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 diffusion, heat flow, etc. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the translation of the Newton's discrete mass-point molecular mechanics into continuum mechanics and the use of the Cauchy linear momentum equation of fluid mechanics and Navier-Lamé equation of mechanics of solids.
Our proposed modifications of Navier-Lamé and energy conservation equations are self-consistent with the literature for solidphase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport. We do show that the local diffusion processes do not change the centre of mass of the system and that the stress and viscosity depend only on the local volume velocity.