In a previous work, the addition of basic screened Coulombic electrostatic forces to an existing commercial discrete element modeling (DEM) software was reported. Triboelectric experiments were performed to charge glass spheres rolling on inclined planes of various materials. Charge generation constants and the Q/m ratios for the test materials were calculated from the experimental data and compared to the simulation output of the DEM software. In this paper, we will discuss new values of the charge generation constants calculated from improved experimental procedures and data. Also, planned work to include dielectrophoretic, Van der Waals forces, and advanced mechanical forces into the software will be discussed

Calle, Carlos I.

Curry, D. R.

Hogue, Michael D.

Weitzman, P. S.

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Proc. ESA Annual Meeting on Electrostatics 2008 
Discrete Element Modeling (DEM) of 
Triboelectrically Charged Particles: 
Revised Experiments 
M.D. Hogue
Electrostatics & Surface Physics Laboratory 
NASA, Kennedy Space Center
KSC, FL USA 32899
phone: (1) 321-867-7549 
e-mail: Michael.D.Hogue(inasa.gov  
C.I. Calle
Electrostatics & Surface Physics Laboratory 
NASA, Kennedy Space Center
KSC, FL USA 32899 
e-mail: Carlos. I.Calle(nasa. gov 
D.R. Curry
DEM Solutions, Inc.
20 York Place
Edinburgh, UK EH1 3EP

e-mail: dcurrv(dem-solutions.com  
P.S. Weitzman
DEM Solutions (USA) Inc. 
24 Hanover Street, Suite 10 
Lebanon, New Hampshire, 03766 
Abstract— In a previous work, the addition of basic screened Coulombic electrostatic 
forces to an existing commercial discrete element modeling (DEM) software was reported. 
Triboelectric experiments were performed to charge glass spheres rolling on inclined planes 
of various materials. Charge generation constants and the Q/m ratios for the test materials 
were calculated from the experimental data and compared to the simulation output of the 
DEM software. In this paper, we will discuss new values of the charge generation constants 
calculated from improved experimental proceedures and data. Also, planned work to include 
dielectrophoretic, Van der Waals forces, and advanced mechanical forces into the software 
will be discussed.
Proc. ESA Annual Meeting on Electrostatics 2008 
I. INTRODUCTION 
Theoretical and experimental work was presented on the incorporation of screened Cou-
lombic electrostatic force into a discrete element modeling (DEM) software used to 
model particle flow [I]. Experimental values of a triboelectric charging constant, a, was 
used to calculate simulated values of Q/m for comparision to experimental values of Q/m. 
The experimental procedure was changed to insure better discharging of the glass 
spheres used prior to the start of each experiment. The resulting values of a give values 
of Q/m in the DEM simulation that compare better to experimental ones. 
Work is proceeding on incorporating advanced electrostatic forces into the DEM soft-
ware such as the dielectrophoretic and Van der Waals forces. This work is part of a lar-
ger project with Glenn Research Center (GRC) and DEM Solutions, Inc. to expand the 
capability of the currrent EDEMTM software for planetary as well as terrestrial applica-
tions. The Kennedy Space Center (KSC) is working on methods to mitigate dust on the 
Moon and Mars [2]. One of these methods uses applied AC electric fields to move the 
dipolar dust simulants off of surfaces. Accurate computer modeling of this electrostatic 
dust screen is a goal of this project. 
II. REVISED EXPERIMENTS 
A. Procedure Modj/Ications 
The experiment consists of an inclined plane apparatus to triboelectrify 2.0 mm diameter 
borosilicate glass spheres that roll down the plane [1]. In the previous experiments, the 
means of neutralizing any initial charge on the spheres was inefficient due to the fact that 
spheres interior to the pile inside the sphere cup were shielded from the deionizer by the 
outer spheres. This resulted in simulation values of Q/m that did not match experimental 
values well [11 This appartus is shown in Fi
	
