Role of interparticle forces and interparticle friction on the bulk friction in charged granular
media subjected to shearing
S. J. Antony and M. A. Sultan
Institute of Particle Science and Engineering, University of Leeds, LS2 9JT, United Kingdom
Received 28 June 2006; revised manuscript received 6 October 2006; published 27 March 2007
We study the consequences of the interplay between electrostatic forces, mechanical contact forces, and
frictional properties of grains upon the bulk frictional properties of charged granular media subjected to
quasistatic shearing. We show that, the variations in short-range electrostatic forces between the grains which
are often ignored in the existing studies dominantly affect the bulk friction. Charging enhances the fabric
anisotropy of heavily loaded contacts—this enhances the bulk friction, more significantly, in the case of low
frictional granular systems.
DOI: 10.1103/PhysRevE.75.031307 PACS numbers: 45.70.-n, 46.55.+d, 47.10.ab
Granular materials behave differently both from ordinary
molecular fluids when they flow and from ordinary solids
when they remain at rest 1,2. Fundamental understanding
on the collective behavior of particulate systems under com-
bined electromechanical loading environments is sought in
several interdisciplinary applications. A few examples are, in
the design of electrostatic granular valves, piezoelectric pow-
der compacts/sensors, electromechanical separators for min-
erals and ores, powder injectors, and microbial particulate
fuel cells e.g., 3–7. The developments in micro/nano tech-
nologies are pushing the limits of miniature particulate fab-
rications by designing particle interfaces with enhanced
functionalities. This is achieved by precisely controlling the
nature of interparticle forces acting between particles 7.
Further, Ambient Intelligence AmI and Virtual Process Cre-
ation Tools VPCT are expected to aid our classrooms in the
future 8. Design of AmI for granular media under com-
bined loading environments should be on the one hand
simple computationally less expensive, and on the other
hand should not compromise the physics that govern the col-
lective behavior of granular media. The speed of simulations
for granular systems largely depends on the interparticle
force-separation models used. Hence, a clear understanding
of the roles played by force components will help us to de-
duce the normally nonlinear terms in their force-separation
relations, as appropriate. Existing literature on the mechani-
cal and electrostatic phenomena in granular systems are ex-
haustive e.g., 3–7, but our understanding of the mechan-
ics and physics behind the collective behavior of granular
systems subjected to combined electromechanical loading
conditions is as of yet, limited. In this work, we attempt to
answer certain aspects of this problem—the effects of the
interplay between the individual interparticle force compo-
nents in charged systems, such as, the short-range and long-
range electrostatic forces, the mechanical contact forces, and
the pull-off force between cohesive particles, on the micro-
macroscopic characteristics. Are all the interparticle force
components contribute to the bulk friction in charged granu-
lar systems? What is the effect of interparticle friction on the
bulk friction in charged granular systems? We aim to get
some answers to these vital questions here, by studying the
micromechanical behavior of granular systems in a charged
environment in a systematic way using computer simula-
tions.
In this study, we used particle-based Discrete Element
Method DEM9–14 to simulate the micromechanical
characteristics of charged systems, by appropriately imple-
menting the interparticle force-separation relation between
the cohesive particles subjected to electromechanical loading
conditions. That is to say, in the interparticle force model, in
addition to the electrostatic forces, the mechanical forces act-
ing between the particles are also accounted. Let us consider
two dielectric spherical particles equal size at a separation
distance, r, from each other. The applied detaching electric
field is assumed to be in the perpendicular direction 3-3
insert in Fig. 1a. In general, the net electrostatic force
F
NE
on a charged particle in an applied electric field with
a fixed electric strength, E, assuming that the charge is dis-
tributed uniformly on the surface of a particle, can be written
as a sum of four components 5,6: i -
Q
2
16
0
r
2
, ii QE,
iii -
0
R
2
E
2
and iv -W
A
R
*
, where Q is the net par-
ticle charge,
0
is the permittivity of free space given as
8.854 10
-12
Nm
2
/C
2
and , , and are correction factors,
which depend on the polarization of the dielectric particle
6. These dimensionless coefficients are the functions of di-
electric constant of the particle, the particle permittivity and
geometric configuration, such as particle size ratio, distance
between the particles and the electrodes 6,15,16. W
A
repre-
sents the work of adhesion 17. =3/2, 2 according to the
Johnson, Kendall, and Roberts JKR and Derjaguin, Muller,
and Toporov DMT theories, respectively 17. For the case
of same size particles, the reduced radius R
*
is equal to half
the radius of the particle R 5,17. The first term represents
the electrostatic adhesion due to the attraction between the
net charges on the particle and its image charge in the elec-
trode and this also accounts for the variation in the short-
range electrostatic force as a function of separation distance
between the particles, r R. Existing studies often ignore
the variation in short-range force contribution 18. The sec-
ond term represents the Coulomb force due to the external
field acting on the particle charge and this term accounts for
the long-range contribution of electrostatic forces. The third
term accounts for the long-range contribution of electrostatic
force due to electrostatic adhesion arising from the attraction
between the field-induced dipole in an uncharged particle in
an electric field and its dipole image 6. In order to evaluate
the magnitude of electrostatic forces, the value of dimension-
PHYSICAL REVIEW E 75, 031307 2007
1539-3755/2007/753/0313075 ©2007 The American Physical Society 031307-1