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Transport coefficients for granular gases of electrically charged particles

Published online by Cambridge University Press:  03 February 2022

Satoshi Takada Open the ORCID record for Satoshi Takada [Opens in a new window] ,
Dan Serero  and
Thorsten Pöschel Open the ORCID record for Thorsten Pöschel [Opens in a new window]
Satoshi Takada*
Affiliation:
Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Naka-cho, Koganei, Tokyo 184-8588, Japan
Dan Serero
Affiliation:
Lehrstuhl für Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058 Erlangen, Germany
Thorsten Pöschel
Affiliation:
Lehrstuhl für Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058 Erlangen, Germany
*
†Email address for correspondence: takada@go.tuat.ac.jp
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Abstract

We consider a dilute gas of electrically charged granular particles in the homogeneous cooling state. We derive the energy dissipation rate and the transport coefficients from the inelastic Boltzmann equation. We find that the deviation of the velocity distribution function from the Maxwellian yields overshoots of the transport coefficients, and especially, the negative peak of the Dufour-like coefficient, $\mu$, in the intermediate granular temperature regime. We perform the linear stability analysis and investigate the granular temperature dependence of each mode, where the instability mode is found to change against the granular temperature. The molecular dynamics simulations are also performed to compare the result with that from the kinetic theory.

JFM classification

Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A38
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Brey, J.J., Buzón, V., Maynar, P. & García de Soria, M.I. 2015 Hydrodynamics for a model of a confined quasi-two-dimensional granular gas. Phys. Rev. E 91, 052201.CrossRefGoogle Scholar
Brey, J.J. & Cubero, D. 2001 Hydrodynamic transport coefficients of granular gases. In Granular Gases, Granular gases edn. (ed. T. Pöschel & S. Luding), Lecture Notes in Physics, vol. 564, pp. 59–78. Springer.CrossRefGoogle Scholar
Brey, J.J., Dufty, J.W., Kim, C.S. & Santos, A. 1998 Hydrodynamics for granular flow at low density. Phys. Rev. E 58, 4638–4653.CrossRefGoogle Scholar
Brey, J.J. & Ruiz-Montero, M. 2004 Simulation study of the Green–Kubo relations for dilute granular gases. Phys. Rev. E 70, 051301.CrossRefGoogle ScholarPubMed
Brey, J.J., Ruiz-Montero, M.J., Maynar, P. & García de Soria, M. 2005 Hydrodynamic modes, Green–Kubo relations, and velocity correlations in dilute granular gases. J. Phys.: Condens. Matter 17, S2489.Google Scholar
Brilliantov, N.B., Salueña, C., Pöschel, T. & Schwager, T. 2004 Clustering and vortex formation as a transient process in granular gases. Phys. Rev. Lett. 93, 134301.CrossRefGoogle Scholar
Brilliantov, N.V. & Pöschel, T. 2000 Deviation from Maxwell distribution in granular gases with constant restitution coefficient. Phys. Rev. E 61, 2809–2812.CrossRefGoogle Scholar
Brilliantov, N.V. & Pöschel, T. 2003 Hydrodynamics and transport coefficients for dilute granular gases. Phys. Rev. E 67, 061304.CrossRefGoogle ScholarPubMed
Brilliantov, N.V. & Pöschel, T. 2006 Breakdown of the Sonine expansion for the velocity distribution of granular gases. Europhys. Lett. 74, 424–430.CrossRefGoogle Scholar