1 
Fig. I. Triboelectric apparatus with aluminum InJineLl planL. sphere cup, and dam. Total 
charge of the glass spheres. . is measured in the Faraday cup shown.
Proc. ESA Annual Meeting on Electrostatics 2008 
To reduce the initial triboelectric charge on the glass spheres, the experimental proce-
dures were modified to allow better deionization of the spheres prior to each experiment. 
25 spheres were used instead of 500 as before. This number of spheres was easier to 
deionize in the sphere cup prior to the experiment while still providing sufficient spheres 
to observe the flow pattern on the inclined plane. 
The inclined plane was set at 30°. The inclined plane materials used were Aluminum, 
polyvinyl chloride (PVC), low density polyethylene (LDPE), Nylon 6/6, and polytetra-
fluoroethylene (PTFE). To remove any initial electrostatic charge, the spheres are dis-
charged by use of an air ionizer. The spheres are then allowed to roll down the inclined 
plane into the Faraday cup by removing the sphere dam. The time of triboelectric contact 
with the inclined plane was measured by a stop watch. The sphere cup, dam, and in-
clined plane are all of the same material to insure that the triboelectric charging is caused 
by contact only against the test material. 
B. Data 
Ten experiments were performed for each inclined plane material and the results aver-
aged. The values of Qim and a from these experiments are summarized in Table 1. 
TABLE 1: VALUES OF Q/MAND a FOR REVISED 300 EXPERIMENTS (RANGES ARE ± ONE
STANDARD DEVIATION) 
Inclined Plane Material Q/m (nC.g') a (s') 
Aluminum 0.524 ± 0.363 0.023 ± 0.0 15 
PVC 5.874± 1.610 0.237±0.042 
LDPE 0.524±0.187 0.018±0.005 
Nylon 6/6 1.459 ± 0.411 0.057 ± 0.012 
PTFE 2.469±0.561 0.100±0.015
C. Data Analysis 
Comparison of previous values of a [1] with the values in Table 1 are shown in Fig. 2. 
The much larger a values in Fig. 2 lead to better agreement between the EDEM simula-
tion and experimental values of Q/m. This data is shown in Fig. 3. These revised ex-
periments highlight the sensitivity of a to the initial conditions of the surfaces in qustion 
and the physical environment. More on this will be discussed in Sections III A and III B. 
2.5 
2 
1.5 
1 
0.5 
0
	
Proc. ESA Annual Meeting on Electrostatics 2008	 4 
Conarison of New and Cd 1ôJpha Values 
	
025	 -	 - 
	
:!I	
- 
'	
1LJJ: 
PVC	 LDPE	 N'lon 6/6	 FIFE 
Inclined Plane Material 
Fig. 2. Comparison of new and old values of the charge generation constant a. 
3
• E.iporim.ntal 
• EDEM Simulation 
LI,, 
Al	 PVC	 LDPE	 Nylon 6/6
	
