processes
Article
DEM Study on the Segregation of a Non-Spherical Intruder in a
Vibrated Granular Bed
Jinpeng Qiao
1
, Kejun Dong
2,
* and Chenlong Duan
1,
*
Citation: Qiao, J.; Dong, K.; Duan, C.
DEM Study on the Segregation of a
Non-Spherical Intruder in a Vibrated
Granular Bed. Processes 2021, 9, 448.
https://doi.org/10.3390/pr9030448
Academic Editor: Alberto Di Renzo
Received: 1 February 2021
Accepted: 26 February 2021
Published: 2 March 2021
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1
Key Laboratory of Coal Processing and Efficient Utilization of Ministry of Education, School of Chemical
Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, China;
joe.9911@cumt.edu.cn
2
Centre for Infrastructure Engineering, School of Engineering, Western Sydney University,
Sidney, NSW 2751, Australia
* Correspondence: Kejun.Dong@westernsydney.edu.au (K.D.); clduan@cumt.edu.cn (C.D.)
Abstract: The segregation process of a single large intruder in a vibrated bed of small particles has
been widely studied, but most previous studies focused on spherical intruders. In this work, the
discrete element method was used to study the effects of vibration conditions and intruder shape on
the dimensionless ascending velocity (v
a
) of the intruder. The intruder was in a prolate shape with
aspect ratio varied but its equivalent diameter fixed. Three equivalent diameters, namely volume-
equivalent diameter, surface-area-equivalent diameter, and Sauter diameter, were used. It was found
that v
a
increases and then decreases with the rise of the dimensionless vibration amplitude (A
d
) and
the dimensionless vibration frequency (f
d
), and v
a
increases with the decrease of the sphericity of
the intruder (Φ). Moreover, the porosity variation in the vibrated bed and the granular temperature
were analyzed, which can be linked to the change of v
a
. It was further found that v
a
can be uniformly
correlated to A
d
· f
0.5
d
, while the critical change of the response of v
a
to A
d
and f
d
occurs at Γ = 4.83,
where Γ is the vibration intensity. Based on these findings, a piecewise equation was proposed to
predict v
a
as a function of A
d
, f
d
, and Φ.
Keywords: non-spherical particle; ascending velocity; segregation; discrete element method
1. Introduction
The segregation of granular mixtures under vibration is often encountered in various
industrial processes [1–3]. A good understanding of the segregation mechanism can help
the optimization and control of the related processes. The research of such a phenomenon
often starts with the segregation of a single large intruder in an otherwise homogeneous
granular bed of small particles [4–6]. Under vibration, the large intruder normally ascends
in the granular bed. Based on the statistical analysis on the interaction between the intruder
and the surrounding small particles, several kinds of segregation mechanisms have been
proposed for such an ascending phenomenon, including void filling, global convection,
etc. [7–11]. In addition, in different experimental and numerical studies, the ascending
velocity, which is the average velocity of the intruder in its rising process from the bottom to
the top of the vibrated bed, was often modeled against different controlling variables [12].
The literature indicates the dependence of the ascending velocity on the following
variables: particle properties including the density ratio (ρ
r
)[13–15] and the size ratio
(d
r
)[16,17]; particle bed features including the aspect ratio [18], friction [19], and filling
height [20]; and vibration conditions including vibration amplitude [21], frequency [12],
and intensity [10,22]. For particle properties, a general observation is that the increase of
the size ratio and density ratio both increase the ascending velocity [17,20,22]. The shape
of the container would affect the granular flow direction [18,23] and control the particle
convection [24]. In addition, with or without friction between particles and the wall, the
rise time of the intruder is rather different [25]. For vibration conditions, the increase of
Processes 2021, 9, 448. https://doi.org/10.3390/pr9030448 https://www.mdpi.com/journal/processes