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Elastohydrodynamic friction of robotic and human fingers on soft micropatterned substrates


Frictional sliding between patterned surfaces is of fundamental and practical importance in the haptic engineering of soft materials. In emerging applications such as remote surgery and soft robotics, thin fluid films between solid surfaces lead to a multiphysics coupling between solid deformation and fluid dissipation. Here, we report a scaling law that governs the peak friction values of elastohydrodynamic lubrication on patterned surfaces. These peaks, absent in smooth tribopairs, arise due to a separation of length scales in the lubricant flow. The framework is generated by varying the geometry, elasticity and fluid properties of soft tribopairs and measuring the lubricated friction with a triborheometer. The model correctly predicts the elastohydrodynamic lubrication friction of a bioinspired robotic fingertip and human fingers. Its broad applicability can inform the future design of robotic hands or grippers in realistic conditions, and open up new ways of encoding friction into haptic signals.

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Fig. 1: Experimental set-ups and Stribeck curves for flat and patterned soft materials.
Fig. 2: EHL lubrication film thickness on patterned surfaces.
Fig. 3: Modelling the critical EHL transitions for patterned geometries.
Fig. 4: Material- and geometry-based framework for the transition EHL friction coefficient.

Data availability

Source data are provided with this paper. All other data that support the results in this study are available from the corresponding author on reasonable request.

Code availability

The MATLAB codes for solving Supplementary equation (S10) are available at


  1. Wong, T. S. et al. Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity. Nature 477, 443–447 (2011).

    CAS  Google Scholar 

  2. Bau, O., Poupyrev, I., Israr, A. & Harrison, C. TeslaTouch: electrovibration for touch surfaces. In: Proc. 23rd Annual ACM Symposium on User Interface Software and Technology 283–292 (Association for Computing Machinery, 2010).

  3. Levesque, V. et al. Enhancing physicality in touch interaction with programmable friction. In: Proc. SIGCHI Conference on Human Factors in Computing Systems 2481–2490 (Association for Computing Machinery, 2011).

  4. Basdogan, C., Giraud, F., Levesque, V. & Choi, S. A review of surface haptics: enabling tactile effects on touch surfaces. IEEE Trans. Haptics 13, 450–470 (2020).

  5. Adams, M. J. et al. Finger pad friction and its role in grip and touch. J. R. Soc. Interface 10, 20120467 (2013).

    Google Scholar 

  6. Saintyves, B., Jules, T., Salez, T. & Mahadevan, L. Self-sustained lift and low friction via soft lubrication. Proc. Natl Acad. Sci. USA 113, 5847–5849 (2016).

    CAS  Google Scholar 

  7. Wang, Y. M., Dhong, C. & Frechette, J. Out-of-contact elastohydrodynamic deformation due to lubrication forces. Phys. Rev. Lett. 115, 248302 (2015).

    Google Scholar 

  8. Dzidek, B., Bochereau, S., Johnson, S. A., Hayward, V. & Adams, M. J. Why pens have rubbery grips. Proc. Natl Acad. Sci. USA 114, 10864–10869 (2017).

    CAS  Google Scholar 

  9. Delmas, P., Hao, J. & Rodat-Despoix, L. Molecular mechanisms of mechanotransduction in mammalian sensory neurons. Nat. Rev. Neurosci. 12, 139–153 (2011).

    CAS  Google Scholar 

  10. Smith, A. M., Chapman, C. E., Deslandes, M., Langlais, J.-S. & Thibodeau, M.-P. Role of friction and tangential force variation in the subjective scaling of tactile roughness. Exp. Brain Res. 144, 211–223 (2002).

    Google Scholar 

  11. Robles-De-La-Torre, G. & Hayward, V. Force can overcome object geometry in the perception of shape through active touch. Nature 412, 445–448 (2001).

    CAS  Google Scholar 

  12. Janko, M., Wiertlewski, M. & Visell, Y. Contact geometry and mechanics predict friction forces during tactile surface exploration. Sci. Rep. 8, 4868 (2018).

    Google Scholar 

  13. Ayyildiz, M., Scaraggi, M., Sirin, O., Basdogan, C. & Persson, B. N. J. Contact mechanics between the human finger and a touchscreen under electroadhesion. Proc. Natl Acad. Sci. USA 115, 12668–12673 (2018).

    CAS  Google Scholar 

  14. Gueorguiev, D., Bochereau, S., Mouraux, A., Hayward, V. & Thonnard, J.-L. Touch uses frictional cues to discriminate flat materials. Sci. Rep. 6, 25553 (2016).

    CAS  Google Scholar 

  15. Weber, A. I. et al. Spatial and temporal codes mediate the tactile perception of natural textures. Proc. Natl Acad. Sci. USA 110, 17107–17112 (2013).

    CAS  Google Scholar 

  16. Flanagan, J. R., Burstedt, M. K. & Johansson, R. S. Control of fingertip forces in multidigit manipulation. J. Neurophysiol. 81, 1706–1717 (1999).

