Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor

Journal of Fluid Mechanics

Volumn 658, Issue , 2010, Pages 409-437

  Kamrin, Ken ^a   Bazant, Martin Z ^b   Stone, Howard A ^c  

^a HARVARD UNIVERSITY   (United States)

^b Massachusetts Institute of Technology Cambridge   (United States)

^c Princeton University   (United States)

Author keywords

general fluid mechanics; micro nanofluid dynamics; Stokesian dynamics

Indexed keywords

APPROXIMATION ALGORITHMS; BOUNDARY CONDITIONS; FLOW OF FLUIDS; FLUID MECHANICS; HOLE MOBILITY; MICROFLUIDICS; PERTURBATION TECHNIQUES;

APPROXIMATE FORMULAS; GENERAL FLUID MECHANICS; GENERAL FORMULAS; LAMINAR SHEAR FLOW; PATTERNED SURFACE; PERIODIC SURFACES; SLIP BOUNDARY CONDITIONS; STOKESIAN DYNAMICS;

SHEAR FLOW;

BOUNDARY CONDITION; FLUID DYNAMICS; FLUID FLOW; LAMINAR FLOW; NAVIER-STOKES EQUATIONS; SHEAR FLOW;

EID: 77957157518     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010001801     Document Type: Article

References (32)

1. Ajdari, A. 2002 Transverse electrokinetic and microfluidic effects in micropatterned channels: lubrication analysis for slab geometries. Phys. Rev. E 65 (1), 016301.
2. Batchelor, G. K. 1970 Slender-body theory for particles of arbitary cross-section in Stokes flow. J. Fluid Mech. 44, 419-440.
3. Bazant, M. Z. & Vinogradova, O. I. 2008 Tensorial hydrodynamic slip. J. Fluid Mech. 613, 125-134.
4. Bechert, D. W. & Bartenwerfer, M. 1989 The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105-129.
5. Bocquet, L. & Barrat, J. L. 2007 Flow boundary conditions from nano-to micro-scales. Soft Matter 3, 685-693.
6. Davis, A. M. J. & Lauga, E. 2009 Geometric transition in friction for flow over a bubble mattress. Phys. Fluids 21, 011701.
7. Feuillebois, F., Bazant, M. Z. & Vinogradova, O. I. 2009 Effective slip over superhydrophobic surfaces in thin channels. Phys. Rev. Lett. 102, 026001.
8. Higdon, J. J. L. 1985 Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities. J. Fluid Mech. 159, 195-226.
9. Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.
10. Hocking, L. M. 1976 A moving fluid interface on a rough surface. J. Fluid Mech 76, 801-817.
11. Jung, Y. & Torquato, S. 2005 Fluid permeabilities of triply periodic minimal surfaces. Phys. Rev. E 72, 056319.
12. Kunert, C. & Harting, J. 2008 Simulation of fluid flow in hydrophobic rough microchannels. Intl J. Comput. Fluid D 27 (7), 475-480.
13. Lauga, E., Brenner, M. P. & Stone, H. A. 2007 Handbook of Experimental Fluid Dynamics, Ch. 19, pp. 1219-1240.
14. Springer. Lauga, E. & Stone, H. A. 2003 Effective slip in pressure-driven Stokes flow. J. Fluid Mech. 489, 55-77.
15. Luchini, P., Manzo, F. & Pozzi, A. 1991 Resistance of a grooved surface to parallel flow and cross-flow. J. Fluid Mech. 228, 87-109.
16. Miksis, M. J. & Davis, S. H. 1994 Slip over rough and coated surfaces. J. Fluid Mech. 273, 125-139.
17. Panzer, P., Liu, M. & Einzel, D. 1992 The effects of boundary curvature on hydrodynamic fluid flow: calculation of slip lengths. Intl J. Mod. Phys. B 6 (20), 3251.
18. Priezjev, N. V. & Troian, S. M. 2006 Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular-scale simulations versus continuum predictions. J. Fluid Mech. 554, 25-46.
19. Sarkar, K. & Prosperetti, A. 1996 Effective boundary conditions for Stokes flow over a rough surface. J. Fluid Mech. 316, 223-240.
20. Sbragaglia, M. & Prosperetti, A. 2007 Effective velocity boundary condition at a mixed slip surface. J. Fluid Mech. 578, 435-451.
21. Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices. Annu. Rev. Fluid Mech. 36, 381-411.
22. Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezić, I., Stone, H. A. & Whitesides, G. M. 2002a Chaotic mixer for microchannels. Science 295, 647-651.
23. Stroock, A. D., Dertinger, S. K., Whitesides, G. M. & Ajdari, A. 2002b Patterning flows using grooved surfaces. Anal. Chem. 74, 5306-5312.
24. Torquato, S. 2002 Random Heterogeneous Materials. Springer.
25. Tuck, E. O. & Kouzoubov, A. 1995 A laminar roughness boundary condition. J. Fluid Mech. 300, 59-70.
26. Vinogradova, O. I. 1999 Slippage of water over hydrophobic surfaces. Intl J. Miner. Proc. 56, 31-60.
27. Wang, C.-Y. 1978 Drag due to a striated boundary in slow Couette flow. Phys. Fluids 21 (4), 697-698.
28. Wang, C.-Y. 1994 The Stokes drag clue to the sliding of a smooth plate over a finned plate. Phys. Fluids 6 (7), 2248-2252.
29. Wang, C.-Y. 2003 Flow over a surface with parallel grooves. Phys. Fluids 15, 1114-1121.
30. Wang, C.-Y. 2004 Stokes flow through a channel with three-dimensional bumpy walls. Phys. Fluids 16 (6), 2136-2139.
31. Wilkening, J. 2009 Practical error estimates for Reynolds' lubrication approximation and its higher order corrections. SIAM J. Math. Anal. 41, 588-630.
32. Zhou, H., Martinuzzi, R. J. & Straatman, A. G. 1995 On the validity of the perturbation approach for the flow inside weakly modulated channels. Intl J. Numer. Methods Fluids 39, 1139-1159.