KONA Powder and Particle Journal No. 41 (2024) 229–241/https://doi.org/10.14356/kona.2024016

Original Research Paper

Effects of DEM Parameters and Operating Conditions on
Particle Dynamics in a Laboratory Scale Rotating Disc †Rondinelli M. Lima, Gisele M. Souza, Rodolfo J. Brandão,Claudio R. Duarte and Marcos A.S. Barrozo *School of Chemical Engineering, Federal University of Uberlândia, Brazil

Rotating discs are usually used as granulators in many industrial processes. The efficiency of the
granulation process in this device is directly related to the particle motion behavior in different
flow regimes. In this work, the granular flow in a rotating disc was investigated experimentallyand numerically. The Discrete Element Method (DEM) was used in the simulations, while
Central Composite Designs (CCD) were employed to quantify the effects of DEM input
parameters and operating conditions (filling degree (FD), angle of inclination (AI), and rotational
speed) on the contacts between particles. The results showed that the particle–wall static friction
coefficient had the most significant impact on the studied response. Additionally, the effect ofoperating variables on the collision force between particles, the angle of departure and particle
velocities were successfully investigated, with corresponding DEM simulation predictions. It wasalso verified that the simulations performed with experimentally measured DEM input parametervalues were able to reproduce the flow regimes in the rotating disc.
Keywords: rotating disc, flow regimes, DEM, DEM parameters, number of contacts

1. Introduction

The granulation process is widely employed in different
industries, such as fertilizer, pharmaceutical, food, chemical, steel, and ceramics. This particle size enlargement
technique allows the production of useful structural forms,
modifies the material rheology, increases its flowability,
reduces material loss and dust emissions, and controls porosity (Capes, 1980; Litster and Ennis, 2004).
Industrial granulators promote agglomeration throughparticle mixing and collision. Compared to other types ofequipment, rotating discs stand out due to their pronounced
segregation ability and flexibility to operate different typesof materials (Litster and Ennis, 2004). Moreover, their geometry is relatively simple, consisting of a disc with a certain diameter (D), an angle of inclination (θ) and a rim (L)that rotates around its axis (Fig. 1).
Although rotating discs have been widely used as a granulator (Azrar et al., 2016; Ball, 1959; Chadwick andBridgwater, 1997), only qualitative descriptions of solids
flow have been usually made, with little quantitative information on particle dynamics (Chadwick and Bridgwater,
1997). The effects of different operating variables, such as
rotational speed, filling degree (FD) and angle of inclina†*

Received 30 March 2023; Accepted 1 May 2023
J-STAGE Advance published online 31 August 2023
Corresponding author: Marcos A.S. Barrozo;
Add: Bloco K, Campus Santa Mônica, 38400-902, Uberlandia, MG,
BrazilE-mail: masbarrozo@ufu.br
FAX: +55-34-32394188

tion (AI), on the motion and contacts of particles are still
not fully understood (Lima et al., 2022). Furthermore, as
granulation is a dynamic process, investigating both the
responses that are directly related to the granule formation(i.e., particle velocity, and number and force of contacts
between particles) and flow regimes can also be a potential
tool to optimize the granulation process in rotating discs(Gladky et al., 2021).
Depending on the operating conditions, different regimes of solids motion can be identified in a rotating disc:slipping, rolling, cascading, cataracting, and centrifuging,each with a specific flow behavior. Detailed descriptions ofthese flow regimes can be found in Mellmann (2001).
In the rolling regime, the granular bed can be divided
into two distinct regions: the passive layer, where the particles are dragged up by the disc wall as a rigid body, and theactive layer, where the particles roll over the bed surface
downwards. For higher velocities, a kidney-shaped curve
develops on the bed surface and a larger area of the disc isused, corresponding to the cascading regime. Regarding
the granulation process, the rolling and cascading regimes
in particular have the advantage of promoting more effective contacts between particles than the others (Azrar et al.,2016; Salman et al., 2006).
In addition to experimental studies, numerical simulations have become a complementary tool in granular flow
analysis. Introduced by Cundall and Strack (1979), theDiscrete Element Method (DEM) has been extensively applied to investigate granular dynamics in different types ofequipment. In this method, each particle is described

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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Original Research Paper

Table 1 Nonlinear Hertz–Mindlin model equations (Cundall and Strack,
1979; Di Maio and Di Renzo, 2005; Tsuji et al., 1992).

