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$\unicode[STIX]{x1D701}$
is derived by the continuum medium methodology, which provides a further understanding of the bulk viscosity, i.e.
$\unicode[STIX]{x1D701}$
is equal to the product of the bulk modulus
$K$
and the relaxation time
$\unicode[STIX]{x1D70F}$
(
$\unicode[STIX]{x1D701}=K\unicode[STIX]{x1D70F}$
). The continuum and kinetic theories present consistent results from macro- and microperspectives respectively, only differing in terms of a coefficient. The theoretical predictions of the BVC in diatomic molecules, such as
$\text{N}_{2}$
,
$\text{O}_{2}$
and CO, show good agreement with the experimental data over a wide range of temperature. In addition, the vibrational contributions to
$\unicode[STIX]{x1D701}$
are controlled by a rapid exponential decrease at high temperatures, while at low temperatures a slow linear increase proceeds for the rotational cases. The relaxation time
$\unicode[STIX]{x1D70F}$
, collision number
$Z$
, BVC
$\unicode[STIX]{x1D701}$
and ratio of bulk-to-shear viscosities
$\unicode[STIX]{x1D701}/\unicode[STIX]{x1D707}$
in the vibrational mode are found to be several orders of magnitude larger than those in the rotational mode.
