A local superposed-constituent volume-fraction mixture theory based on relative motion (Q1804470)

Whereas classical mixture theories use the concept of mass fractions (or concentrations) of the constituents and the concept of barycentric motion of the mixture as a whole and are mostly restricted on Eulerian field representation, here the author develops a more general framework. The mixture motion is defined by the fundamental assumption on the dependence of the mixture velocity on the velocities of components. All field quantities can be related to the reference region of the mixture, to the reference regions of constituents, to the regions actually occupied by the constituents, and to the actual region of the mixture. The transformations between these representations are derived by means of the respective velocities and deformation gradients. The distribution of the components is characterized by corresponding volume fractions. On this base several forms of general balance equations are introduced and then specialized in the balances of mass, momentum, angular momentum, energy and entropy. Thus comfortable start conditions for detailed investigations of mixture problems are stated. The highly abstract presentation given here is suitable rather for the pretentious theoretician than for the engineer or chemist interested in the theory.