  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.
