Analysis of transport phenomena with finite speed of perturbations propagation

Abstract

Known governing equations for transport phenomena predict infinite speed of perturbations propagation. From molecular point of view, infinite speed of perturbations propagation does not seem to be a reasonable physical assumption, because for instance in a gas, any perturbation propagates as a result of molecules collisions. At the same time, governing equations for transport phenomena assuming infinite speed of propagation have been obtained long ago using the molecular-kinetic approach. Such an internal contradiction requires an additional molecular-kinetic analysis whose aim is to answer the following questions: Is the speed of perturbations propagation in transport phenomena infinite or finite? If it is finite, why the known equations being based on molecular-kinetic considerations, predict infinite speed of propagation? If the speed of perturbations propagation is finite, what are the new kinetic and governing equations satisfying this condition, and how they relate to the known equations? In the paper, solution to these problems is proposed. It is based on analysis of Boltzmann equation applied to molecular interaction between non-equilibrium perturbed subregion and non-perturbed subregion which is in equilibrium. A special averaging procedure over positive velocities of molecules crossing the border of perturbed subregion, is developed. It allows to formulate equations describing transport phenomena with finite speed of perturbations propagation which is determined as mean positive transversal molecular velocity. It is shown that classical equations for transport phenomena are a particular case of these new equations valid only for steady state conditions.