PTFE 
Fig. 3. Comparison of EDEM simulation and experimental values of Q/m using the new 
charge generation constant. Q/m values are given in nC.g'. 
III. THEORETICAL ASPECTS 
A. Charge Dissipation Constant 
The data analysis in section II highlights one of the inherent difficulties in using experi-
mental values of the charge generation constant in that experimentally derived values of 
Proc. ESA Annual Meeting on Electrostatics 2008 
the constant can be influenced by initial charge on the surfaces of the contacting bodies. 
This can be especially true when the model equation used assumes zero initial charge on 
the contacting surfaces[ I J[3] when there is some initial charge. 
Potential parameters of a include, but are not necessarily limited to, temperature, pres-
sure, % relative humidity, perpendicular force, parallel velocity, surface area, work func-
tion, and number of occupiable surface sites. The first three are environmental factors, 
the next two are kinematic factors, and the last three are material specific factors. The 
environmental factors can play significant roles in determining the value of a especially 
for insulators [4][5]. More on the initial charge will be discussed in section B. 
B. Revised Triboelectric Charge Generation Equation 
Many tribocharging situations of interest will have initial charge on the particles. To 
account for initial charge on the spheres, Greason's triboelectric charge generation equa-
tion [3],
dq (1) 
is re-integrated but this time with limits on the charge integral of q = q at t = 0 in-
stead of q = 0 at I = 0. Here a and flare the charge generation and dissipation constants 
respectively and q is the saturation charge (here taken to be atmospheric breakdown). 
Performing this integration gives 
q(t) q0e"'	 q	 {i - e''' J.	 (2) =	 +1+fi 
The second term of Eq. (3) is the Greason equation disscussed in [I] while the first term 
deals with initial charge on the spheres. Assuming negligible charge dissipation during 
the time frame of the inclined plane experiment (fi 0), we get 
q(t)=qoe' +q(i_eo).	 (3) 
For many particles, we multiply Eq. (3) through by the total number of particles, N, and 
rearrange to get
Nq(t) = Q(t) = Nq5 - (Nq -	 (4) 
Here, Qo is the total initial charge on all the particles. To use Eq. (4) one would have to 
measure the initial charge on the particles, Qo, before the start of any tribocharging ex-
periment or process. For our inclined plane experiment, we would need to measure the 
total charge on the glass spheres in the sphere cup prior to removal of the dam. A way to 
do this is to replace the sphere cup with a second Faraday cup as the sphere reservoir. 
This will also allow Q/m measurements to be taken both before and after the triboelectric
Proc. ESA Annual Meeting on Electrostatics 2008 
charging. Eq. (4) can be solved for the triboelectric charging constant a. 
a = ijNq5 -(')1 
t [Nq5—Q0j	 (5) 
Here the parameters N, Q(t), Qo, and t are measured quantities while the saturation 
charge, q, for the inclined plane experiment is the electrical breakdown limit of of air 
under standard conditions (2.66 x iO C . m 2) [ I]. 
C. Electrostatic Force Between a Particle and a Plane 
Another factor to be considered is the electrostatic attraction between the spheres and 
the inclined plane (or other planar surfaces). Initial spheres from the sphere cup will 
encounter an uncharged plane (the plane was discharged prior to each experiment). 
However, the initial rolling spheres will tribocharge the plane and subsequent spheres 
will encounter an oppositely charged plane. The resulting attractive electrostatic force 
will have to be taken into account as a retarding force on the spheres like air resistance 
and friction. 
The electrostatic attraction between a particle and a plane can be physically modeled 
by a charged particle of radius b above a charged circular surface area of radius a. To 
make a point charge approximation, let b << a and the surface charge density on the cir-
cular area, a, be uniform and constant. This is shown in Fig. 4. 
Sphere of radius b << a 
and charge q 
fo	 IR
dq = a r dr dç 
y 
x 
Figure 4. Charged particle of radius b near a charged circular plane of radius a. 
In cylindrical coordinates, the unit vector R is given by[6][7]
Proc. ESA Annual Meeting on Electrostatics 2008 
-	
-.	 a	 —rr+Z0Z R = —rr + z0z 
with -- = _______ .	 (6) R 
Using Eq. (6) and the geometry from Fig. 4, the differential force element can then be 
written as [6]
dJ= q (—rF+z0i 
4eoR2Vr2+z2 ]ardrd.	 (7) 
Before Eq. (7) is integrated, it should be noted that all the radial components will can-
cel from symmetry. Integrating Eq. (7) gives 
cc	
r	 qozo('1	 1 
_____ Iz. (8) (r + z0 )	 2e Lo -	 + z J 2	 2\3/2
Letting z0 b for close proximity between the sphere and other surfaces we get 
b	 (9) 
	