Normal forceDω

Damping normal forceθ

Equivalent contact radiusL
Equivalent mass

Fig. 1

Schematic diagram of a rotating disc.

individually through the application of a balance of forces
and contact laws. The precision of the DEM model for
predicting the granular flow relies on the selected contact
model and the input parameters, which depend on both theparticle properties and the particle-contact properties.
DEM simulations provide microscopic results at theparticle level, such as trajectories of particles and forcesthat act on them, making it possible to obtain important
information about particle dynamics. In this context, theknowledge of the solids flow in rotating discs is crucial for
their design and applicability. However, there are a limited
number of studies on the fluid dynamics of rotating discs
using numerical analysis in conjunction with experimental
results. Thus, through the use of DEM simulations and experimental data the present work aims to investigate how
numerical parameters and different operating conditions
influence particle dynamics in a rotating disc. The flow regimes and particle velocity distributions were also studied.

2. Discrete element method

DEM uses a time-stepping algorithm where the modeling is repeated in each time interval. Each particle istracked contact by contact and its positions are updated
based on the results of the previous time step (Nascimento
et al., 2022; O’Sullivan, 2011). During each time step,
Newton’s second law is applied to determine the particle
trajectory, while the particle–particle and particle–wallcontact forces are evaluated based on the force–displacement law (Brandao et al., 2020; Cundall and Strack, 1979;
Potyondy and Cundall, 2004). The motion of individual
particles is determined by Eqns. (1) and (2):d vi  Fij
dt
j

(1)

dωi
Ii
  τ ij
(1) d tj(2)

miwhere t, mi, Ii, vi, and ωi are the time, mass, moment of inertia,(2) linear velocity, and angular velocity of particle i, respectively, and Fij and τij are the force and torque between

230

3

Fn 

4 * * 2
E R δn35
β S n m* vnrel
6

Fnd  2

(3)

1
1
1


*
R
Ri R j

(4)

1
1
1


*
m
mi m j

(3)
(4)
(5)
(6)

Equivalent Young’s modulus(5)11  υi2 1  υ 2j


*
E
Ei
Ej

(7)

Normal stiffness

(6)

(8)

Damping coefficient(7)

S n  2E * R*δn
ln e
β

(8)
Tangential force
Tangential damping force
Tangential stiffness
Equivalent shear modulus(10)

Ft  δt S t(9)
Ftd  2

(10)

(9)

ln 2 e  π 2

5
β S t m* vtrel
6

S t  8G * R *δn(11)
1
2  υi 2  υ j


*
G
Gi
Gj
(12)

(11)
(12)
(13)

particles i and j, respectively.(13)The contact model used herein was the nonlinear Hertz–
Mindlin. The main equations of this model are summarizedin Table 1.
The equations in the Table 1 involve normal and tangential overlaps(δn, δt), normal and tangential relative veloci ties vnrel , v trel  , restitution coefficient (e), and Poisson’s ratio(υ).

3. Materials and methods[31]
Laboratory
tests and numerical simulations were conducted using a disc granulator made of stainless steel witha smooth surface and diameter of 35 cm, length of 20 cm,
and variable angle of inclination. The granular material
used was glass beads with a diameter of 6.35 ± 0.01 mm,
density of 2455 ± 24 kg/m3, and sphericity of 0.99 ± 0.01.
The DEM simulations were performed on the commercial EDEM® software. To ensure the numerical stability ofthe simulation, a time step of 4 × 10–5 s, which is equivalent to 20 % of the Rayleigh time, was adopted. The simulation conditions are listed in Table 2.

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3.1 Measurement of DEM input parameters

The restitution coefficient (e), which quantifies the energy conserved in shocks between solid bodies, can beexperimentally measured by the ratio between the relative
velocities after (V1) and before (V0) the impact of two colliding bodies (Lima et al., 2021; Machado et al., 2017;
Marinack Jr. et al., 2013), as shown in Eqn. (14):the launching device (Fig. 2) at a certain height (h0), andthen allowed to travel through the entire device. The distance traveled by the particle after leaving the launching
device until its resting point (Dr) was subsequently measured. The rolling friction coefficient was calculated using
Eqn. (16):
μR 

V
e 1
V0

(14)

To determine the velocity before and after collision, theexperimental apparatus described in previous studies was(14)
employed(Bharadwaj et al., 2010; Hastie, 2013; Marinack
Jr. et al., 2013). It consists of a vacuum pump responsible
for a suction pressure that holds particles at a height of
50 mm from the plate. In this procedure, the pump is
switched off to allow particles to fall, while their trajectoryis filmed by a high-speed video camera (Fastec IL5—up to
44,000 frames/s).
In order to measure the static friction coefficient (μS), theinclined plane method was applied (ASTM G115-10,2013). In this method, the plane is gradually inclined andthe angle of inclination (Ф) from which the particles start toslide is used to calculate the μS (Eqn. (15)).
(15)

μS  tan ΦTo replicate the particle–wall interactions, the surface of
the inclined plane was covered with a stainless steel plate.
(15)
The particle–particle interaction behavior was studied bycovering the surface of the plane with a fixed granular bedof glass beads (Brandao et al., 2020; Lima et al., 2021).
To calculate the rolling friction coefficient (μR), a measurement procedure based on that described in Lima et al.
(2022) was adopted. The particle was placed on the top of

Table 2 DEM simulation conditions.

