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On the applicability of Stokes’ hypothesis to low-Mach-number flows

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Abstract

Stokes’ hypothesis states that the bulk viscosity of a Newtonian fluid can be set to zero. Although not valid for many fluids, it is common practice to invoke this hypothesis in the study of low-Mach-number, variable-density flows. Based on scaling arguments, we provide a necessary condition for neglecting the bulk viscous pressure from the governing equations. More specifically, we show that the Reynolds number defined with respect to the bulk viscosity must be very large. We further show that even when this condition is not satisfied, the bulk viscous pressure does not need to be taken explicitly into account in the computation of the velocity field because it can be combined with the hydrodynamic pressure.

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Authors and Affiliations

  1. Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Miltiadis V. Papalexandris

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  1. Miltiadis V. Papalexandris
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Correspondence to Miltiadis V. Papalexandris.

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Communicated by Andreas Öchsner.

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Papalexandris, M.V. On the applicability of Stokes’ hypothesis to low-Mach-number flows. Continuum Mech. Thermodyn. 32, 1245–1249 (2020). https://doi.org/10.1007/s00161-019-00785-z

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  • DOI: https://doi.org/10.1007/s00161-019-00785-z

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