Electrical conduction and Joule effect in one-dimensional chains of ...

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P. Béquin, V. Tournatroughly equal or larger than the length of the chain of beads:5 × 11 mm) shows that the current induced by the spark isproportional to 1/r 2.1 (obtained through a linear regressionon log[I sp ]). These results are consistent with those obtainedin [21] whereaninducedcurrentproportionalto1/r m withm ≃ 1.2 fordistancesr varying between 0.1 and 2.2 mis observed. Note that the spatial dependence of monochromaticelectromagnetic wave amplitude is respectively proportionalto 1/r 2 in the near field and proportional to 1/r inthe far field.At this level, the lack of information on the electromagneticfield (amplitude, frequency spectrum and directivity)does not allow the development of a realistic model to becompared to experimental results. These particular electromagneticbehaviors as a function of distance (near field/farfield) will have to be taken into account in the models andexperiments dedicated to the electromechanical behavior ofagranularmediumwithlargedimensions.6ConclusionContinued interest in granular materials has stimulated newexperiments and models to characterize these complex structures.In this article the electrical and thermal behaviors of achain of beads carrying a dc and an impulse electric currenthave been investigated. This work provides theoretical andexperimental continuations to the studies of Refs. [13,14,21]mostly carried out in the context of the Branly effect.The passage of an electric current in a chain of beadsaffects the nature of the contact between beads by causingaheatingandasofteningofthemetalneartheinterface.These changes are consequent to the heat which is generatedin the constricted region of the current flow and lead to anincrease in the contact surface. We developed specifically anexperimental setup suited to the measurement of the electriccurrent and voltage for a chain of metallic beads. The analysisof the voltage–current characteristics of such a chainindicates that the diameter of the contact surface varies linearlywith electric current I .Subjectedtoacycliccurrent,the chain of beads presents an electromechanical behaviorof hysteretic type. The larger are the electric current and thenumber of beads the larger is the hysteretic effect (the loop)and the greater is the heat released in the chain.Steady states models derived on the assumption of equilibriumbetween Joule heating in the contact area andthermal dissipation by conduction within the material areproposed. The simplified models of Eq. 8 and the modeldeveloped in [13,14], all based on the Wiedemann–Franz’slaw (W–F) (which states that the product of the thermal conductivityand the electrical resistivity of a metal is proportionalto the temperature), are observed to be inadequate todescribe electromechanical conduction in chains of beadswith cyclic currents under a weak static compression force∼1N.AnextendedmodelEq.6 is then developed without therestrictions of the W–F’s law. The comparisons with experimentaldata provide the variations of parameters α and βcorresponding respectively to the linear evolution of the electricalresistivity and to the thermal conductivity (Eq. 5). Theseresults could benefit in the future from temperature measurementson the beads and from the use of various materials andbead diameters.The effect of an electromagnetic pulse producing a pulseof electric current through a chain of beads is finally studied.The electromagnetic wave pulse is created by an electric discharge(electric spark) placed near the chain of beads. Theexperimental results show that the current can cause appreciablechanges in the contact surface when the magnitude ofthe induced current is sufficient but also when the dccurrent remain weak. Evolution of the induced current withthe chain/spark distance in near field (100 mm) in Ref.