484 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
material composition (Trigwell et al., 2003 Xie et al.,
2016 Cruise et al., 2022).
While tribocharging in material conveyance is often
seen as undesirable (Cezan et al., 2019 Mukherjee et al.,
2021 Sayfidinov et al., 2018 Pingali et al., 2009), it is
beneficial for recycling separation (Iuga et al., 2005, 2016
Silveira et al., 2018 Zelmat et al., 2013 Benhafssa et al.,
2016 Rodrigues &Saron, 2022 Li et al., 2015 Bilici
et al., 2011), printer toner application (Shinbrot et al.,
2008 Noshiro et al., 1999 Anderson 1994, 1996 Takagi
et al., 2003 Law et al., 1994), and dry mineral beneficia-
tion (Kelly &Spottiswood, 1989a, b, c Manouchehri et
al., 2000a, b Inculet et al., 1972 Ireland 2010a, b, 2012
Ireland &Nicholson, 2011 Trigwell et al., 2003 Rasera et
al., 2020 Yu et al., 2024).
For separation applications, it is necessary to optimise
the design of the tribocharger to maximise the charge trans-
ferred to particles of each mineral type. The aim of this
work is to extend of our previous investigations into the
use of the discrete element method (DEM) as a means to
optimise the design of a tribocharger. We begin by present-
ing our modelling approach and optimised design under
terrestrial conditions using PTFE spheres. We consider the
suitability of the optimised tribocharger design to different
materials and size classes. Finally, having validated model-
ling approach and demonstrated the suitability of the opti-
mised design, extend our modelling to identify an optimal
tribocharger design for use on the Moon.
MODELLING METHODOLOGY
Cundall and Strack’s discrete element method is of particu-
lar interest for modelling triboelectrification (Cundall 1971
Cundall &Strack 1979 Rasera et al., 2022a Laurentie et
al., 2010, 2013 Kolehmainen et al., 2016, 2017a, b Ali et
al., 1998 Pei et al., 2015 Sippola et al., 2018 Konopka
et al., 2017). The DEM lends itself to coupling with tri-
bocharging models, as parameters necessary for evaluating
charge transfer are extracted easily.
Substantial effort has been put toward developing
and evaluating means to model the charge transfer process
(Rasera et al., 2022a. b Yu et al., 2017 Xie et al., 2013 Hu
et al., 2012 Laurentie et al., 2010, 2013 Kolehmainen,
2016, 2017a,b Ali et al., 1998 Pei et al., 2015 Sippola
et al., 2018 Konopka et al., 2017 Lacks, 2012 Duff &
Lacks, 2008 Forward et al., 2009a). The tribocharg-
ing model employed in our studies uses the high-density
limit of surface state theory to describe the charge trans-
ferred between two surfaces, following Schein et al. (1992),
Matsusaka et al. (2000), Laurentie et al. (2010, 2013), and
Kolehmainen et al (2016, 2017a, b). This model is given by
the following equation:
E n
c
i j
contact ij 0 v l f de
z z
=
-
-d n
Here, σ is the charge transferred per unit area κc is the
empirically-derived charging efficiency εe is the permit-
tivity of free space δe is the separation distance between
two particles at which point charge transfer ceases e is the
magnitude of the electron charge ϕi and ϕj are the effective
work functions E
contact is the electrostatic field at the point
of contact and, n
ij is the unit normal vector pointing from
particle i to j at the point of contact. While the use of this
model has been demonstrated previously in the literature
with good agreement to experimental data, this elaboration
is dependent on effective work functions, a property that is
not suitable for describing insulating materials (Rasera et
al., 2022a, b Schein et al., 1992). Furthermore, other stud-
ies assume the charging efficiency to simply be 1, however,
we demonstrated that this term is a critical parameter for
modelling the charge transfer process.
To address the first issue, the work function term is
replaced by the charge transfer limitation parameter, Γ,
which is effectively the electrostatic field required to drive
Δq to 0. The equation above it thus rearranged in terms of
the quantity of charge transferred, Δq, as a function of the
change in contact area during a collision, ΔA, as follows:
q E n
c contact ij 0 f D DAl C =-_i
This form of the equation makes it well-suited for imple-
mentation in a DEM solver. The parameters Γ and κc must
be determined experimentally for both particle-particle
and particle-wall interactions, and for each material pair-
ing a method for calculating these can be found in Rasera
et al. (2022a, b). The algorithm for modelling triboelectric
charging is as follows:
1. Update the particle positions and velocities using
the laws of motion.
2. Identify contacting bodies (particles and/or walls).
3. Determine the overlap and evaluate the change in
contact area.
4. Find the electrostatic field at the centroid of each
particle. If the contact is between two particles, use
linear interpolation to find the field at the point
of contact. If the contact is between a particle and
a wall, calculate the field at the point of contact
directly.