Model

Hertz–MindlinTime step (s)4 × 10–5

Original Research Paper

h0
Dr

(16)

The experimental parameter values were used herein as
inputs to the DEM model. Brandao et al. (2020) showed
(16)
that
the simulations performed with experimentally measured parameters were in good agreement with the experimental responses.

3.2 Sensitivity analysis of DEM parameters

In order to quantify the effect of DEM parameters (i.e.,
restitution, static, and rolling friction coefficients) on thecontact between particles in the rotating disc, a fractional
Central Composite Design (CCD) (26-1, with 2x6 axial
points and one central point) was used for the DEM calibration procedure. The CCD levels are shown in Table 3.
The CCD data was used to better understand the influence of the DEM parameters on the rotating disc simulation. Therefore, the CCD can help in both the calibration
process and the development of new disc designs.
This CCD was applied to angles of inclination of 40°,
50° and 60°, and the rotating disc was filled with glass
beads (2 % per volume). The rotational speed was set at
10 rpm. The dependent variable (response) was the average
number of contacts between particles (NCpp), since it is arelevant parameter in the granulation process. The greater
the contact between particles, the more effective the granulation process.
For each CCD run, the real-time simulation was 30 s.
The NCpp average was obtained in the last 10s of simulation, since the rotating disc was operating in steady state.
The steady-state condition was considered when the granular bed reached a constant height.

Poisson’s ratio (-)
Glass beads

0.22

Table 3 CCD levels used in the sensitivity analysis of DEM parameters.

Stainless steel

0.30

Factor coding

epp, epw, μSpp, μSpw

μRpp, μRpw

–α (–1.78)

0.054

0.005

Shear modulus (Pa)Glass beads

1 × 106

–1

0.250

0.025

Stainless steel

7 × 1010

0

0.500

0.050

1

0.750

0.075

+α (+1.78)

0.946

0.095

Dr

h0
Fig. 2

Rolling friction coefficient apparatus.

*epp, epw, μSpp, μSpw, μRpp, μRpw correspond to the restitution, static,
and rolling friction coefficients, respectively. The subscripts pp
and pw indicate the particle–particle and particle–wall interactions, respectively.

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Table 4 CCD levels used in the sensitivity analysis of operating conditions.

Coded Factor

FD (%)AI (°)RS (rpm)–α (–1.47)

0.59

35.29

5.29

–1

2.00

40.00

10.00

0

5.00

50.00

20.00

+1

8.00

60.00

30.00

+α (+1.47)

9.41

64.71

34.71

*FD: filling degree, AI: angle of inclination, RS: rotational speed.

(a) Rolling

(a)

(b)

(b) Cascading

α(c) Cataracting

Original Research Paperα(d) Centrifugingr
Reference line
Fig. 4 Determination of particle velocity distribution: (a) crosssection representation parallel to the base of the rotating disc; and (b)schematic representation for particle velocity measurement.

α

3.5 Simulation of particle velocity distributions
Fig. 3

Analyzed flow regimes and angle of departure measurement.

3.3 Sensitivity analysis of operating conditions

Another CCD was applied to evaluate the sensitivity ofoperating conditions on the number of contacts between
particles. For these simulations the DEM parameters were
kept constant following the values defined in Section 3.1.
The analyzed operating conditions and the corresponding
CCD levels are listed in Table 4.

3.4 Simulation of flow regimes

The flow regimes (i.e., rolling, cascading, cataracting,and centrifuging) were numerically investigated and compared with experimental results of our previous work
(Lima et al., 2022). The angle of departure (α) was definedas the angle at which the particles detached from the equipment wall; it was measured using the Meazure software(Fig. 3).
The analyses were carried out at filling degrees of 2 %,5 % and 8 % and angles of inclination of 40°, 50° and 60°.
The flow regimes were simulated using experimental values of DEM parameters.

232

In order to determine the passive and active layers of therolling regime, the particle velocities were measured. Dueto the inclination of the rotating disc, these layers were located in the inner part of the granular bed. Therefore, it wasnecessary to perform a cross-sectional cut parallel to thebase of the rotating disc, as illustrated in Fig. 4(a).
The particle velocity was determined along the referenceline drawn in the middle of the granular bed (Fig. 4(b))
under different conditions (Delele et al., 2016; Resende etal., 2017; Santos et al., 2013, 2015). The reference line wasdiscretized and normalized at evenly distributed points, andat each point the velocity of five different particles was determined.
The conditions used to investigate the velocity profilesof glass beads in the rotating disc were filling degrees of
2 % and 5 %, angles of inclination of 50° and 60°, and rotational speeds of 10 rpm, 15 rpm and 20 rpm.

