Thermodynamically consistent bi-velocity mass transport phenomenology

A thermodynamically consistent framework is developed to combine the convection and dissipative contributions with the mass and energy fluxes in multicomponent materials. The method, which is known as bi-velocity or Darken method, is based on the postulate of the unique (independent on the frame of reference) transport of the mass due to diffusion. In this work we merge: (i) the combined statements of the first and second laws of thermodynamics (linear irreversible thermodynamics) and (ii) the Euler and Liouville theorems. We derive an expression for the rate of the entropy production that does not depend on the frame of reference and is always positive. We show that the derived set of partial differential equations describing the mechanochemical mass transport is thermodynamically consistent and can be used in advanced modeling.