixels were taken at a rate of 30 frames per second for all

experiments. Furthermore, a high-speed camera (Factcam mini UX50)

was employed to record the flow characteristics of the granular mix-

ture once the flow field had stabilized. For each experiment, we cap-

tured 4000 frames at a rate of 1000 frames per second, each with an

image resolution of 890 pixels

920 pixels. Each frame was digitally

converted into a grayscale, ranging from 0 to 255 in relation to the

color difference between the white POM beads and the red beans.

These digital images were transferred to a personal computer and

archived for subsequent analysis. The drum diameter (280mm)

Physics of Fluids

ARTICLE

pubs.aip.org/aip/pof

Phys. Fluids

, 023342 (2024); doi: 10.1063/5.0190892

, 023342-2

Published under an exclusive license by AIP Publishing

26 February 2024 18:29:15

corresponded to 840 pixels, yielding a scaling factor of 0.333 mm per

pixel. A PTV

21,22,31

–

technique was employed to determine the transla-

tional velocity of each tracer particle between every two successive

images. A brief review of this methodology is provided in the

Appendix

The translational velocities of every tracer particle were computed

by utilizing the particle coordinates in each frame, the scaling factor of

0.333 mm per pixel, and a rate of 1000 frames per second.

Figure 2

illustrates the process of image manipulation, including the localization

of tracer particles and the generation of translational velocities of every

tracer particle from two consecutive images. This further allowed us to

delve into the dynamic characteristics of granular flows in the rotating

drum, such as the segregation intensity, local average velocity, granular

temperature, and dynamic angle of repose, which will be elaborated in

Sec.

III

Table I

shows the experimental configurations of the current

study.

III. DEFINITION OF TRANSPORT PROPERTIES

FOR GRANULAR MIXTURES IN ROTATING DRUMS

The transport properties of the granular mixture in the rotating

drum are defined below. The domain occupied by all particles in the

rotating drum was divided into

cells, and the segregation intensity

(

segregation

) is expressed as

4,5,20

–

23,31,32

segregation

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðÞ

;

(1)

where

is the area concentration of white tracer particles in the

th cell;

and

is the average area concentration of all cells in the rotating drum.

Based on the findings of previous studies,

4,5,26

a20pixels

20 pixels

FIG. 1.

Illustration of the experimental setup: (a) a schematic representation of the experimental setup, (b) spherical polyformaldehyde (POM) beads and c

ylindrical red beans,

Physics of Fluids

ARTICLE

pubs.aip.org/aip/pof

Phys. Fluids

, 023342 (2024); doi: 10.1063/5.0190892

, 023342-3

Published under an exclusive license by AIP Publishing

26 February 2024 18:29:15