4. Results and discussions

4.1 Sensitivity analysis of DEM parameters

A CCD (see levels in Table 3) was employed to evaluate
the influence of DEM parameters on the number of contacts between particles (NCpp) in a rotating disc. To this end,a total of 45 simulations were performed for the rotating
disc operating at angles of inclination of 40°, 50°, and 60°,
a filling degree of 2 %, and a rotational speed of 10 rpm.

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Original Research Paper

The obtained results are depicted in Appendix A (Supplementary material: Table A1).
From these results, it was possible to quantify such effects for each angle of inclination by regression techniques.
The prediction equations (Eqns. (17)–(19)) resulted incorrelation coefficients (R2) of 0.94, 0.95 and 0.95 for angles of inclination of 40°, 50° and 60°, respectively.

to determine such values (Cunha et al., 2016; El Kassem etal., 2021; Marigo and Stitt, 2015; Nascimento et al., 2022;
Santos et al., 2016). One of the disadvantages of the calibration process is the high number of simulations required
to find the parameter values. Therefore, the analysis of theeffects of DEM parameters becomes essential to quantify
the influence of each parameter on the rotating disc. As
μ 2 has a muchgreater influence than the other parameN Cpp-40º 
1.17  0.05x1  0.05x12  0.05x22  0.09 x3  0.36 x4  0.16Spwx  0.06 x52  0.05x62
ters,4 an alternative
is to only calibrate this parameter, thusx12  0.05x22  0.09 x3  0.36 x4  0.16 x42  0.06 x52  0.05x62
reducingthenumberof simulations.
(17)
Another factor to be analyzed is that μSpw has a negative(17)
effect, i.e., the number of contacts between particles deN Cpp-50º 
1.18  0.05x1  0.06 x12  0.06 x22  0.12 x3  0.06 x32  0.40 x4  0.17 x42  0.07 x52  0.06 x62  0.04 x1x4
creases as the coefficient value increases. This information
2
2
2
2
2
2
is necessary for the design and optimization of rotating
1  0.06 x 2  0.12 x3  0.06 x3  0.40 x 4  0.17 x 4  0.07 x5  0.06 x6  0.04 x1 x 4
discs, because depending on the interaction between the
(18)
(18)
granular material and the equipment wall, the contact between particles can decrease, thus hindering the granula22
2
N Cpp-60º 
1.19  0.05x1  0.06 x1  0.06 x2  0.13x3  0.06 x3  0.41x4  0.18 x42  0.07 x52  0.06 x62  0.03x1x4
tion process.
x12  0.06 x22  0.13x3  0.06 x32  0.41x4  0.18 x42  0.07 x52  0.06 x62  0.03x1x4
Rong et al. (2020) used a 3k factorial design to evaluate
the sensitivity of particle–particle DEM parameters in a
(19)
(19)
rotating drum. The authors found that the sliding friction
The DEM parameters of these equations are presented incoefficient, when compared with the rolling friction coefficoded form as follows:
cient and the restitution coefficient, was the determining
parameter on the mean power draw of the rotating drum.
epp  0.50
epw  0.50
With the increase in the sliding friction coefficient, more
x1 
x2 
0.25
0.25
power was required due to the increased resistance of parμSpw  0.50
μSpp  0.50
ticles when they come into contact with other particles.
x4 
x3 
0.25
0.25
[32]
[33]
μRpp  0.050
μ Rpw  0.050
x5 
x6 
0.025
0.025
[35]
[34]
Table 5 CCD used to analyze the influence of operating conditions on
where x1 = particle–particle restitution coefficient, x2 =NCpp.
particle–wall restitution coefficient, x3 = particle–particle
[36]
[37]
static friction coefficient, x4 = particle–wall static frictionRun
FD (%)AI (°)RS (rpm)NCppcoefficient, x5 = particle–particle rolling friction coeffi1
2.00
40.00
10.00
1.31
cient, and x6 = particle–wall rolling friction coefficient, all
2
2.00
40.00
30.00
0.79
in coded form.
3
2.00
60.00
10.00
1.34
In Eqns. (17)–(19), only the statistically significant parameters were included. It was possible to observe that all
4
2.00
60.00
30.00
0.86
DEM parameters had a significant effect on NCpp at a signif5
8.00
40.00
10.00
1.59
icance level of 5 %.
6
8.00
40.00
30.00
1.15
The coefficients of Eqns. (17)–(19) show that epw (x2 incoded form), μRpp (x5 in coded form), and μRpw (x6 in coded
7
8.00
60.00
10.00
1.65
form) were only influenced by the quadratic term. On the
8
8.00
60.00
30.00
1.26
other hand, μSpw (x4 in coded form) was the parameter that
9
0.59
50.00
20.00
0.71
most influenced NCpp, with an effect four times greater thanthat of μSpp (x3 in coded form)—the second most relevant
10
9.41
50.00
20.00
1.42
parameter—and eight times greater than that of epp (x1 in
11
5.00
35.29
20.00
1.19
coded form). In addition, the change in the angle of inclina12
5.00
64.71
20.00
1.28
tion of the rotating disc practically did not influence theintensity of the parameter effects.
13
5.00
50.00
5.29
1.73
In order to obtain accurate simulations based on the
14
5.00
50.00
34.71
1.03
DEM approach, a correct set of input parameter values is
15
5.00
50.00
20.00
1.29
required. Several studies have used the calibration process233

