An intimate physical connection exists between a fluid’s mass and its volume, with the density ρ serving as a proportionality factor relating these two extensive thermodynamic properties when the fluid is homogeneous. This linkage has led to the erroneous belief among many researchers that a...

This paper illustrates, by example, the incompleteness of the Navier–Stokes–Fourier (NSF) equations for the case of thermally compressible fluids, namely fluids possessing a nonzero coefficient of thermal expansion. The work is a follow-up to a recent publication that offered elementary...

Linear irreversible thermodynamic principles are used to demonstrate, by counterexample, the existence of a fundamental incompleteness in the basic pre-constitutive mass, momentum, and energy equations governing fluid mechanics and transport phenomena in continua. The demonstration is effected...

The principles of linear irreversible thermodynamics are used to show that near-equilibrium linear constitutive equations governing the diffuse fluxes through fluids of momentum, energy, and other extensive properties, and valid for the case of general unsteady flows, can be derived by...

The diffuse flux of volume jv in a single-component liquid or gas, the subject of this paper, is a purely molecular quantity defined as the difference between the flux of volume nv and the convective flux of volume nmvˆ carried by the flowing mass, with nm the mass flux, vˆ=1/ρ the specific...

The present contribution supplements the previous findings regarding the need for two independent velocities rather than one when quantifying mass, momentum and energy transport phenomena in fluid continua. Explicitly, for the case of single-component fluids the present paper furnishes detailed...

Theoretical evidence derived from linear irreversible thermodynamics (LIT) jointly with Burnett’s solution of Boltzmann’s gas-kinetic equation is used to show that fluid mechanics and transport processes in both gaseous and liquid continua require the use of two independent velocities rather...

Öttinger's recent nontraditional incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat...

A purely continuum theory for the thermophoretic velocity of aerosol and hydrosol particles in the zero Knudsen number, near continuum limit, Kn=0+, valid for both gases and liquids, is proposed. This theoretical result is based upon a fundamentally modified version of the traditional equations...

A revision of Newton's law of viscosity appearing in the role of the deviatoric stress tensor in the Navier–Stokes equation is proposed for the case of compressible fluids, both gaseous and liquid. Explicitly, it is hypothesized that the velocity v appearing in the velocity gradient term ∇v...