2e0	 a2+b2J 
Eq. (9) can be used to approximate the electrostatic force between a charged particle 
and a charged surface.
IV. DEM SIMULATION 
DEM Solutions, Inc. has performed additional particle-particle and particle-surface tribo-
electric simulations modeling a physical situation similar to the experiment described in 
Section II. In this simulation [12], four angles (00, 15 0 30 0 45 0) are modeled simulta-
neously. This geometery is shown in Fig. 5. Box structures are used as the particle fac-
tories. The generic particles (20 for each factory) modeled are 0.5 mm in diameter with a 
mean density of 1200 kg m 3 and a shear modulus of 7.7 x 106 Pa. The charge genera-
tion constant, a, was set at -0.5 s 1 to insure that the particles would charge negatively 
and the sloped trough would charge positively.
j_r 
Proc. ESA Annual Meeting on Electrostatics 2008 
Figure 5. EDEM Model of four inclined curved surfaces at 00, 15°, 30° and 45°. Box 
structures on the end are the particle factories. 
Charge build-up on the inclined surfaces are calculated in EDEM and are shown graphi-
cally in Fig. 6. The higher charge build-up on the lower inclines is due to the longer con-
tact time of the spheres. Additional normal force due to gravity in the lower inclines is 
negligible with such small particles but could be a factor for larger ones. 
Figure 6. Charge build-up on the inclined surfaces at 0°, 15, 30°, and 45°.
Proc. ESA Annual Meeting on Electrostatics 2008 
The zero degree slope generated the highest charge even though relatively little particle 
motion occurred [121. Average charge on the spheres for each angle is shown in Fig. 7. 
0.002 
0 
-0.002 
-0.004 
0.006 
-0.008 
-0.01 
-0.012 
-0.014 
-0.016 
0.3	 0. 
—0deees 
— l5degrees 
—30deees 
—45deees
_________________________
Figure 7. Average charge on the spheres for each angle [12]. 
The charge on the spheres at zero degrees in Fig. 7 is unphysical and is a consequence 
of contact time between the spheres and the inclined surfaces, not triboelectric charge 
exchange. This highlights a limitation of Greason's charge generation equation [3] in 
that it assumes rolling or sliding triboelectric contact between the two surfaces. The 
EDEM code will have to be revised to take non-motion contact into account. 
V. FUTURE WORK 
A. Additional Experiments 
The experiments described in Section II need to be revised further to insure the removal 
or measurement of any initial charge on the spheres. This will include changing the ex-
perimental proceedure to discharge the spheres as they are being loaded into the sphere 
cup by a deionizer and to load them slowly. Also, as mentioned in Section II B, the 
sphere cup can be replaced with a Faraday cup to measure the initial Qim of the spheres 
prior to release and the resulting data compared to the previous experiments. 
Additional materials will be used for the experiment to increase the data set. Addi-
tional sphere materials are: Copper, Carbon Steel, Acrylic, Polytetrafluroetylene (PTFE), 
High Density Polyethylene (HDPE), Carbon, and Nylon 6/6. These spheres range in 
diameter from 1.6 mm to 2.34 mm. 
The number of spheres will be reduced from previous experiments [1] from 500 to 
250. This number will still allow flow patterns to be observed on the plane and facilitate 
the discharge of the spheres prior to the start of the experiment. 
Proc. ESA Annual Meeting on Electrostatics 2008
	 10 
B. Addition of the Dielectrophoretic and Van der Waals Forces 
KSC and Glenn Research Center (GRC) are engaged with DEM Solutions, Inc. to add 
advanced electrostatic and mechanical forces to the DEM software produced by DEM 
Solutions, Inc. KSC is assisting DEM Solutions, Inc. to add the dielectrophoretic force 
to the software. The dielectrophoretic force is the force exerted on the induced dipole 
moment of an uncharged dielectric particle by the presence of a non-uniform electric 
