Numerical estimates for the bulk viscosity of ideal gases

Abstract

We estimate the bulk viscosity of a selection of well known ideal gases. A relatively simple formula is combined with published values of rotational and vibrational relaxation times. It is shown that the bulk viscosity can take on a wide variety of numerical values and variations with temperature. Several fluids, including common diatomic gases, are seen to have bulk viscosities which are hundreds or thousands of times larger than their shear viscosities. We have also provided new estimates for the bulk viscosity of water vapor in the range 380–1000 K. We conjecture that the variation of bulk viscosity with temperature will have a local maximum for most fluids. The Lambert-Salter correlation is used to argue that the vibrational contribution to the bulk viscosities of a sequence of fluids having a similar number of hydrogen atoms at a fixed temperature will increase with the characteristic temperature of the lowest vibrational mode.

A systematic study of Rayleigh-Brillouin scattering in air, N2, and O2 gases

“…Since it follows from previous studies, that the bulk viscosity exhibits a linearly increasing trend with the temperature 30,31 , as it is expected from theoretical considerations 42 , values of the bulk viscosity are derived for the different temperature settings for the experiments, for the three different gases. The thus obtained values for the derived bulk viscosities for air, N 2 and O 2 as a function of temperature (for further discussion see below) are employed to interpolate the values for the other settings in p − T parameter space as listed in Table II.…”

“…In general cases, however, the bulk viscosity is known as a frequency-dependent parameter. Of course, η b is a temperature-dependent parameter, since at higher temperatures more degrees of freedom will participate in the internal motion of the molecules and the relaxation time for the internal motion are shorter as collisions more frequently happen 42 . Most information about the numerical values of the bulk viscosity η b for diluted gases comes from ultrasound experiments at MHz frequencies 43 .…”

Effect of bulk viscosity in supersonic flow past spacecraft

“…The case studied in this work is rather clear and allows one to qualitatively trace how the relaxation of internal degrees of freedom affects the values of the transport coefficients, in particular, the BVC. Under the assumptions of the kinetic equation (Boltzmann equation) by generalizing the Chapmen-Enskog method in the first approximation, it is possible to obtain Navier-Stokes equations for a gas with internal degree of freedom [6,7]. The stress tensor in this case has…”

Continuum perspective of bulk viscosity in compressible fluids

“…To facilitate discussion in the following section, we will adopt the modelling assumptions (Cramer 2012) that the rotational and vibrational degrees of freedom proceed independently; in particular, all of the rotational modes or all of the vibrational modes relax with a single relaxation time. According to (2.24), the rotational and vibrational contributions to the bulk viscosity can therefore be summed up as…”

“…ζ = ζ rot + ζ vib in (3.1), has a local maximum over a large temperature range. Reasons for such a phenomenon in polyatomic gases have been qualitatively given by Cramer (2012): ζ will vanish as c v → 0 or T → 0, and at high temperatures, ζ shows a strong decrease associated with the Landau-Teller law, so that it leads to a local maximum; the total bulk viscosity is only controlled by the gradually increasing rotational contributions at very low temperatures, because the rotational component of ζ is always present. When the total bulk viscosity is quantitatively considered in actual cases, there exists a discontinuous transition between the rotational and vibrational modes from low to high temperatures.…”