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4.2 Analysis of the effects of operating conditions

Table 5 shows the results of the CCD used to analyze theinfluence of filling degree (FD), angle of inclination (AI)and rotational speed (RS) on NCpp (see levels in Table 4).
The data in Table 5 were subjected to regression analysis to quantify the effects of each independent variable andits corresponding interactions on the response (NCpp). The
variables FD, AI and RS were coded as x7, x8, and x9, respectively. The obtained equation (Eqn. (20)) has a correlation coefficient (R2) equal to 0.97.
N Cpp 1.27  0.19 x7  0.09 x72  0.03x8  0.23x9  0.06 x92(20)
FD  5%AI  50
where:; x8 
;(20) x7 
3%10RS  20 rpm
and x9 
10 rpm[38][39]analyzed had a significant effect
All operating conditions

on NCpp at a significance level of 5 %. It is noteworthy that
there[40]was no interaction between the variables, i.e., eachvariable alone had a direct influence on NCpp.
As it can be seen in Eqn. (20), the effect of FD was
positive, that is, the number of contacts between particles
increased as a function of the number of particles in therotating disc. An opposite effect was observed for rotational
speed, i.e., the RS increased with decreasing NCpp. According to Capes (1980), during the granulation process theparticle residence time can be lengthened by increasing therotational speed. However, at high rotational speeds therotating disc tends to operate in the cataracting regime,
which can result in agglomerate degradation and breakage
depending on the agitation intensity. A strict control of therotational speed is then necessary for the rotating disc tooperate in the rolling and cascading regimes, consequently
improving the efficiency of the granulation process(Pietsch, 1997; Salman et al., 2006).
The change in the disc inclination had little influence on
NCpp when compared to the other variables. This result
confirms what was observed in the sensitivity analysis of
DEM parameters.
Other variables such as size distribution of feed, liquid
content in the feed powder, and liquid surface tension can
Table 6 DEM parameter values obtained experimentally.

DEM parameters

Values

epp

0.900

epw

0.690

μSpp

0.620

μSpw

0.330

μRpp

0.014

μRpw

0.013

234

Original Research Paper

also influence the granulation process (Capes, 1980). Nevertheless, Eqn. (20) can elucidate the granulation process,assisting in the operation, design and optimization of rotating discs.

4.3 Simulation of flow regimes

DEM simulations were also used to predict the behaviorof flow regimes in a rotating disc. In these simulations, theinput parameters obtained from the experimental proceduredescribed in Section 3.1 were employed. Table 6 shows
the values of DEM parameters obtained by the respective
experimental measurement. To verify the validity of these
DEM input parameters, the numerical and experimental
results were compared. Two analyses were carried out: aqualitative one, where images of the flow regimes wereconfronted, and a quantitative one, where the angle of departure values were compared.
Figs. 5 to 7 compare the images of the experimental andsimulated results for the different flow regimes in the rotating disc, operating at different angles of inclination (AI). As
it can be seen, the DEM simulations accurately predictedeach flow regime.
Regarding the quantitative analysis, Fig. 8 compares thenumerical and experimental angles of departure for thestudied disc inclinations. As observed, the experimental
and simulated results were very similar for the entire rangeof flow regimes (i.e., rolling, cascading, cataracting, andcentrifuging). The average percentage deviation of the angle of departure was less than 2 %. Therefore, both qualitative (Figs. 5 to 7) and quantitative (Fig. 8) analyses
confirmed that the direct experimental measurements of the
DEM input parameters were able to reproduce the bulk
behavior of particles in the rotating disc. For this reason, it
was not necessary to perform the calibration of DEM parameters, allowing the preservation of their physical meanings.
Barrios et al. (2013) verified that experimental measurements of DEM parameters for a single particle proved to bea viable alternative to estimate the parameter values of ironore pellets. According to the authors, the computational
effort is reduced since the parameter values are obtained
directly, without requiring a calibration process.
Brandao et al. (2020) used DEM Simulations to study
the mixing and segregation of materials in a rotating drum.
The authors measured the DEM parameters experimentallyand performed a calibration approach. They verified thatthe parameter values obtained by the calibration process
were similar to the experimental ones.
From the validation of the DEM model it can be verified
that the DEM parameters successfully represent the evaluated experimental results. Therefore, it is possible to analyze the influence of the experimental operating conditions
on the maximum collision force (FC,max). To determine themaximum collision force, all particles were tracked along

