Skip to main content
SpringerLink
Log in

Effective slip for flow through a channel bounded by lubricant-impregnated grooved surfaces

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

This study aims to investigate effective slip arising from pressure-driven flow through a slit channel bounded by lubricant-impregnated grooved surfaces. The problem for flow over longitudinal grooves is solved analytically using the methods of domain decomposition and eigenfunction expansion, while that for flow over transverse grooves is solved numerically using the front tracking method. It is found that the effective slip length and the lubricant flow rate can depend strongly on the geometry of the microstructure, the direction of flow, and the lubricant viscosity. In particular, the effective slip can be effectively enhanced by increasing the thickness of a lubricating film atop the ribs. Under the same conditions, a flow that is parallel to the lubricant-impregnated grooves will have a larger effective slip, but also a larger lubricant flow rate, when compared with the case of flow normal to the grooves. It is also shown that, in the case of transverse grooves, because of the downward displacement of the interface between the working/lubricating fluids, the effective slip length and lubricant flow rate may vary non-monotonically with the groove depth.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anand, S., Paxson, A.T., Dhiman, R., Smith, J.D., Varanasi, K.K.: Enhanced condensation on lubricant-impregnated nanotextured surfaces. ACS Nano 6(11), 10122–10129 (2012)

    Article  Google Scholar 

  2. Bohn, H.F., Federle, W.: Insect aquaplaning: nepenthes pitcher plants capture prey with the peristome, a fully wettable water-lubricated anisotropic surface. Proc. Natl. Acad. Sci. USA 101(39), 14138–14143 (2004)

    Article  Google Scholar 

  3. Carlson, A., Kim, P., Amberg, G., Stone, H.A.: Short and long time drop dynamics on lubricated substrates. EPL 104(3), 34,008 (2013)

    Article  Google Scholar 

  4. Eifert, A., Paulssen, D., Varanakkottu, S.N., Baier, T., Hardt, S.: Simple fabrication of robust water-repellent surfaces with low contact-angle hysteresis based on impregnation. Adv. Mater. Interfaces 1(3), 1300,138 (2014)

    Article  Google Scholar 

  5. Epstein, A.K., Wong, T.S., Belisle, R.A., Boggs, E.M., Aizenberg, J.: Liquid-infused structured surfaces with exceptional anti-biofouling performance. Proc. Natl. Acad. Sci. 109(33), 13182–13187 (2012)

    Article  Google Scholar 

  6. Huang, X., Chrisman, J.D., Zacharia, N.S.: Omniphobic slippery coatings based on lubricant-infused porous polyelectrolyte multilayers. ACS Macro Lett. 2(9), 826–829 (2013)

    Article  Google Scholar 

  7. Kim, P., Wong, T.S., Alvarenga, J., Kreder, M.J., Adorno-Martinez, W.E., Aizenberg, J.: Liquid-infused nanostructured surfaces with extreme anti-ice and anti-frost performance. ACS Nano 6(8), 6569–6577 (2012)

    Article  Google Scholar 

  8. Lafuma, A., Quéré, D.: Slippery pre-suffused surfaces. EPL 96(5), 56,001 (2011)

    Article  Google Scholar 

  9. Lalia, B.S., Anand, S., Varanasi, K.K., Hashaikeh, R.: Fog-harvesting potential of lubricant-impregnated electrospun nanomats. Langmuir 29(42), 13081–13088 (2013)

    Article  Google Scholar 

  10. Li, J., Kleintschek, T., Rieder, A., Cheng, Y., Baumbach, T., Obst, U., Schwartz, T., Levkin, P.A.: Hydrophobic liquid-infused porous polymer surfaces for antibacterial applications. ACS Appl. Mater. Interfaces 5(14), 6704–6711 (2013)

    Article  Google Scholar 

  11. Liu, H., Zhang, P., Liu, M., Wang, S., Jiang, L.: Organogel-based thin films for self-cleaning on various surfaces. Adv. Mater. 25(32), 4477–4481 (2013)

    Article  Google Scholar 

  12. Ng, C.O., Chen, B.: Microchannel flows with superhydrophobic surfaces: Effects of phase shift of wall patterns. In: Proceedings of the 14th Asian Congress of Fluid Mechanics, pp. 1037–1041 (2013)

  13. Ng, C.O., Chu, H.C.W., Wang, C.Y.: On the effects of liquid–gas interfacial shear on slip flow through a parallel-plate channel with superhydrophobic grooved walls. Phys. Fluids 22(10), 102,002 (2010)

    Article  Google Scholar 

  14. Ng, C.O., Wang, C.Y.: Stokes shear flow over a grating: implications for superhydrophobic slip. Phys. Fluids 21(1), 013,602 (2009)

    Article  MATH  Google Scholar 

  15. Ng, C.O., Wang, C.Y.: Stokes flow through a periodically grooved tube. J. Fluids Eng. 132(10), 101,204 (2010)

    Article  Google Scholar 

  16. Ng, C.O., Wang, C.Y.: Effective slip for stokes flow over a surface patterned with two-or three-dimensional protrusions. Fluid Dyn. Res. 43(6), 065,504 (2011)

