# 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.

## Key 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.