The Conservation of Momentum and Energy in Open Systems. Diffusional Approach to the Mass Transport in Solids

The Navier‐Stokes equations do not describe the mixing of mass in a continuous medium. In this work the motion of a mixture in which mass flows from the region of higher mass density to the lower one is analyzed. In such a case the mass is transported as a result of pressure, viscosity, external forces, and diffusion. The motion of a continuous medium in which diffusional flux of mass occurs is considered. The momentum balance of a mixture in which diffusion is considered causes a new term to appear in the Navier‐Stokes equation. Apart from terms responsible for pressure, viscosity, and external forces there is the diffusional one. It is analyzed whether the internal energy of mixture depends on diffusion. The conclusion is that diffusional flux does not change 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.