5. Evaluate the quantity of charge exchanged.
6. Determine the electrostatic force acting on each
particle.
material composition (Trigwell et al., 2003 Xie et al.,
2016 Cruise et al., 2022).
While tribocharging in material conveyance is often
seen as undesirable (Cezan et al., 2019 Mukherjee et al.,
2021 Sayfidinov et al., 2018 Pingali et al., 2009), it is
beneficial for recycling separation (Iuga et al., 2005, 2016
Silveira et al., 2018 Zelmat et al., 2013 Benhafssa et al.,
2016 Rodrigues &Saron, 2022 Li et al., 2015 Bilici
et al., 2011), printer toner application (Shinbrot et al.,
2008 Noshiro et al., 1999 Anderson 1994, 1996 Takagi
et al., 2003 Law et al., 1994), and dry mineral beneficia-
tion (Kelly &Spottiswood, 1989a, b, c Manouchehri et
al., 2000a, b Inculet et al., 1972 Ireland 2010a, b, 2012
Ireland &Nicholson, 2011 Trigwell et al., 2003 Rasera et
al., 2020 Yu et al., 2024).
For separation applications, it is necessary to optimise
the design of the tribocharger to maximise the charge trans-
ferred to particles of each mineral type. The aim of this
work is to extend of our previous investigations into the
use of the discrete element method (DEM) as a means to
optimise the design of a tribocharger. We begin by present-
ing our modelling approach and optimised design under
terrestrial conditions using PTFE spheres. We consider the
suitability of the optimised tribocharger design to different
materials and size classes. Finally, having validated model-
ling approach and demonstrated the suitability of the opti-
mised design, extend our modelling to identify an optimal
tribocharger design for use on the Moon.
MODELLING METHODOLOGY
Cundall and Strack’s discrete element method is of particu-
lar interest for modelling triboelectrification (Cundall 1971
Cundall &Strack 1979 Rasera et al., 2022a Laurentie et
al., 2010, 2013 Kolehmainen et al., 2016, 2017a, b Ali et
al., 1998 Pei et al., 2015 Sippola et al., 2018 Konopka
et al., 2017). The DEM lends itself to coupling with tri-
bocharging models, as parameters necessary for evaluating
charge transfer are extracted easily.
Substantial effort has been put toward developing
and evaluating means to model the charge transfer process
(Rasera et al., 2022a. b Yu et al., 2017 Xie et al., 2013 Hu
et al., 2012 Laurentie et al., 2010, 2013 Kolehmainen,
2016, 2017a,b Ali et al., 1998 Pei et al., 2015 Sippola
et al., 2018 Konopka et al., 2017 Lacks, 2012 Duff &
Lacks, 2008 Forward et al., 2009a). The tribocharg-
ing model employed in our studies uses the high-density
limit of surface state theory to describe the charge trans-
ferred between two surfaces, following Schein et al. (1992),
Matsusaka et al. (2000), Laurentie et al. (2010, 2013), and
Kolehmainen et al (2016, 2017a, b). This model is given by
the following equation:
E n
c
i j
contact ij 0 v l f de
z z
=
-
-d n
Here, σ is the charge transferred per unit area κc is the
empirically-derived charging efficiency εe is the permit-
tivity of free space δe is the separation distance between
two particles at which point charge transfer ceases e is the
magnitude of the electron charge ϕi and ϕj are the effective
work functions E
contact is the electrostatic field at the point
of contact and, n
ij is the unit normal vector pointing from
particle i to j at the point of contact. While the use of this
model has been demonstrated previously in the literature
with good agreement to experimental data, this elaboration
is dependent on effective work functions, a property that is
not suitable for describing insulating materials (Rasera et
al., 2022a, b Schein et al., 1992). Furthermore, other stud-
ies assume the charging efficiency to simply be 1, however,
we demonstrated that this term is a critical parameter for
modelling the charge transfer process.
To address the first issue, the work function term is
replaced by the charge transfer limitation parameter, Γ,
which is effectively the electrostatic field required to drive
Δq to 0. The equation above it thus rearranged in terms of
the quantity of charge transferred, Δq, as a function of the
change in contact area during a collision, ΔA, as follows:
q E n
c contact ij 0 f D DAl C =-_i
This form of the equation makes it well-suited for imple-
mentation in a DEM solver. The parameters Γ and κc must
be determined experimentally for both particle-particle
and particle-wall interactions, and for each material pair-
ing a method for calculating these can be found in Rasera
et al. (2022a, b). The algorithm for modelling triboelectric
charging is as follows:
1. Update the particle positions and velocities using
the laws of motion.
2. Identify contacting bodies (particles and/or walls).
3. Determine the overlap and evaluate the change in
contact area.
4. Find the electrostatic field at the centroid of each
particle. If the contact is between two particles, use
linear interpolation to find the field at the point
of contact. If the contact is between a particle and
a wall, calculate the field at the point of contact
directly.
5. Evaluate the quantity of charge exchanged.
6. Determine the electrostatic force acting on each
particle.