    CAS  Google Scholar 

  17. Abraira, V. E. & Ginty, D. D. The sensory neurons of touch. Neuron 79, 618–639 (2013).

    CAS  Google Scholar 

  18. Kandaswamy, D., Murthy, M., Alexander, M. & Krothapalli, S. B. Handling objects with very wet skin reduce variability during precision grip task. Neurosci. Lett. 703, 177–183 (2019).

    CAS  Google Scholar 

  19. Stuart, H., Wang, S., Khatib, O. & Cutkosky, M. R. The Ocean One hands: an adaptive design for robust marine manipulation. Int. J. Rob. Res. 36, 150–166 (2017).

    Google Scholar 

  20. Jones, L. Haptics (MIT Press, 2018).

  21. Khojasteh, B., Janko, M. & Visell, Y. Complexity, rate, and scale in sliding friction dynamics between a finger and textured surface. Sci. Rep. 8, 13710 (2018).

    Google Scholar 

  22. Greene, G. W. et al. Adaptive mechanically controlled lubrication mechanism found in articular joints. Proc. Natl Acad. Sci. USA 108, 5255–5259 (2011).

    CAS  Google Scholar 

  23. Urueña, J. M. et al. Normal load scaling of friction in gemini hydrogels. Biotribology 13, 30–35 (2018).

    Google Scholar 

  24. Moyle, N. et al. Enhancement of elastohydrodynamic friction by elastic hysteresis in a periodic structure. Soft Matter 16, 1627–1635 (2020).

    CAS  Google Scholar 

  25. Peng, Y., Serfass, C. M., Hill, C. N. & Hsiao, L. C. Bending of soft micropatterns in elastohydrodynamic lubrication tribology. Exp. Mech. (2021).

  26. Varenberg, M. & Gorb, S. N. Hexagonal surface micropattern for dry and wet friction. Adv. Mater. 21, 483–486 (2009).

    CAS  Google Scholar 

  27. Grubin, A. Investigation of the Contact Machine Components Ch. 2 (Central Scientific Research Institute for Technology and Mechanical Engineering, 1949).

  28. Greenwood, J. An extension of the Grubin theory of elastohydrodynamic lubrication. J. Phys. D 5, 2195 (1972).

    Google Scholar 

  29. Hamrock, B. J. & Dowson, D. Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus I—fully flooded conjunction. J. Lubr. Technol. 100, 236–245 (1978).

    Google Scholar 

  30. Gropper, D., Wang, L. & Harvey, T. J. Hydrodynamic lubrication of textured surfaces: a review of modeling techniques and key findings. Tribol. Int. 94, 509–529 (2016).

    Google Scholar 

  31. Schilling, J., Sengupta, K., Goennenwein, S., Bausch, A. R. & Sackmann, E. Absolute interfacial distance measurements by dual-wavelength reflection interference contrast microscopy. Phys. Rev. E 69, 021901 (2004).

    Google Scholar 

  32. Davies, H. S. et al. Elastohydrodynamic lift at a soft wall. Phys. Rev. Lett. 120, 2–7 (2018).

    Google Scholar 

  33. Luo, J., Wen, S. & Huang, P. Thin film lubrication. Part I. Study on the transition between EHL and thin film lubrication using a relative optical interference intensity technique. Wear 194, 107–115 (1996).

    CAS  Google Scholar 

  34. Born, M. & Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Elsevier, 2013).

    Google Scholar 

  35. Fowell, M., Myant, C., Spikes, H. & Kadiric, A. A study of lubricant film thickness in compliant contacts of elastomeric seal materials using a laser induced fluorescence technique. Tribol. Int. 80, 76–89 (2014).

    CAS  Google Scholar 

  36. Myant, C., Reddyhoff, T. & Spikes, H. Laser-induced fluorescence for film thickness mapping in pure sliding lubricated, compliant, contacts. Tribol. Int. 43, 1960–1969 (2010).

    CAS  Google Scholar 

  37. Lugt, P. M. & Morales-Espejel, G. E. A review of elasto-hydrodynamic lubrication theory. Tribol. Trans. 54, 470–496 (2011).

    Google Scholar 

  38. Scaraggi, M. Lubrication of textured surfaces: a general theory for flow and shear stress factors. Phys. Rev. E 86, 026314 (2012).

    Google Scholar 

  39. Banquy, X., Burdyńska, J., Lee, D. W., Matyjaszewski, K. & Israelachvili, J. Bioinspired bottle-brush polymer exhibits low friction and Amontons-like behavior. J. Am. Chem. Soc. 136, 6199–6202 (2014).

    CAS  Google Scholar 

  40. Davies, G. A. & Stokes, J. R. On the gap error in parallel plate rheometry that arises from the presence of air when zeroing the gap. J. Rheol. 49, 919–922 (2005).

    CAS  Google Scholar 

  41. Scaraggi, M., Carbone, G. & Dini, D. Experimental evidence of micro-EHL lubrication in rough soft contacts. Tribol. Lett. 43, 169–174 (2011).

