Granular Matter

, Volume 16, Issue 3, pp 281–297 | Cite as

Rolling, sliding and torsion of micron-sized silica particles: experimental, numerical and theoretical analysis

  • Regina Fuchs
  • Thomas Weinhart
  • Jan Meyer
  • Hao Zhuang
  • Thorsten Staedler
  • Xin Jiang
  • Stefan Luding
Original Paper


The contact mechanics of individual, very small particles with other particles and walls is studied using a nanoindenter setup that allows normal and lateral displacement control and measurement of the respective forces. The sliding, rolling and torsional forces and torques are tested with borosilicate microspheres, featuring radii of about \(10\,\upmu \hbox {m}\). The contacts are with flat silicon substrates of different roughness for pure sliding and rolling and with silicon based, ion-beam crafted rail systems for combined rolling and torsion. The experimental results are discussed and compared to various analytical predictions and contact models, allowing for two concurrent interpretations of the effects of surface roughness, plasticity and adhesion. This enables us to determine both rolling and torsion friction coefficients together with their associated length scales. Interestingly, even though normal contacts behave elastically (Hertzian), all other modes of motion display effects due to surface roughness and consequent plastic deformation. The influence of adhesion is interpreted in the framework of different models and is very different for different degrees of freedom, being largest for rolling.


Nanoindentation Friction Contact mechanics Granular solids Tribology Adhesion 



The authors would like to thank Lothar Brendel for many helpful discussions. We also thank the German Research Foundation (DFG) for financial support. This work is carried out within the framework of the Key Research Program (SPP 1486 PiKo “Particles in Contact”) Grants LU 450/10-1, LU 450/10-2, STA 1021/1-1 and STA 1021/1-2. The numerical solutions of the contact models in this paper were carried out using the open-source code MercuryDPM (


