Bi-velocity hydrodynamics. Multicomponent fluids

Previous work, limited to single-component fluids, demonstrating the need for not one but two independent velocity fields in order to quantify mass, momentum and energy continuum fluid mechanics and transport processes, is here extended to include multicomponent mixtures. These multicomponent results and conclusions, which are supported molecularly by the Boltzmann equation, are also closely supported by the macroscopic contributions of the “Russian school” of generalized nonequilibrium thermodynamics (GNT), despite the fact that GNT is founded upon classical, single-velocity (“monovelocity”) fluid mechanics. Our bi-velocity theory, for both single- and multicomponent fluids, is shown to predict the existence of mechanodiffusion phenomena, the latter referring to coupling arising between diffuse momentum transport (embodied in the fluid’s viscous stress tensor) and species or energy diffusion stemming respectively from gradients in species concentration and temperature. Previously, except primarily for the work of the Russian school, mechanodiffusion phenomena were believed to be noncontinuum in nature, at least in the case of gases. Our work, as well as that of the Russian school, places mechanodiffusion phenomena on the same continuum level as thermodiffusion phenomena (the latter referring to conventional Ludwig-Soret and Dufour thermal diffusion effects). The net effect of our findings is the conclusion that the Navier–Stokes–Fourier–Fick equation set can no longer be regarded as fully descriptive of the behavior of fluid continua owing to its failure to address mechanodiffusion phenomena.