    CAS  Google Scholar 

  42. Bonnevie, E. D. et al. Sub-critical impact inhibits the lubricating mechanisms of articular cartilage. J. Biomech. 53, 64–70 (2017).

    Google Scholar 

  43. Deen, W. M. Analysis of Transport Phenomena 2nd edn (Oxford Univ. Press, 2011).

  44. Stachowiak, G. & Batchelor, A. W. Engineering Tribology (Butterworth-Heinemann, 2013).

  45. Taylor, J. Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (University Science Books, 1996).

  46. Kalra, A., Lowe, A. & Al-Jumaily, A. Mechanical behaviour of skin: a review. J. Mater. Sci. Eng. 5, 1000254 (2016).

    Google Scholar 

  47. Bongaerts, J. H. H., Fourtouni, K. & Stokes, J. R. Soft-tribology: lubrication in a compliant PDMS–PDMS contact. Tribol. Int. 40, 1531–1542 (2007).

    CAS  Google Scholar 

  48. Seror, J., Zhu, L. Y., Goldberg, R., Day, A. J. & Klein, J. Supramolecular synergy in the boundary lubrication of synovial joints. Nat. Commun. 6, 6497 (2015).

    CAS  Google Scholar 

  49. Hsiao, L. C. & Pradeep, S. Experimental synthesis and characterization of rough particles for colloidal and granular rheology. Curr. Opin. Colloid Interface Sci. 43, 94–112 (2019).

    CAS  Google Scholar 

  50. Pradal, C. & Stokes, J. R. Oral tribology: bridging the gap between physical measurements and sensory experience. Curr. Opin. Food Sci. 9, 34–41 (2016).

    Google Scholar 

  51. Jerolmack, D. J. & Daniels, K. E. Viewing Earth’s surface as a soft-matter landscape. Nat. Rev. Phys. 1, 716–730 (2019).

    Google Scholar 

  52. Johnston, I. D., McCluskey, D. K., Tan, C. K. L. & Tracey, M. C. Mechanical characterization of bulk Sylgard 184 for microfluidics and microengineering. J. Micromech. Microeng. 24, 035017 (2014).

    CAS  Google Scholar 

  53. Xia, Y. N. et al. Replica molding using polymeric materials: a practical step toward nanomanufacturing. Adv. Mater. 9, 147–149 (1997).

    CAS  Google Scholar 

  54. Xia, Y. N. et al. Complex optical surfaces formed by replica molding against elastomeric masters. Science 273, 347–349 (1996).

    CAS  Google Scholar 

  55. Fiorini, G. S., Jeffries, G. D. M., Lim, D. S. W., Kuyper, C. L. & Chiu, D. T. Fabrication of thermoset polyester microfluidic devices and embossing masters using rapid prototyped polydimethylsiloxane molds. Lab Chip 3, 158–163 (2003).

    CAS  Google Scholar 

  56. Wang, L. & Dandy, D. S. High-throughput inertial focusing of micrometer- and sub-micrometer-sized particles separation. Adv. Sci. 4, 1700153 (2017).

    Google Scholar 

  57. Pinto-Iguanero, B., Olivares-Pérez, A. & Fuentes-Tapia, I. Holographic material film composed by Norland Noa 65® adhesive. Opt. Mater. 20, 225–232 (2002).

    CAS  Google Scholar 

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The authors thank R. Ewoldt, J. F. Brady, R. G. Larson, J. Frechette and A. Dunn for discussions. Y.P., C.M.S., C.N.H. and L.C.H. were supported in part by the National Science Foundation (NSF) through award no. CBET-2042635 and the AAAS Marion Milligan Mason Award. K.G. was funded by the Eugene V. Cota-Robles Fellowship from the University of California, Los Angeles. Y.V. was supported by the NSF through award no. 1751348.

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Authors and Affiliations



Y.P. and L.C.H. designed the study and validated the theory. Y.P., C.M.S. and C.N.H. produced the micropatterned substrates. Y.P., A.K., Y.S. and Y.V. conducted the human finger experiments. Y.P., K.G. and V.J.S. conducted the robotic finger experiments. All authors reviewed the data and wrote the paper.

Corresponding author

Correspondence to Lilian C. Hsiao.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–12 and Tables 1–4.

Supplementary Video 1

Demonstration of sliding experiments between a robotic finger and soft patterned substrates.

Supplementary Video 2

Demonstration of sliding experiments between a human finger and soft patterned substrates.

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Source Data Fig. 1

Raw data for Fig. 1i.

Source Data Fig. 2

Raw data for Fig. 2b.

Source Data Fig. 3

Raw data for Fig. 3.

Source Data Fig. 4

Raw data for Fig. 4.

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Peng, Y., Serfass, C.M., Kawazoe, A. et al. Elastohydrodynamic friction of robotic and human fingers on soft micropatterned substrates. Nat. Mater. 20, 1707–1711 (2021).

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