Hostname: page-component-54dcc4c588-sdd8f Total loading time: 0 Render date: 2025-09-22T11:34:42.184Z Has data issue: false hasContentIssue false
  • English
  • Français

EFFECTIVE SLIP LENGTH: SOME ANALYTICAL AND NUMERICAL RESULTS

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  25 August 2015

XINGYOU (PHILIP) ZHANG ,
NAT J. LUND  and
SHAUN C. HENDY
XINGYOU (PHILIP) ZHANG*
Affiliation:
Computational and Data Sciences, Callaghan Innovation, PO Box 31-310, Lower Hutt5040, New Zealand email philip.zhang@callaghaninnovation.govt.nz
NAT J. LUND
Affiliation:
Department of Physics, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand email natjlund@gmail.com
SHAUN C. HENDY
Affiliation:
Department of Physics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand email shaun.hendy@auckland.ac.nz
*
✉philip.zhang@callaghaninnovation.govt.nz
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

More and more experimental evidence demonstrates that the slip boundary condition plays an important role in the study of nano- or micro-scale fluid. We propose a homogenization approach to study the effective slippage problem. We show that the effective slip length obtained by homogenization agrees with the results obtained by the traditional method in the literature for the simplest Stokes flow; then we use our approach to deal with two examples which seem quite hard by other analytical methods. We also include some numerical results to validate our analytical results.

Keywords

Stokes floweffective slip lengthhomogenizationanisotropic slipfinite element method

MSC classification

Primary: 35Q35: PDEs in connection with fluid mechanics

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 1 , July 2015 , pp. 79 - 88
Copyright
© 2015 Australian Mathematical Society 

References

Bazant, M. Z. and Vinogradova, O. I., “Tensorial hydrodynamic slip”, J. Fluid Mech. 613 (2008) 125–134; doi:10.1017/S002211200800356X.CrossRefGoogle Scholar
Bensoussan, A. B., Lions, J. L. and Papanicolaou, G., Asymptotic analysis for periodic structure (North-Holland, Amsterdam, 1978) ; http://www.ams.org/bookstore-getitem/item=chel-374-h.Google Scholar
Bocquet, L. and Barrat, J.-L., “Flow boundary conditions from nano- to micro-scales”, Soft Matter 3 (2007) 685–693; doi:10.1039/B616490K.CrossRefGoogle ScholarPubMed
Cottin-Bizonne, C., Barentin, C., Charlaix, E., Bocquet, L. and Barrat, J.-L., “Dynamics of simple liquids at heterogeneous surfaces: molecular dynamics simulations and hydrodynamic description”, Eur. Phys. J. E 15 (2004) 427–438; doi:10.1140/epje/i2004-10061-9.CrossRefGoogle ScholarPubMed
Glowinski, R., Numerical methods for fluids, Volume 9 of Handbook of numerical analysis (Elsevier Science, Amsterdam, 2002) ;http://www.sciencedirect.com/science/handbooks/15708659/9.Google Scholar
Hecht, F. et al. , http://www.freefem.org/ff++/.Google Scholar
Hendy, S. C. and Lund, N., “Effective slip boundary conditions for flow over nanoscale chemical heterogeneities”, Phys. Rev. E 76(6) (2007) 066313; doi:10.1103/PhysRevE.76.066313.CrossRefGoogle ScholarPubMed
Karniadakis, G., Beskok, A. and Aluru, N., Microflows and nanoflows (Springer, New York, 2005); doi:10.1007/0-387-28676-4.Google Scholar
Lauga, E., “Microfluidics: the no-slip boundary conditions”, in: Handbook of experimental fluid dynamics (eds Tropea, C., Yarin, A. and Foss, J. F.), (Springer, New York, 2007) 1219–1240; doi:10.1007/978-3-540-30299-5-19.Google Scholar
Lauga, E. and Stone, H., “Effective slip in pressure-driven Stokes flow”, J. Fluid Mech. 489 (2003) 55–77; doi:10.1017/S0022112003004695.CrossRefGoogle Scholar
Lund, N., Zhang, X. P., Mahelona, K. and Hendy, S. C., “Calculation of effective slip on rough chemically heterogeneous surfaces using a homogenization approach”, Phys. Rev. E 86 (2012) 046303; doi:10.1103/PhysRevE.86.046303.CrossRefGoogle ScholarPubMed
Philip, J. R., “Flow satisfying mixed no-slip and no-shear conditions”, J. Appl. Math. Phys. (ZAMP) 23 (1972) 353–372; doi:10.1007/BF01595477.CrossRefGoogle Scholar
Sbragaglia, M. and Prosperetti, A., “A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces”, Phys. Fluids 19 (2007) 043603; doi:10.1063/1.2716438.CrossRefGoogle Scholar
Sbragaglia, M. and Prosperetti, A., “Effective velocity boundary condition at a mixed slip surface”, J. Fluid Mech. 578 (2007) 435–451; doi:10.1017/S0022112007005149.CrossRefGoogle Scholar