A recently modified formulation of fluid-mechanical transport processes, which has been shown to correctly predict the thermophoretic force on a rigid isolated particle in a single-component fluid continuum (gas or liquid), is combined with steady-state Stokes–Einstein-type...

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...

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...

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...

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...

A method-of-moments scheme is invoked to compute the asymptotic, long-time mean (or composite) velocity and dispersivity (effective diffusivity) of a two-state particle undergoing one-dimensional convective–diffusive motion accompanied by a reversible linear transition (“chemical reaction”...

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 transport and production of the generally non-conserved extensive property of volume V within a flowing gas or liquid is addressed. Specifically, a convective/diffusive/production-type transport equation, ρDmv^/Dt+∇·jv=πv, governing the transport of volume, is derived for the evolution...

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...