In the present work we derive the volume continuity equation and demonstrate its use to define the volume frame of reference in the multicomponent, compressible systems. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass...

A modification of the classical Navier–Stokes equations has recently been proposed by Brenner [Is the tracer velocity of a fluid continuum equal to its mass velocity? Phys. Rev. E 70 (2004) Art. No. 061201; Kinematics of volume transport, Physica A 349 (2005) 11–59; Navier–Stokes revisited,...