[21] wherethe1/r dependence is observed.The control of the contact surface between beads usingasuitableelectromagneticwavecouldfindapplicationsinparticular in the study of the fundamental processes involvedin the acoustic propagation through granular media [29–32].Acknowledgments We would like to thank James Blondeau, StéphaneLebon and Eric Egon for their assistance in the experiments andtheir technical advice. We particularly thank Jean-Marie Genet for hisexperimental work.References1. Duran, J.: Sands, Powders and Grains. Springer-Verlag, NewYork (1999)2. Kakalios, J.: Granular physics or nonlinear dynamics in a sandbox.Am. J. Phys. 73(1), 8–22 (2005)3. Nesterenko, V.F.: Dynamics of Heterogeneous Materials. Springer-Verlag, New York (2001)4. 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Electrical conduction in chains of beads11. Greenwood, J.A., Harris, J.: Electrical conduction in solids.Part III: the contact of iron surfaces. Proc. R. Soc. Lond. Ser.A 257(1288), 83–97 (1960)12. Timsit, R.S. : Ch.1 electrical contact resistance: fundamental principles.In: Slade, P.G. Electrical Contacts—Principles and Applications,CRC Press, New York (1999)13. Falcon, E., Castaing, B., Creyssels, M.: Nonlinear electrical conductivityin a 1D granular medium. Eur. Phys. J. B 38, 475–483 (2004)14. Falcon, E., Castaing, B.: Electrical conductivity in granularmedia and Branly’s coherer: a simple experiment. Am. J.Phys. 73(4), 302–307 (2005)15. Géminard, J.-C., Bouraya, D., Gayvallet, H.: Thermal conductivityassociated with a bead-bead contact decorated by a liquidbridge. Eur. Phys. J. B 48, 509–517(2005)16. Creyssels, M., Dorbolo, S., Merlen, A., Laroche, C., Castaing, B.,Falcon, E.: Some aspects of electrical conduction in granular systemsof various dimensions. Eur. Phys. J. E 23, 255–264(2007)17. Raizer, Y.P.: Gas Discharge Physics. Springer-Verlag,Berlin (1991)18. Dorbolo, S., Ausloos, M., Vandewalle, N.: Hysteretic behavior inmetallic granular matter. Appl. Phys. Lett. 81(5), 936–938 (2002)19. Dorbolo, S., Ausloos, M., Vandewalle, N., Houssa, M.: Aging processof electrical contacts in granular matter. Appl. Phys. Lett. 94,1040302(R) (2003)20. Dorbolo, S., Ausloos, M., Vandewalle, N.: Reexamination of theBranly effect. Phys. Rev. E 67(12), 7835–7838 (2003)21. Dorbolo, S., Merlen, A., Creyssels, M., Vandewalle, N., Castaing,B., Falcon, E.: Effects of electromagnetic waves on the electricalproperties of contacts between grains. EPL 79(54001), 7835–7838 (2007)22. Davis, J.R. (ed.): ASM Specialty Handbook: Stainless Steels. ASMInternational, New York (1994)23. Omel’chenko, V.T.: Determination of the excess temperatureof electrical contacts with continous current variation. J. Eng.Phys. 10(1), 45–47 (1966)24. Fournet, G.: Phenomena in conductors having temperature dependentelectrical and thermal conductivities. J. Phys. III 7, 2003–2029 (1997)25. European Stainless Steel Development Association.: StainlessSteel: Tables of Technical Properties. http://www.euro-inox.org(2000)26. Gale, W.F., Totemeir, T.C. (eds.): Smithells Metals ReferenceBook, 8th edn. ASM International, London (2004)27. Tan, X., Conway, P.P., Sarvar, F.: Thermo-mechanical propertiesand regression models of alloys: AISI 305, CK 60, CuBe 2 andlaiton MS 63. J. Mater. Process. Technol. 168, 152–163(2005)28. Ayrault, C., Béquin, P., Legros, M.: Experimental study of a sparkdischarge as an acoustic source. In: Proceedings of 19th InternationalCongress on Acoustics. I.C.A., Madrid, Spain (2007)29. Job, S., Melo, F., Sokolow, A., Sen, S.: How hertzian solitarywaves interact with boundaries in a 1d granular medium. Phys.Rev. Lett. 94, 178002(2005)30. Daraio, C., Nesterenko, V.F., Herbold, E.B., Jin, S.: Stronglynonlinear waves in a chain of teflon beads. Phys. Rev.E 72, 016603(2005)31. Hladky-Hennion, A.-C., de Billy, M.: Experimental validation ofband gaps and localization in a one-dimensional diatomic phononiccrystal. J. Acoust. Soc. Am. 122, 2594–2600(2007)32. Porter, M.A., Daraio, C., Herbold, E.B., Szelengowicz, I., Kevrekidis,P.G.: Highly nonlinear solitary waves in phononic crystaldimers. Phys. Rev. E 77, 015601(R)(2008)123
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