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AI (°)
FD (%)

Original Research Paper2
10 rpm40
510 rpm8
10 rpm25 rpm20 rpm15 rpm40 rpm35 rpm35 rpm90 rpm65 rpm65 rpmRolling

CascadingCataracting

Centrifuging

Fig. 5AI (°)
FD (%)

Experimental and numerical results of the qualitative analysis of flow regimes for an angle of inclination of 40°.

2
10 rpm50
510 rpm8
10 rpm30 rpm25 rpm20 rpm40 rpm35 rpm30 rpm130 rpm

100 rpm

90 rpmRolling

CascadingCataracting

Centrifuging

Fig. 6

Experimental and numerical results of the qualitative analysis of flow regimes for an angle of inclination of 50°.

235

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AI (°)
FD (%)

Original Research Paper2
10 rpm60
510 rpm8
10 rpm45 rpm40 rpm35 rpm70 rpm45 rpm40 rpm165 rpm

125 rpm

105 rpm

Rolling

CascadingCataracting

Centrifuging

Fig. 7

Experimental and numerical results of the qualitative analysis of flow regimes for an angle of inclination of 60°.

(a)

(b)

(c)

Fig. 8236

Experimental and numerical results of the quantitative analysis of angles of departure for angles of inclination of (a) 40°, (b) 50° and (c) 60°.

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the simulation time.
A 3k factorial design was used to evaluate the effects ofthe following operating conditions on FC,max: filling degree(FD), angle of inclination (AI) and rotational speed (RS).
The levels used for the independent variables (FD, AI, andRS) were the same as the experimental ones. This analysis
can be used to help prevent agglomerate degradation andbreakage.
Table 7 shows the conditions and results (FC,max) of the
3k factorial design.
The effects of FD, AI and RS on FC,max were quantified
by regression techniques using the experimental data in
Table 7. From Eqn. (21), which has a correlation coefficient (R2) equal to 0.82, it is possible to predict the maxiTable 7 3k factorial design used to analyze the influence of operating
conditions of a rotating disc on FC,max.

1

2

40

10

1.10

2

2

(21)

40

30

1.52

3

2

40

50

1.98

4

2

50

10

1.21

5

2

50

30

1.33

6

2

50

50

1.62

7

2

60

10

1.18

8

2

60

30

1.72

9

2

60

50

1.93

10

5

40

10

1.24

11

5

40

30

1.46

12

5

40

50

2.31

13

5

50

10

1.21

14

5

50

30

1.43

15

5

50

50

1.80

16

5

60

10

1.45

17

5

60

30

1.91

18

5

60

50

1.72

19

8

40

10

1.35

20

8

40

30

1.74

21

8

40

50

2.91

22

8

50

10

1.55

23

8

50

30

1.49

24

8

50

50

1.68

25

8

60

10

1.52

26

8

60

30

1.50

27

8

60

50

1.75

2  0.33x  0.12 x x  0.19 x x  0.09 x
FC,max  1.61  0.10 x10  0.10 x11
12
10 11
11 12

2  0.33x  0.12 x x  0.19 x x  0.09 x x 2  0.10 x 2 x
FC,maxx10  0.10x11AI (°) 1.61 
RS0.10(rpm)
FC,max(N) 12
10 11
11 12
11 12
11 12

(21)

(21)
FD  5%AI  50
where: x10 ; x11 ;3%
10
RS  30 rpm
20 rpm[41][42]
The effect of operating conditions on FC,max was similar
to that observed for the angle of departure and this result is[43]

and x12 (a)V

FD (%)

mum collision force between particles (FC,max) as a functionof the operational variables and quantify its respective effects. The independent variables FD, AI, and RS are presented in coded forms (x10, x11 and x12, respectively).
All operating conditions had a positive effect on FC,max at
a significance level of 5 %. FC,max increased as a function ofboth FD (x10 in coded form) and RS (x12 in coded form),with the latter affecting this variable three times more than
the former. This analysis highlights the care that must be
taken when operating rotating discs at high rotational
speeds, as this can result in degradation of the agglomerates
formed, thus impairing the granulation process. On theother hand, AI (x11 in coded form) had a negative effect on
FC,max, and although it did not affect linearly the collision
force, it interacted with other variables.

