Newtonian flow with nonlinear Navier boundary condition
 M. T. Matthews,
 J. M. Hill
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The generalized nonlinear Navier boundary condition advocated by Thompson and Troian in the journal Nature, and motivated from molecular dynamical simulations, is applied to the conventional continuum mechanical description of fluid flow for three simple pressuredriven flows through a pipe, a channel and an annulus, with a view to examining possible nonuniqueness arising from the nonlinear nature of the boundary condition. For the pipe and the channel it is shown that the results with the nonlinear Navier boundary condition may be obtained from a pseudo linear Navier boundary condition but with a modified slip length. For the annulus, two sets of physically acceptable solutions are obtained corresponding to the chosen sign of the normal derivative of the velocity at each solid boundary. Closer examination reveals that although the generalized Navier boundary condition is highly nonlinear, in terms of the assumed form of solution the integration constants obtained are still unique for the three simple pressuredriven flows presented here, provided that care is taken in its application and noting that the multiplicity of solutions obtained for the annulus arise as a consequence of adopting different signs for the normal derivatives of velocity at the boundaries.
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 Title
 Newtonian flow with nonlinear Navier boundary condition
 Journal

Acta Mechanica
Volume 191, Issue 34 , pp 195217
 Cover Date
 20070701
 DOI
 10.1007/s0070700704548
 Print ISSN
 00015970
 Online ISSN
 16196937
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 M. T. Matthews ^{(1)}
 J. M. Hill ^{(1)}
 Author Affiliations

 1. Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, 2522, N.S.W, Australia