Inconsistency of a dissipative contribution to the mass flux in hydrodynamics

Abstract

The possibility of dissipative contributions to the mass flux is considered in detail. A general, thermodynamically consistent framework is developed to obtain such terms, the compatibility of which with general principles is then checked--including Galilean invariance, the possibility of steady rigid rotation and uniform center-of-mass motion, the existence of a locally conserved angular momentum, and material objectivity. All previously discussed scenarios of dissipative mass fluxes are found to be ruled out by some combinations of these principles, but not a new one that includes a smoothed velocity field v-bar. However, this field v-bar is nonlocal and leads to unacceptable consequences in specific situations. Hence we can state with confidence that a dissipative contribution to the mass flux is not possible.

18 pages; submitted to Phys. Rev. E

References in corpus (1)

• The structure of shock waves as a test of Brenner's modifications to the Navier-Stokes equations

Cited by in corpus (13)

• Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics
• Extra mass flux in fluid mechanics
• Measure-valued solutions to the complete Euler system revisited
• Gradient and GENERIC evolution towards reduced dynamics
• Galilean relativistic fluid mechanics
• Holographic fluids: a thermodynamic road to quantum physics
• Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations
• A convective model for poro-elastodynamics with damage and fluid flow towards Earth lithosphere modelling
• On the thermodynamics of volume/mass diffusion in fluids
• Visco-elastodynamics at large strains Eulerian
• Staggered Schemes for Fluctuating Hydrodynamics
• Recasting Navier-Stokes Equations
• A new Eulerian model for viscous and heat conducting compressible flow