A New Continuum Formulation for Materials--Part I. The Equations of Motion for a Single-Component Fluid

Abstract: The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas the actual mass density is treated as a thermodynamic variable. A new set of balance laws is proposed, including a mass balance equation with a non-convective flux. The basic principles of irreversible thermodynamics are used to obtain linear constitutive equations that are expansions of--not only the usual affinities involving gradients of temperature and velocity--but also the gradient of the chemical potential. Transport coefficients are then chosen based on an elementary diffusion model, which yields simple constitutive laws featuring just two transport parameters: one for the longitudinal part of the motion and one for the rotational part. The resulting formulation differs from the Navier-Stokes-Fourier equations of fluid motion. In order to highlight key similarities and differences between the two approaches, several examples in fluid mechanics are treated in part II, including sound propagation, light scattering, steady-state shock waves, thermophoresis, and Poiseuille flow.