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

Papalexandris, Miltiadis
(2020) Continuum Mechanics and Thermodynamics : analysis of complex materials and judicious evaluation of the environment — Vol. 32, n° 4, p. 1245-1249 (2020)

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Abstract
Stokes’ hypothesis states that the bulk viscosity of a Newtonian fluid can be set to zero. Althoughnot 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 bulkviscous pressure from the governing equations. More specifically, we show that the Reynolds number definedwith respect to the bulk viscosity must be very large. We further show that even when this condition is notsatisfied, the bulk viscous pressure does not need to be taken explicitly into account in the computation of thevelocity field because it can be combined with the hydrodynamic pressure.
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Papalexandris, M. (2020). On the applicability of Stokes’ hypothesis to low-Mach-number flows. Continuum Mechanics and Thermodynamics : analysis of complex materials and judicious evaluation of the environment, 32(4), 1245-1249. https://doi.org/10.1007/s00161-019-00785-z (Original work published 2020)