    Article  MATH  Google Scholar 

  17. Ng, C.O., Zhou, Q.: Electro-osmotic flow through a thin channel with gradually varying wall potential and hydrodynamic slippage. Fluid Dyn. Res. 44(5), 055,507 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nishimoto, S., Bhushan, B.: Bioinspired self-cleaning surfaces with superhydrophobicity, superoleophobicity, and superhydrophilicity. RSC Adv. 3(3), 671–690 (2013)

    Article  Google Scholar 

  19. Peskin, C.S.: Numerical analysis of blood flow in the heart. J. Comput. Phys. 25(3), 220–252 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  20. Philip, J.R.: Flows satisfying mixed no-slip and no-shear conditions. ZAMP 23(3), 353–372 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  21. Quéré, D.: Non-sticking drops. Rep. Prog. Phys. 68(11), 2495 (2005)

    Article  Google Scholar 

  22. Rajagopal, M.C., Das, S.K.: Analyses of drag on viscoelastic liquid infused bio-inspired patterned surfaces. J. Non-Newton. Fluid Mech. 228, 17–30 (2016)

    Article  MathSciNet  Google Scholar 

  23. Rykaczewski, K., Anand, S., Subramanyam, S.B., Varanasi, K.K.: Mechanism of frost formation on lubricant-impregnated surfaces. Langmuir 29(17), 5230–5238 (2013)

    Article  Google Scholar 

  24. Rykaczewski, K., Paxson, A.T., Staymates, M., Walker, M.L., Sun, X., Anand, S., Srinivasan, S., McKinley, G.H., Chinn, J., Scott, J.H.J., et al.: Dropwise condensation of low surface tension fluids on omniphobic surfaces. Sci. Rep. 4, 4158 (2014)

    Article  Google Scholar 

  25. Schönecker, C., Baier, T., Hardt, S.: Influence of the enclosed fluid on the flow over a microstructured surface in the cassie state. J. Fluid Mech. 740, 168–195 (2014)

    Article  MathSciNet  Google Scholar 

  26. Schönecker, C., Hardt, S.: Longitudinal and transverse flow over a cavity containing a second immiscible fluid. J. Fluid Mech. 717, 376–394 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Schönecker, C., Hardt, S.: Assessment of drag reduction at slippery, topographically structured surfaces. Microfluid. Nanofluid. 19(1), 199–207 (2015)

    Article  Google Scholar 

  28. Smith, J.D., Dhiman, R., Anand, S., Reza-Garduno, E., Cohen, R.E., McKinley, G.H., Varanasi, K.K.: Droplet mobility on lubricant-impregnated surfaces. Soft Matter 9(6), 1772–1780 (2013)

    Article  Google Scholar 

  29. Solomon, B.R., Khalil, K.S., Varanasi, K.K.: Drag reduction using lubricant-impregnated surfaces in viscous laminar flow. Langmuir 30(36), 10970–10976 (2014)

    Article  Google Scholar 

  30. Subramanyam, S.B., Rykaczewski, K., Varanasi, K.K.: Ice adhesion on lubricant-impregnated textured surfaces. Langmuir 29(44), 13414–13418 (2013)

    Article  Google Scholar 

  31. Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., Jan, Y.J.: A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169(2), 708–759 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang, C.Y.: Flow over a surface with parallel grooves. Phys. Fluids 15(5), 1114–1121 (2003)

    Article  MATH  Google Scholar 

  33. Wexler, J.S., Jacobi, I., Stone, H.A.: Shear-driven failure of liquid-infused surfaces. Phys. Rev. Lett. 114(16), 168,301 (2015)

    Article  Google Scholar 

  34. Wilson, P.W., Lu, W., Xu, H., Kim, P., Kreder, M.J., Alvarenga, J., Aizenberg, J.: Inhibition of ice nucleation by slippery liquid-infused porous surfaces (SLIPS). Phys. Chem. Chem. Phys. 15(2), 581–585 (2013)

    Article  Google Scholar 

  35. Wong, T.S., Kang, S.H., Tang, S.K., Smythe, E.J., Hatton, B.D., Grinthal, A., Aizenberg, J.: Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity. Nature 477(7365), 443–447 (2011)

    Article  Google Scholar 

  36. Xiao, L., Li, J., Mieszkin, S., Di Fino, A., Clare, A.S., Callow, M.E., Callow, J.A., Grunze, M., Rosenhahn, A., Levkin, P.A.: Slippery liquid-infused porous surfaces showing marine antibiofouling properties. ACS Appl. Mater. Interfaces 5(20), 10074–10080 (2013)

    Article  Google Scholar 

  37. Yao, X., Hu, Y., Grinthal, A., Wong, T.S., Mahadevan, L., Aizenberg, J.: Adaptive fluid-infused porous films with tunable transparency and wettability. Nat. Mater. 12(6), 529–534 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong

    Rui Sun & Chiu-On Ng

Authors
  1. Rui Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chiu-On Ng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chiu-On Ng.

Additional information

Communicated by Omar M Knio.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, R., Ng, CO. Effective slip for flow through a channel bounded by lubricant-impregnated grooved surfaces. Theor. Comput. Fluid Dyn. 31, 189–209 (2017). https://doi.org/10.1007/s00162-016-0414-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-016-0414-9

Keywords

Search

Navigation