Inconsistency of a dissipative contribution to the mass flux in hydrodynamics

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. However, this field v 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.