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Enhanced Water Flow in Carbon Nanotubes and the Navier Slip Condition

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Progress in Industrial Mathematics at ECMI 2012

Part of the book series: Mathematics in Industry ((TECMI,volume 19))

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Abstract

A possible explanation for the enhanced flow in carbon nanotubes is given using a mathematical model that includes a depletion layer with reduced viscosity near the wall. In the limit of large tubes the model predicts no noticeable enhancement. For smaller tubes the model predicts enhancement that increases as the radius decreases. An analogy between the reduced viscosity and slip-length models shows that the term slip-length is misleading and that on surfaces which are smooth at the nanoscale it may be thought of as a length-scale associated with the size of the depletion region and viscosity ratio. The model therefore provides a physical interpretation of the classical Navier slip condition and explains why “slip-lengths” may be greater than the tube radius.

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Acknowledgements

The author gratefully acknowledges the support of this research through the Marie Curie International Reintegration Grant Industrial applications of moving boundary problems Grant no. FP7-256417 and Ministerio de Ciencia e Innovación Grant MTM2011-23789.

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Authors and Affiliations

  1. Centre de Recerca Matemàtica, Campus de Bellaterra Edifici C, 08193, Barcelona, Spain

    Tim G. Myers

  2. Departament de Matemàtica Aplicada I, Universitat Politécnica de Catalunya, Barcelona, Spain

    Tim G. Myers

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  1. Tim G. Myers
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Correspondence to Tim G. Myers .

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Editors and Affiliations

  1. Lunds Universitet, Centre for Mathematical Sciences, Lund, Sweden

    Magnus Fontes

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  3. Lehrstuhl für Angew.Math. 1, Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Erlangen, Germany

    Nicole Marheineke

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Myers, T.G. (2014). Enhanced Water Flow in Carbon Nanotubes and the Navier Slip Condition. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_27

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