Inconsistency of a dissipative contribution to the mass flux in hydrodynamics

TL;DR

This paper rigorously examines the theoretical possibility of dissipative contributions to mass flux in hydrodynamics, concluding such contributions are incompatible with fundamental physical principles and thus not feasible.

Contribution

The study develops a comprehensive thermodynamically consistent framework and demonstrates that dissipative mass flux contributions are generally incompatible with core physical principles.

Findings

Dissipative mass flux contributions are ruled out by fundamental principles.

A new proposed dissipative term involving a nonlocal velocity field is physically unacceptable.

All previously considered dissipative flux scenarios are incompatible with the principles examined.

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.