Brilliantov, N.V., Spahn, F., Hertzsch, J.-M. & Pöschel, T. 1996 Model for collisions in granular gases. Phys. Rev. E 53, 5382.CrossRefGoogle ScholarPubMed
Brilliantov, N.V. & Pöschel, T. 2004 Kinetic Theory of Granular Gases. Oxford University Press.CrossRefGoogle Scholar
Chamorro, M.G., Reyes, F.V. & Garzó, V. 2013 Homogeneous steady states in a granular fluid driven by a stochastic bath with friction. J. Stat. Mech. P07013.CrossRefGoogle Scholar
Dufty, J.W. & Brey, J. 2002 Green–Kubo expressions for a granular gas. J. Stat. Phys. 109, 433–448.CrossRefGoogle Scholar
Esipov, S.E. & Pöschel, T. 1997 The granular phase diagram. J. Stat. Phys. 86, 1385.CrossRefGoogle Scholar
Garzó, V. 2005 Instabilities in a free granular fluid described by the Enskog equation. Phys. Rev. E 72, 021106.CrossRefGoogle Scholar
Garzó, V. 2019 Granular Gaseous Flows: A Kinetic Theory Approach to Granular Gaseous Flows. Springer.CrossRefGoogle Scholar
Garzó, V., Brito, R. & Soto, R. 2018 Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid. Phys. Rev. E 98, 052904.CrossRefGoogle Scholar
Genareau, K., Wardman, J.B., Wilson, T.M., McNutt, S.R. & Izbekov, P. 2015 Lightning-induced volcanic spherules. Geology 43, 319–322.CrossRefGoogle Scholar
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293.CrossRefGoogle Scholar
Goldhirsch, I., Noskowicz, S.H. & Bar-Lev, O. 2003 The homogeneous cooling state revisited. In Granular Gas Dynamics (ed. T. Pöschel & N. Brilliantov), Lecture Notes in Physics, vol. 624, pp. 37–63. Springer.CrossRefGoogle Scholar
Goldhirsch, I. & Zanetti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619.CrossRefGoogle ScholarPubMed
Goldshtein, A. & Shapiro, M. 1995 Mechanics of collisional motion of granular materials. Part 1: general hydrodynamic equations. J. Fluid Mech. 282, 75–114.CrossRefGoogle Scholar
González, R.G. & Garzó, V. 2019 Transport coefficients for granular suspensions at moderate densities. J. Stat. Mech. 2019, 093204.CrossRefGoogle Scholar
Gupta, V.K., Shukla, P. & Torrilhon, M. 2020 Higher-order moment theories for dilute granular gases of smooth hard spheres. J. Fluid Mech. 836, 451–501.CrossRefGoogle Scholar
Haff, P.K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401–430.CrossRefGoogle Scholar
Jungmann, F., Steinpilz, T., Teiser, J. & Wurm, G. 2018 Sticking and restitution in collisions of charged sub-mm dielectric grains. J. Phys. Commun. 2, 095009.CrossRefGoogle Scholar
Kanazawa, S., Ohkubo, T., Nomoto, Y. & Adachi, T. 1995 Electrification of a pipe wall during powder transport. J. Electrostat. 35, 47–54.CrossRefGoogle Scholar
Kolehmainen, J., Ozel, A., Boyce, C.M. & Sundaresan, S. 2016 A hybrid approach to computing electrostatic forces in fluidized beds of charged particles. AIChE J. 62, 2282–2295.CrossRefGoogle Scholar
Kumar, D., Sane, A., Gohil, S., Bandaru, P.R., Bhattacharya, S. & Ghosh, S. 2014 Spreading of triboelectrically charged granular matter. Sci. Rep. 4, 5275.CrossRefGoogle ScholarPubMed
Lacks, D.J. & Shinbrot, T. 2019 Long-standing and unresolved issues in triboelectric charging. Nat. Rev. Chem. 3, 465–476.CrossRefGoogle Scholar
Laurentie, J.C., Traoré, P. & Dascalescu, L. 2013 Discrete element modeling of triboelectric charging of insulating materials in vibrated granular beds. J. Electrostat. 71, 951–957.CrossRefGoogle Scholar