  1. 1.
    Ducker, W.A., Senden, T.J., Pashley, R.M.: Direct measurement of colloidal forces using an atomic force microscope. Nature 353(6341), 239–241 (1991)ADSCrossRefGoogle Scholar
  2. 2.
    Butt, H.J.: Measuring electrostatic, van der Waals, and hydration forces in electrolyte-solutions with an atomic force microscope. Biophys. J. 60(6), 1438–1444 (1991)ADSCrossRefGoogle Scholar
  3. 3.
    Sitti, M., Hashimoto, H.: Controlled pushing of nanoparticles: modeling and experiments. IEEE-ASME Trans. Mechatron. 5(2), 199–211 (2000)CrossRefGoogle Scholar
  4. 4.
    Sitti, M.: Atomic force microscope probe based controlled pushing for nanotribological characterization. IEEE-ASME Trans. Mechatron. 9(2), 343–349 (2004)CrossRefGoogle Scholar
  5. 5.
    Sumer, B., Sitti, M.: Rolling and spinning friction characterization of fine particles using lateral force microscopy based contact pushing. J. Adhes. Sci. Technol. 22(5–6), 481–506 (2008)CrossRefGoogle Scholar
  6. 6.
    Liu, D.L., Martin, J., Burnham, N.A.: Optimal roughness for minimal adhesion. Appl. Phys. Lett. 91(4), 043107 (2007)Google Scholar
  7. 7.
    Rabinovich, Y.I., Adler, J.J., Ata, A., Singh, R.K., Moudgil, B.M.: Adhesion between nanoscale rough surfaces—i. Role of asperity geometry. J. Colloid Interface Sci. 232(1), 10–16 (2000)CrossRefGoogle Scholar
  8. 8.
    Rabinovich, Y.I., Adler, J.J., Ata, A., Singh, R.K., Moudgil, B.M.: Adhesion between nanoscale rough surfaces—ii. Measurement and comparison with theory. J. Colloid Interface Sci. 232(1), 17–24 (2000)CrossRefGoogle Scholar
  9. 9.
    Matope, S., Rabinovich, Y.I., Van der Merwe, A.F.: Van der Waals interactions between silica spheres and metallic thin films created by e-beam evaporation. Colloids Surf. Physicochem. Eng. Aspects 411, 87–93 (2012)CrossRefGoogle Scholar
  10. 10.
    Korayem, M.H., Zakeri, M.: Dynamic modeling of manipulation of micro/nanoparticles on rough surfaces. Appl. Surf. Sci. 257(15), 6503–6513 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Saito, S., Miyazaki, H.T., Sato, T., Takahashi, K.: Kinematics of mechanical and adhesional micromanipulation under a scanning electron microscope. J. Appl. Phys. 92(9), 5140–5149 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    Murthy Peri, M.D., Cetinkaya, C.: Adhesion characterization based on rolling resistance of individual microspheres on substrates: review of recent experimental progress. J. Adhes. Sci. Technol. 22(5–6), 507–528 (2008)CrossRefGoogle Scholar
  13. 13.
    Ding, W., Howard, A.J., Murthy Peri, M.D., Cetinkaya, C.: Rolling resistance moment of microspheres on surfaces: contact measurements. Philos. Mag. 87(36), 5685–5696 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    Vilt, S.G., Martin, N., McCabe, C., Kane Jennings, G.: Frictional performance of silica microspheres. Tribol. Int. 44(2), 180–186 (2011)CrossRefGoogle Scholar
  15. 15.
    Hertz, H.: Über die Berührung fester elastischer Körper. J. für die reine u. angew. Math. 92, 156 (1882)Google Scholar
  16. 16.
    Luding, S.: Cohesive, frictional powders: contact models for tension. Granul. Matter 10(4), 235–246 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Tomas, J.: Adhesion of ultrafine particles: energy absorption at contact. Chem. Eng. Sci. 62(21), 5925–5939 (2007)CrossRefGoogle Scholar
  18. 18.
    Singh, A., Magnanimo, V., Luding, S.: Mesoscale contact models for sticky particles. Powder Technol. 2013 (submitted)Google Scholar
  19. 19.
    Sun, W., Zeng, Q., Yu, A.: Calculation of noncontact forces between silica nanospheres. Langmuir 29(7), 2175–2184 (2013)CrossRefGoogle Scholar
  20. 20.
    Shojaaee, Z., Brendel, L., Török, J., Wolf, D.E.: Shear flow of dense granular materials near smooth walls. ii. Block formation and suppression of slip by rolling friction. Phys. Rev. E 86, 011302 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    Wang, X., Zhu, H.P., Luding, S., Yu, A.B.: Regime transitions of granular flow in a shear cell: a micromechanical study. Phys. Rev. E 88, 032203 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    Morita, M., Ohmi, T., Hasegawa, E., Kawakami, M., Suma, K.: Control factor of native oxide growth on silicon in air or in ultrapure water. Appl. Phys. Lett. 55(6), 562–564 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    van Zwol, P.J., Palasantzas, G., van de Schootbrugge, M., de Hosson, J.T.M., Craig, V.S.J.: Roughness of microspheres for force measurements. Langmuir 24(14), 7528–7531 (2008)CrossRefGoogle Scholar
  24. 24.
    Fuchs, R., Meyer, J., Staedler, T., Jiang, X.: Sliding and rolling of individual micrometre sized glass particles on rough silicon surfaces. Tribol. Mater. Surf. Interfaces 7(2), 103–107 (2013)CrossRefGoogle Scholar
  25. 25.
    Butt, H.-J., Jaschke, M.: Calculation of thermal noise in atomic force microscopy. Nanotechnology 6(1), 1 (1995)ADSCrossRefGoogle Scholar
  26. 26.
    Kuhn, M.R., Bagi, K.: Contact rolling and deformation in granular media. Int. J. Solids Struct. 41(21), 5793–5820 (2004) Google Scholar
  27. 27.
    Tykhoniuk, R., Tomas, J., Luding, S., Kappl, M., Heim, L., Butt, H.-J.: Ultrafine cohesive powders: from interparticle contacts to continuum behaviour. Chem. Eng. Sci. 62(11), 2843–2864 (2007)CrossRefGoogle Scholar
  28. 28.
    Brilliantov, N.V., Pöschel, T.: Rolling friction of a viscous sphere on a hard plane. EPL (Europhys. Lett.) 42(5), 511 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    Luding, S.: Collisions & contacts between two particles. NATO ASI Series E Appl. Sci. Adv. Study Inst. 350, 285–304 (1998)Google Scholar
  30. 30.
    Kuwabara, G., Kono, K.: Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 1 26(8), 1230–1233 (1987)Google Scholar
  31. 31.
    Thornton, C., Cummins, S.J., Cleary, P.W.: An investigation of the comparative behaviour of alternative contact force models during inelastic collisions. Powder Technol. 233, 30–46 (2013)CrossRefGoogle Scholar
  32. 32.
    Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259 (1949)Google Scholar
  33. 33.
    Mindlin, R.D., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327 (1953)Google Scholar
  34. 34.
    Brendel, L., Török, J., Kirsch, R., Bröckel, U.: A contact model for the yielding of caked granular materials. Granul. Matter 13(6), 777–786 (2011)CrossRefGoogle Scholar
  35. 35.
    Yang, R.Y., Zou, R.P., Yu, A.B.: Computer simulation of the packing of fine particles. Phys. Rev. E 62(3), 3900 (2000)ADSCrossRefGoogle Scholar
  36. 36.
    Beer, F.P., Russell Johnston, J.E., Johnston Jr, E.R., Eisenberg, E.R., Clausen, W.E., Staab, G.H.: Vector Mechanics for Engineers: Statics and Dynamics. McGraw-Hill, New York (2003)Google Scholar
  37. 37.
    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1984)Google Scholar
  38. 38.
    Deresiewicz, H.: Contact of elastic spheres under an oscillating torsional couple. J. Appl. Mech. 21, 52–56 (1954)zbMATHGoogle Scholar
  39. 39.
    Dintwa, E., van Zeebroeck, M., Tijskens, E., Ramon, H.: Torsion of viscoelastic spheres in contact. Granul. Matter 7(2), 169–179 (2005)CrossRefzbMATHGoogle Scholar
  40. 40.
    Farkas, Z., Bartels, G., Unger, T., Wolf, D.E.: Frictional coupling between sliding and spinning motion. Phys. Rev. Lett. 90(24), 248302 (2003)Google Scholar
  41. 41.
    Tabor, D.: Indentation hardness: fifty years on a personal view. Philos. Mag. Phys. Condens. Matter Struct. Defects Mech. Prop. 74(5), 1207–1212 (1996)Google Scholar
  42. 42.
    Bhushan, B.: Contact mechanics of rough surfaces in tribology: multiple asperity contact. Tribol. Lett. 4(1), 1–35 (1998)CrossRefGoogle Scholar
  43. 43.
    Brendel, L.: Private CommunicationGoogle Scholar
  44. 44.
    Briggs, G.A.D., Briscoe, B.J.: Effect of surface-roughness on rolling friction and adhesion between elastic solids. Nature 260(5549), 313–315 (1976)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Regina Fuchs
    • 1
  • Thomas Weinhart
    • 2
  • Jan Meyer
    • 1
  • Hao Zhuang
    • 1
  • Thorsten Staedler
    • 1
  • Xin Jiang
    • 1
  • Stefan Luding
    • 2
  1. 1.Institute of Materials EngineeringUniversity of SiegenSiegenGermany
  2. 2.Multiscale Mechanics, CTW, MESA+University of TwenteEnschedeThe Netherlands

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