field [8]. This is the force that moves the dipolar Lunar and Martian regolith simulants 
offofKSC's dust screen [2]. The basic equation of the dielectrophoretic force is 
FDEP =21R _ 2	
1	 E2	 (10) 
e2 
where e is the electric permittivity of the medium, 2 is the electric permittivity of the 
particle, R is the particle radius, and E is the non-uniform electric field [8]. Eq. (10) is 
valid for most non-uniform electric fields but if the non-uniformity of the field is very 
large (an approximate definition for "large" is where the non-uniform electric field is 
stronger than other fields or forces present), then a multipolar treatment is necessary 
[8][9}. The multi-polar force acting on a sphere with the electric field in the z-direction 
[8] is given by
F = 2,re1 KR 2 a (Ô'EZ 2 
n!(n-1)	 ôz" J	 (11) 
2l where K =	 (also called the Clausius-Mossotti factor). 
+ 2e 
When n = 1, Eq. (10) is recovered. The question to be answered is how intense of a 
field gradient is required for higher multipolar terms of Eq. (11) to become significant? 
Reference [9] indicates that higher multipoles of the dielectrophoretic force are not neg-
ligible within a few particle diameters unless the external field is weak. 
Van der Waals forces is the term generally ascribed to intermolecular forces other than 
covalent or electrostatic [10][l 1]. In more macroscopic systems, sub-micron particles 
can adhere to each other or to surfaces via Van der Waals forces alone. GRC will pro-
vide the necessary theoretical support to DEM Solutions, to incorporate these forces into 
EDEM and provide experimental verification of the resulting simulation data. 
VI. ACKNOLEDGEMENTS 
The authors would like to acknowledge NASA, Kennedy Space Center, Applied Tech-
nology Directorate and DEM Solutions, Inc. for their assistance in this work.
Proc. ESA Annual Meeting on Electrostatics 2008 
REFERENCES 
[I] M. D. Hogue, C. I. Calle, P. S. Weitzman, D. R. Cuny, "Calculating the trajectories of triboelectncally 
charged particles using Discrete Element Modeling (DEM), Journal of Electrostatics 66 (2008) PP. 32-38. 
[2] Calle, Cl., J.G. Mantovani, CR. Buhler, A. Chen, iS. Clements, S. Trigwell, E.E. Arens, J.M. McFall, 
and M.L. Ritz, "Dust Mitigation Technologies for Lunar Exploration," International Conference on Explo-
ration and Utilization of the Moon, Sorrento, Italy, October 22-26, 2007. 
[3] W. D. Greason, "Investigation of a test methodology for triboelectrification", Jour. Electrostat. 49, Issue 3-
4 (Aug, 2000) Pp. 245-25 6. 
[4] M. D. Hogue, E. R. Mucciolo, C. I. Calle, C. R. Buhler, "Two-phase equilibrium model of insulator-
insulator contact charging with electrostatic potential", Jour. Electrostat. 63 (2005) Pp. 179-188. 
[5] M. D. Hogue, E. R. Mucciolo, C. I. Calle, "Triboelectric, corona, and induction charging of insulators as a 
function of pressure", Jour. Electrostat. 65 (2007) Pp. 274-279. 
[6] J. A. Edminister, Schaum's Outline Series, Electromagnetics, McGraw-Hill, 1979, ch.2. 
[7] J. D. Jackson, Classical Electrodynamics, 3" ed., Wiley, 1999, ch. I. 
[8] T. B. Jones, Electromechanics of Particles, Cambridge University Press, 1995, Ch. 2. 
[9] M. Washizu, T. B. Jones, "Dielectrophoretic Interaction of Two Spherical Particles Calculated by Equiva-
lent Multipole-Moment Method", IEEE Transactions on Industry AppI. Vol. 32, No. 2, March/April 1996. 
[10] V. A. Parsegian, Van der Waals Forces A Handbookfor Biologists, Chemists. Engineers, and Physicists, 
Cambridge University Press, 2006. 
[II] J. I. Israelachvili, Intermolecular & Surface Forces, 2 ed., Academic Press, 1992, Ch. 6. 
[12] D. R. Curry, Technical Correspondence, DEM Solutions, Inc. April 8,2008.


Discrete Element Modeling (DEM) of Triboelectrically Charged Particles: Revised Experiments

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