(b)

r

V

Run

Original Research Paperr

Fig. 9 Velocity profiles of glass beads for an angle of inclination of
50°: (a) 2 % and (b) 5 %.

237

Rondinelli M. Lima et al. / KONA Powder and Particle Journal No. 41 (2024) 229–241(a)Table 8 Analysis of active and passive layer thicknesses.

Filling
degree[%]Layer thickness [m]Passive(P)

Active
(A)

50°

2

0.040

0.029

0.714

5

0.063

0.046

0.727

2

0.034

0.023

0.667

5

0.057

0.034

0.600

V

Angle ofinclination

60°

r

V

(b)

r

Fig. 10 Velocity profiles of glass beads for an angle of inclination of
60°: (a) 2 % and (b) 5 %.

in agreement with the behavior observed by Lima et al.
(2022).

4.4 Simulation of particle velocity distributions

Due to the rotating disc inclination, the active and passive layers of the rolling regime were found to be located in
the inner regions of the granular bed. Therefore, they could
only be observed through simulations.
Figs. 9 and 10 display the particle velocity distributions,where Vp is the particle velocity and r is the particle position along the reference line (Fig. 4(b)). The variable r
starts from the disc wall and ends at the granular bed
surface. In this work, only the cases in which the rotating
disc was operating in the rolling regime were considered,i.e., at angles of inclination of 50 (Fig. 9) and 60° (Fig. 10),filling degrees of 2 and 5 %, and velocities of 10, 15 and20 rpm.
The two different bed structure regions visualized in theFigs. 9 and 10 demonstrate that as the value of r increased,
the particle velocities decreased until reaching a minimum
value (close to zero), evidencing the interface between thepassive and active layers. This behavior is typical of thepassive layer in the rolling regime, in which the particles
move as a solid body and are dragged up by the disc wall.
From the interface, the solids velocities started to increase
along r, characterizing the active layer. In this region, the238

Original Research Paper

Ratio
(A/P)

particles had a higher dynamics, moving in the opposite
direction to the passive layer. As observed, the highest velocity values were found to be near the granular bed surface.
It can also be seen that higher rotational speeds resulted
in greater velocities in both layers, but without changing
the interface position. When the rotational speed was kept
constant and the filling degree was increased, the particle
velocities also increased in both layers, and such effect was
higher in the active layer. Regarding the angle of inclination, it can be observed that the disc operating at 50°
achieved higher particle velocities in the active layer. In
this case, the granular bed reached a higher angle of departure, increasing the potential energy of the particles andtherefore their dynamics.
In contrast to the rotational speed, changes in the filling
degree and angle of inclination modified the interface position, suggesting the significant impact of these variables on
the active layer thickness. The correct prediction of the active and passive layers for a rotating disc operating in therolling regime is very important for the granulation process. It is worth mentioning that the best particle interactions, mixing and segregation, as well as the highest ratesof heat and mass transfer, occur in the active layer. Table 8
presents the thicknesses of the active layers and their ratio
to the passive layer thicknesses for angles of inclination of
50° and 60°.
For constant filling degrees, the change in the angle ofinclination from 50° to 60° resulted in a reduced ratio between the layers of 6.58 % and 17.47 % for filling degreesof 2 % and 5 %, respectively, evidencing the movement ofparticles to the passive layer region.
Santos et al. (2015) found similar behavior, when studied, numerically and experimentally, the velocity profile ofsoybean particles in a rotating drum operating in the rolling
regime. They observed that, keeping the filling degree
constant and increasing the rotational speed, there was anincrease in the velocity of the particles in both layers (passive and active), and the point where a reverse of the flow
takes place was kept constant. On the other hand, when therotational speed was kept constant and the filling degree
was changed from 18.81 % to 31.40 %, the inflection point

Rondinelli M. Lima et al. / KONA Powder and Particle Journal No. 41 (2024) 229–241

Original Research Paperchanged from 4 cm to 5.5 cm, respectively.

E

Young’s modulus (Pa)5. Conclusions

E*equivalent Young’s modulus (Pa)F

force (N)G

shear modulus (Pa)G*

equivalent shear modulus (Pa)h0device height (m)Imoment of inertia (m s–2)L

rim height of disc granulator (m)m*equivalent mass (kg)mmass (kg)Ncnumber of contact (-)

R

radius (m)R*equivalent contact radius (m)S

stiffness (Pa m)ttime (s)vlinear velocity (ms–1)

V0

velocity before impact (m s–1)

V1

velocity after impact (m s–1)

Vp

particle velocity (m s–1)

