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Lattice Boltzmann Simulations of Slip Flow of Non-Newtonian Fluids in Microchannels

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Parallel Computational Fluid Dynamics 2008

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 74))

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Abstract

This paper considers the application of Lattice Boltzmann Method (LBM) to non-Newtonian flow in micro-fluidic devices. To set ideas, we first consider the pressure driven gaseous slip flow with small rarefaction through a long micro-channel and formulate the problem in LB framework. The non-Newtonian fluids are characterized by the non-linear stress-strain constitutive models formulated by Casson, Carreau & Yasuda, Herschel, and Cross, and the well known power law model. The formulation of the LBM for slip flow of non-Newtonian flow is presented. For planar constant area micro-channel for power law fluid, it is possible to obtain an analytical solution for both no-slip and slip flow. For other non-Newtonian fluid models, LBM results are compared with the numerical solutions obtained by using the commercial software FLUENT. The LBM results agree well with the analytical solutions and the numerical solutions. Small differences in the results are noticed using the different models characterizing the non-Newtonian flow.

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Author information

Authors and Affiliations

  1. Mechanical, Aerospace and Structural Engineering Department, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Ramesh K. Agarwal & Lee Chusak

Authors
  1. Ramesh K. Agarwal
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  2. Lee Chusak
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Corresponding author

Correspondence to Ramesh K. Agarwal .

Editor information

Editors and Affiliations

  1. , Institut Camille Jordan, Université Lyon 1 - CNRS, Bd du 11 Novembre 1918 43, Villeurbanne, 69622, France

    Damien Tromeur-Dervout

  2. , Institut für Technische Mechanik, TU Clausthal, Adolph-Roemer-Str. 2A2a, Clausthal-Zellerfeld, 38678, Germany

    Gunther Brenner

  3. Daresbury Laboratory, Daresbury Science & Innovation Campus, Science & Technology Facilities Council, Warrington, WA4 4AD, Cheshire, United Kingdom

    David R. Emerson

  4. INRIA - SAGE, Campus de Beaulieu, Rennes, 35042, France

    Jocelyne Erhel

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Agarwal, R.K., Chusak, L. (2010). Lattice Boltzmann Simulations of Slip Flow of Non-Newtonian Fluids in Microchannels. In: Tromeur-Dervout, D., Brenner, G., Emerson, D., Erhel, J. (eds) Parallel Computational Fluid Dynamics 2008. Lecture Notes in Computational Science and Engineering, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14438-7_26

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