Continuum perspective of bulk viscosity in compressible fluids

Abstract

Kinetic theory and acoustic measurements have proven that the bulk viscosity associated with the expansion or compression effect cannot be ignored in compressible fluids except for monatomic gases. A new theoretical formula for the bulk viscosity coefficient (BVC) ζ is derived by the continuum medium methodology, which provides a further understanding of the bulk viscosity, i.e. ζ is equal to the product of the bulk modulus K and the relaxation time τ (ζ = Kτ ). 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 N 2 , O 2 and CO, show good agreement with the experimental data over a wide range of temperature. In addition, the vibrational contributions to ζ 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 τ , collision number Z, BVC ζ and ratio of bulk-to-shear viscosities ζ /µ in the vibrational mode are found to be several orders of magnitude larger than those in the rotational mode.

Reconciliation of Thermodynamic and Mechanical Pressures and Development of a Frequency-Based Formula for Speed of Sound in Gases

“…First, the mathematical theory underlying the computer simulations lead to the accretion of errors depending on the memory limit and computing power of the machine at hand, but this is not the topic of this paper. Second reason for requiring experiments to confirm the numerical results is that the application of Navier-Stokes equations to the current model of a fluid inherently involves a flaw due to a fluid property that is known as bulk viscosity [1]. In order to understand this problem about bulk viscosity, it is first necessary to see what a fluid element is.…”

Transport Properties of Water Confined in a Graphene Nanochannel

“…the case for CO 2 . [61][62][63][64][65][66] The bulk viscosity describes how a fluid's compression and dilation affects transport. In the case of gases, it is entirely related to the relaxation of vibrational and rotational degrees of freedom, 61,62,64,65,[67][68][69][70] whilst for dense fluids it contains additional contributions due to long-range molecular interactions.…”

“…[61][62][63][64][65][66] The bulk viscosity describes how a fluid's compression and dilation affects transport. In the case of gases, it is entirely related to the relaxation of vibrational and rotational degrees of freedom, 61,62,64,65,[67][68][69][70] whilst for dense fluids it contains additional contributions due to long-range molecular interactions. 63,71,72 For some liquids, including water, 66 the vibrational and rotational contributions are negligible, enabling the bulk viscosity to be obtained from fluctuations in the pressure tensor using molecular dynamics simulations.…”