THE CONSERVATION OF MOMENTUM AND ENERGY IN OPEN SYSTEMS - DIFFUSIONALAPPROACH TO THE MASS-TRANSPORT IN SOLIDS

The Navier-Stokes equations do not describe the mixing of mass in a co ntinuous medium. In this work the motion of a mixture in which mass fl ows from the region of higher mass density to the lower one is analyze d. In such a case the mass is transported as a result of pressure, vis cosity, external forces, and diffusion. The motion of a continuous med ium in which diffusional flux of mass occurs is considered. The moment um balance of a mixture in which diffusion is considered causes a new term to appear in the Navier-Stokes equation. Apart from terms respons ible for pressure, viscosity, and external forces there is the diffusi onal one. It is analyzed whether the internal energy of mixture depend s on diffusion. The conclusion is that diffusional flux does not chang e the internal energy of mixture. The specific initial conditions for pure diffusion are defined and it is elucidated that the diffusion is described by the well-known equation of diffusion.