We describe the velocity distribution function of a granular gas of electrically charged particles by means of a Sonine polynomial expansion and study the decay of its granular temperature. We find a dependence of the first non-trivial Sonine coefficient, a2, on time through the value of temperature. In particular, we find a sudden drop of a2 when temperature approaches a characteristic value, , describing the electrostatic interaction. For lower values of T, the velocity distribution function becomes Maxwellian. The theoretical calculations agree well with numerical direct simulation Monte Carlo to validate our theory.
REFERENCES
1.
C. D.
Stow
, “Dust and sand storm electrification
,” Weather
24
, 134
–144
(1969
).2.
H. F.
Eden
and B.
Vonnegut
, “Electrical breakdown caused by dust motion in low-pressure atmospheres: Considerations for Mars
,” Science
180
, 962
–963
(1973
).3.
A. A.
Mills
, “Dust clouds and frictional generation of glow discharges on Mars
,” Nature
268
, 614
(1977
).4.
J. S.
Gilbert
, S. J.
Lane
, R. S. J.
Sparks
, and T.
Koyaguchi
, “Charge measurements on particle fallout from a volcanic plume
,” Nature
349
, 598
–600
(1991
).5.
S.-C.
Liang
, J.-P.
Zhang
, and L.-S.
Fan
, “Electrostatic characteristics of hydrated lime powder during transport
,” Ind. Eng. Chem. Res.
35
, 2748
–2755
(1996
).6.
G.
Hendrickson
, “Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting
,” Chem. Eng. Sci.
61
, 1041
–1064
(2006
).7.
P. K.
Haff
, “Grain flow as a fluid-mechanical phenomenon
,” J. Fluid Mech.
134
, 401
–430
(1983
).8.
I.
Goldhirsch
, S. H.
Noskowicz
, and O.
Bar-Lev
, “The homogeneous cooling state revisited
,” Lect. Notes Phys.
624
, 37
–63
(2003
).9.
I.
Goldhirsch
and G.
Zanetti
, “Clustering instability in dissipative gases
,” Phys. Rev. Lett.
70
, 1619
–1622
(1993
).10.
N.
Brilliantov
, C.
Salueña
, T.
Schwager
, and T.
Pöschel
, “Transient structures in a granular gas
,” Phys. Rev. Lett.
93
, 134301
(2004
).11.
T.
Scheffler
and D. E.
Wolf
, “Collision rates in charged granular gases
,” Granular Matter
4
, 103
–113
(2002
).12.
T.
Pöschel
, N. V.
Brilliantov
, and T.
Schwager
, “Long-time behavior of granular gases with impact-velocity dependent coefficient of restitution
,” Phys. A
325
, 274
–283
(2003
).13.
N. V.
Brilliantov
and T.
Pöschel
, Kinetic Theory of Granular Gases
(Oxford University Press
, New York
, 2004
).14.
I.
Goldhirsch
and T. P. C.
van Noije
, “Green-Kubo relations for granular fluids
,” Phys. Rev. E
61
, 3241
–3244
(2000
).15.
J. W.
Dufty
and J. J.
Brey
, “Green–Kubo expressions for a granular gas
,” J. Stat. Phys.
109
, 433
–448
(2002
).16.
J. J.
Brey
, J. W.
Dufty
, C. S.
Kim
, and A.
Santos
, “Hydrodynamics for granular flow at low density
,” Phys. Rev. E
58
, 4638
–4653
(1998
).17.
S. E.
Esipov
and T.
Pöschel
, “The granular phase diagram
,” J. Stat. Phys.
86
, 1385
–1395
(1997
).18.
A.
Goldshtein
and M.
Shapiro
, “Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations
,” J. Fluid Mech.
282
, 75
–114
(1995
).19.
N. V.
Brilliantov
and T.
Pöschel
, “Velocity distribution in granular gases of viscoelastic particles
,” Phys. Rev. E
61
, 5573
–5587
(2000
).20.
G. A.
Bird
, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(Oxford University Press
, New York
, 1994
).21.
F. J.
Alexander
and A. L.
Garcia
, “The direct simulation Monte Carlo method
,” 11
, 588
–593
(1997
).22.
A. J.
Garcia
, Numerical Methods for Physics
, 2nd ed. (Prentice Hall
, Englewood Cliffs, NJ
, 2000
).23.
24.
K.
Nanbu
, “Direct simulation scheme derived from the Boltzmann equation. I. Monocomponent gases
,” J. Phys. Soc. Jpn.
49
, 2042
–2049
(1980
).25.
K.
Nanbu
, “Interrelations between various direct simulation methods for solving the Boltzmann equation
,” J. Phys. Soc. Jpn.
52
, 3382
–3388
(1983
).© 2017 Author(s).
2017
Author(s)
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