Geometric transition in friction for flow over a bubble mattress

Physics of Fluids

Volumn 21, Issue 1, 2009, Pages

  Davis, Anthony M J ^a   Lauga, Eric ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FRICTION; GEOMETRY; LAMINAR FLOW; REYNOLDS NUMBER; TRIBOLOGY;

BUBBLE GEOMETRY; EFFECTIVE SLIP LENGTHS; FLOW DIRECTION; LOW REYNOLDS NUMBER; NUMERICAL COMPUTATIONS; PROTRUSION ANGLE; SIMPLE MODELING; TWO-DIMENSIONAL ARRAYS;

SHEAR FLOW;

EID: 59649123734     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3067833     Document Type: Article

References (29)

1. H. A. Stone, A. D. Stroock, and A. Ajdari, "Engineering flows in small devices: Microfluidics toward a lab-on-a-chip," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.36.050802.122124 36, 381 (2004).
2. T. M. Squires and S. R. Quake, "Microfluidics: Fluid physics on the nanoliter scale," Rev. Mod. Phys. RMPHAT0034-686110.1103/ RevModPhys.77.977 77, 977 (2005).
3. C. Neto, D. R. Evans, E. Bonaccurso, H.-J. Butt, and V. S. J. Craig, "Boundary slip in Newtonian liquids: A review of experimental studies," Rep. Prog. Phys. RPPHAG0034-488510.1088/0034-4885/68/12/ R05 68, 2859 (2005).
4. E. Lauga, M. P. Brenner, and H. A. Stone, "Microfluidics: The no-slip boundary condition," Handbook of Experimental Fluid Dynamics, edited by A. Y. C. Tropea and J. F. Foss (Springer, New York, 2007).
5. L. Bocquet and J.-L. Barrat, "Flow boundary conditions: From nano-to micro-scales," Soft Matter SMOABF1744-683X10.1039/b616490k 3, 685 (2007).
6. M. Sbragaglia and A. Prosperetti, "Effective velocity boundary condition at a mixed slip surface," J. Fluid Mech. JFLSA70022-112010.1017/S0022112007005149 578, 435 (2007).
7. C. Ybert, C. Barentin, C. Cottin-Bizonne, P. Joseph, and L. Bocquet, "Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries," Phys. Fluids PHFLE61070-663110.1063/ 1.2815730 19, 123601 (2007).
8. A. Steinberger, C. Cottin-Bizonne, P. Kleimann, and E. Charlaix, "High friction on a bubble mattress," Nature Mater. NMAACR1476-112210.1038/nmat1962 6, 665 (2007).
9. J. Hyvaluoma and J. Harting, "Slip flow over structured surfaces with entrapped microbubbles," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.100.246001 100, 246001 (2008).
10. D. Quere, "Non-sticking drops," Rep. Prog. Phys. RPPHAG0034-488510.1088/0034-4885/68/11/R01 68, 2495 (2005).
11. P.-G. de Gennes, F. Brochard-Wyart, and D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer, New-York, 2004).
12. C. Cottin-Bizonne, J. L. Barrat, L. Bocquet, and E. Charlaix, "Low-friction flows of liquid at nanopatterned interfaces," Nature Mater. NMAACR1476-112210.1038/nmat857 2, 237 (2003).
13. K. Watanabe, Y. Udagawa, and H. Udagawa, "Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall," J. Fluid Mech.JFLSA70022-112010.1017/S0022112098003747 381, 225 (1999).
14. J. Ou, B. Perot, and J. P. Rothstein, "Laminar drag reduction in microchannels using ultrahydrophobic surfaces," Phys. Fluids PHFLE61070-663110.1063/1.1812011 16, 4635 (2004).
15. J. Ou and J. P. Rothstein, "Drag reduction and μ-PIV measurements of the flow past ultrahydrophobic surfaces," Phys. Fluids PHFLE61070-663110.1063/1.2109867 17, 103606 (2005).
16. S. Richardson, "On the no-slip boundary condition," J. Fluid Mech. JFLSA70022-112010.1017/S0022112073001801 59, 707 (1973).
17. K. M. Jansons, "Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough-surface with a perfect slip microscopic boundary condition," Phys. Fluids PFLDAS0031-917110.1063/1.866563 31, 15 (1988).
18. D. Legendre and C. Colin, "Enhancement of wall-friction by fixed cap-bubbles," Phys. FluidsPHFLE61070-663110.1063/1.2924361 20, 051704 (2008).
19. N. Ishida, T. Inoue, M. Miyahara, and K. Higashitani, "Nano bubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy," LangmuirLANGD50743-746310.1021/la000219r 16, 6377 (2000).
20. J. W. G. Tyrrell and P. Attard, "Images of nanobubbles on hydrophobic surfaces and their interactions," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.87.176104 87, 176104 (2001).
21. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, 1965).
22. A. M. J. Davis and M. E. O'Neill, "Separation in a stokes flow past a plane with a cylindrical ridge or trough," Q. J. Mech. Appl. Math. QJMMAV0033-561410.1093/qjmam/30.4.355 30, 355 (1977).
23. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. II.
24. Strictly speaking, our two-dimensional model was derived in the low-Φ limit. We consider, however, its results beyond its regime of asymptotic validity, as it is expected to provide a good quantitative model even in the limit of large Φ and reproduce the essentially physical features of the phenomenon.
25. A. M. J. Davis, "Shear flow disturbance due to a hole in the plane," Phys. Fluids A PFADEB0899-821310.1063/1.858104 3, 478 (1991).
26. After noting that, in Eq. (22) of Ref., the toroidal coordinate λ ∼ r in the far field and ζ = y/λ.
27. D. Legendre, C. Colin, and T. Coquard, "Lift, drag and added mass of a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow," Philos. Trans. R. Soc. London, Ser. A PTRMAD0962-8428 366, 2233 (2008).
28. Y. M. Zheng, L. Jiang, J. X. Wang, and D. Han, "Extreme "water repellency" on strong water-spreading surface without tilted degree actuation," Appl. Phys. Lett. APPLAB0003-695110.1063/1.2977611 93, 094107 (2008).
29. N. Bremond, M. Arora, C. D. Ohl, and D. Lohse, "Controlled multibubble surface cavitation," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.96.224501 96, 224501 (2006).