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Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number

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Abstract

The oscillatory Couette flow is important for further advancement of microengineering. In practice the size of the microfluidics can be so small that it can be compared with the molecular mean free path. Moreover, the oscillation frequency can be close to that of the intermolecular collisions. Under such conditions the problem must be solved on the kinetic level. In the present work, the oscillatory Couette flow is considered on the basis of the non-stationary kinetic equation. The solution to the problem is determined by two parameters: the Knudsen number and the ratio of collision frequency to oscillation frequency. The kinetic equation is solved by the discrete velocity method over the wide range of both parameters.

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Acknowledgments

The authors acknowledge the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil) for the support of their research. Professor Dimitris Valougeorgis is acknowledged for the helpful discussion concerning the acceleration scheme. The authors also thank Professor Ali Beskok, who provided his numerical data to perform the precise comparison.

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, Curitiba, 81531-990, Brazil

    Felix Sharipov & Denize Kalempa

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  1. Felix Sharipov
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  2. Denize Kalempa
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Correspondence to Felix Sharipov.

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Sharipov, F., Kalempa, D. Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number. Microfluid Nanofluid 4, 363–374 (2008). https://doi.org/10.1007/s10404-007-0185-0

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  • DOI: https://doi.org/10.1007/s10404-007-0185-0

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