Effective slip length: some analytical and numerical results

Xingyou Philip Zhang; Nat Lund; Shaun C. Hendy

doi:10.21914/anziamj.v57i0.5184

Authors

Xingyou Philip Zhang Computational and Data Sciences, Callaghan Innovation, PO Box 31-310, Lower Hutt 5040, New Zealand
Nat Lund Victoria University of Wellington, PO Box 600, Wellington; Industrial Research Ltd.
Shaun C. Hendy Department of Physics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand

DOI:

https://doi.org/10.21914/anziamj.v57i0.5184

Keywords:

Stokes flow, effective slip length, homogenization, anisotropic slip, finite element method

Abstract

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. doi:10.1017/S1446181115000127

Author Biography

Xingyou Philip Zhang, Computational and Data Sciences, Callaghan Innovation, PO Box 31-310, Lower Hutt 5040, New Zealand

Research Scientist (PhD), Applied Mathematics Team, Industrial Research Ltd, New Zealand