Lee, V., Waitukaitis, S.R., Miskin, M.Z. & Jaeger, H.M. 2015 Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 11, 733–737.CrossRefGoogle Scholar
Muranushi, T. 2010 Dust-dust collisional charging and lightning in protoplanetary discs. Mon. Not. R. Astron. Soc. 401, 2641–2664.CrossRefGoogle Scholar
van Noije, T.P.C. & Ernst, M.H. 1998 Velocity distributions in homogeneous granular fluids: the free and the heated case. Granul. Matt. 1, 57–64.CrossRefGoogle Scholar
Pan, S. & Zhang, Z. 2019 Fundamental theories and basic principles of triboelectric effect: a review. Friction 7, 2–17.CrossRefGoogle Scholar
Pöschel, T. & Brilliantov, N.V. (ed.) 2003 Granular Gas Dynamics, Lecture Notes in Physics, vol. 624. Springer.CrossRefGoogle Scholar
Pöschel, T., Brilliantov, N.V. & Schwager, T. 2003 Long-time behavior of granular gases with impact-velocity dependent coefficient of restitution. Physica A 325, 274–283.CrossRefGoogle Scholar
Puglisi, A. 2015 Transport and Fluctuations in Granular Fluids, Springer Briefs in Physics, vol. 34. Springer.Google Scholar
Santos, A., Garzó, V. & Dufty, J.W. 2004 Inherent rheology of a granular fluid in uniform shear flow. Phys. Rev. E 69, 061303.CrossRefGoogle ScholarPubMed
Santos, A. & Montanero, J.M. 2009 The second and third Sonine coefficients of a freely cooling granular gas revisited. Granul. Matt. 11, 157–168.CrossRefGoogle Scholar
Scheffler, T. & Wolf, D.E. 2002 Collision rates in charged granular gases. Granul. Matt. 4, 103–113.CrossRefGoogle Scholar
Schwager, T. & Pöschel, T. 2008 Coefficient of restitution for viscoelastic spheres: the effect of delayed recovery. Phys. Rev. E 78, 051304.CrossRefGoogle ScholarPubMed
Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41–74.CrossRefGoogle Scholar
Serero, D. 2009 Kinetic theory of granular gas mixture. PhD thesis, Tel Aviv University.Google Scholar
Serero, D., Noskowicz, S.H., Tan, M.L. & Goldhirsch, I. 2009 Binary granular gas mixtures: theory, layering effects and some open questions. Eur. Phys. J.: Spec. Top. 179, 221–247.Google Scholar
Shukla, P., Biswas, L. & Gupta, V.K. 2019 Shear-banding instability in arbitrarily inelastic granular shear flows. Phys. Rev. E 100, 032903.CrossRefGoogle ScholarPubMed
Singh, C. & Mazza, M.G. 2018 Early-stage aggregation in three-dimensional charged granular gas. Phys. Rev. E 97, 022904.CrossRefGoogle ScholarPubMed
Singh, C. & Mazza, M.G. 2019 Electrification in granular gases leads to constrained fractal growth. Sci. Rep. 9, 9049.CrossRefGoogle ScholarPubMed
Takada, S. & Hayakawa, H. 2018 Rheology of dilute cohesive granular gases. Phys. Rev. E 97, 042902.CrossRefGoogle ScholarPubMed
Takada, S., Saitoh, K. & Hayakawa, H. 2016 Kinetic theory for dilute cohesive granular gases with a square well potential. Phys. Rev. E 94, 012906.CrossRefGoogle ScholarPubMed
Takada, S., Serero, D. & Pöschel, T. 2017 Homogeneous cooling state of dilute granular gases of charged particles. Phys. Fluids 29, 083303.CrossRefGoogle Scholar
Watanabe, H., Ghadiri, M., Matsuyama, T., Ding, Y.L., Pitt, K.G., Maruyama, H., Matsusaka, S. & Masuda, H. 2007 Triboelectrification of pharmaceutical powders by particle impact. Intl J. Pharm. 334, 149–155.CrossRefGoogle ScholarPubMed
Yoshimatsu, R., Araújo, N.A.M., Wurm, G., Herrmann, H.J. & Shinbrot, T. 2017 Self-charging of identical grains in the absence of an external field. Sci. Rep. 7, 39996.CrossRefGoogle ScholarPubMed