In this work, DEM simulations were performed to study
the influence of DEM parameters and operating conditions
on particle dynamics in a rotating disc.
The methodology used herein allowed to analyze andquantify the effect of DEM parameters on the number ofcontacts between particles, an important variable in the
granulation process. All DEM parameters had a significant
influence on the analyzed response, with μSpw being theparameter with the greatest effect.
DEM simulations were also used to predict the behaviorof flow regimes in a rotating disc. In these simulations, theinput parameters obtained from the experimental procedure
were used and successfully predicted the experimental behavior of all flow regimes.
With respect to the effects of the operating conditions of
the rotating disc (i.e., filling degree, angle of inclination
and rotational speed) on NCpp and FC,max, it was observedthat the increase in the filling degree had a positive effecton both responses. In contrast, the increase in the rotational
speed led to a reduction in NCpp, but an increase in FC,max,which can impair the efficiency of the granulation process.
Lastly, in relation to the disc inclination, the change in thisparameter had little influence on NCpp. Additionally it wasverified that greater angles of inclination led to a reductionin the intensity of FC,max.
In this study, it is also possible to verify the effect of theoperating conditions of the rotating disc on the particle velocity distributions in the rolling regime. As the filling degree and rotational speed increased, the particle velocity
was also raised in both layers, whilst the change in the angle of inclination affected the active layer. The disc operating at 50° showed the highest ratio between the active andpassive layer thicknesses.

Supplementary information

The online version contains supplementary material
available at https://doi.org/10.14356/kona.2024016.

Acknowledgments

The authors are grateful to the Minas Gerais Research
Funding Foundation (FAPEMIG), the Brazilian National
Council for Scientific and Technological Development(CNPq), and the Coordination for the Improvement ofHigher Education Personnel (CAPES) for their financial
support.

NomenclatureD

diameter of disc granulator (m)Drdistance traveled by the particle (m)erestitution coefficient (-)

Greek Symbol
αangle of departure (°)β

damping coefficient (kg s–1)

δoverlap distance of two particles (m)θangle of inclination of disc granulator (°)μR

rolling friction coefficient (-)μS

static friction coefficient (-)τ

torque (N m–1)

υ

Poisson ratio (-)Φ

angle of inclination used in the friction coefficient measurement (-)ω

angular velocity (s–1)

IndexesC

contactddampingi and jparticle identification indexnnormal directionppparticle–particle interaction

pw

particle–wall interactionttangential direction

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Original Research Paper

Authors’ Short Biographies
Rondinelli Moulin Lima
Dr. Rondinelli Moulin Lima received his Ph. D. in Chemical Engineering from the Federal University of Uberlândia in 2021. He has experience in Chemical Engineering, with emphasis on Computational Fluid Dynamics and Discrete Element Method in the area of particulate systems andseparation processes. He is currently a researcher at the Institutional Training Program at the Center
for Mineral Technology (CETEM), with the development of agglomerated stones.

Gisele Márcia de Souza
MSc. Gisele Márcia de Souza received her master’s degree in Metallurgical and Mining Engineering from the Federal University of Minas Gerais. Currently, she is a Ph. D. candidate at the Federal
University of Uberlândia in the area of particulate systems and separation processes. She has experience in Chemical Engineering, with emphasis on Transport Phenomena, Unit Operations, Computational Fluid Dynamics and Discrete Element Method.

Rodolfo Junqueira Brandão
Dr. Rodolfo Junqueira Brandão is Adjunct Professor I at the Technology Center at the Federal
University of Alagoas. He received his Ph. D. in Chemical Engineering from the Federal Universityof Uberlândia in 2019. He is currently Coordinator of the Technology Center and Tutor of the Special
Engineering Training Program. He works mainly in the area of particulate systems, separation processes and numerical simulation.

Claudio Roberto Duarte
Dr. Claudio Roberto Duarte is a Full Professor at the Federal University of Uberlândia in Brazil.
He received his Ph. D. in Chemical Engineering from the Federal University of Uberlândia in 2006.
He served as the Coordinator of the Postgraduate Program in Chemical Engineering at the Federal
University of Uberlândia from 2019 to 2022. He works mainly on the following topics: granulation,
rotating drums, mills, drying, pyrolysis, solid-liquid separation, spouted bed, modelling, computational fluid dynamics, and cyclone.

Marcos Antonio de Souza Barrozo
Dr. Marcos Antonio de Souza Barrozo is a Full Professor at the Federal University of Uberlândia
in Brazil. He received his Ph. D. in Chemical Engineering from the Federal University of São Carlos
in 1995. He is an A1 researcher at the National Council for Scientific and Technological Development (CNPq) and a member of the Standing Committee of the Brazilian Congress of Particulate
Systems. He has experience in Particulate Systems, working mainly on the following topics: fluid
dynamics of particulate systems, solid-fluid separation, drying, coating, granulation, flotation, pyrolysis, and hydrothermal carbonization.

241