A theory of mixtures

This paper is concerned with a dynamical theory of mixtures, composed of n reactive constituents in relative motion to each other. The theory is developed in terms of the constituent ingredients using a balance of energy and an entropy production inequality for each constituent of the mixture, together with invariance requirements under superposed rigid body motions of the whole mixture. The balance of energy and the entropy production inequality for each of the constituents, which include contributions arising from interactions, combine to yield a single energy equation and a single entropy production inequality in terms of the ingredients of the mixture as a whole; the relations between the thermodynamical variables of the mixture and those of its constituents depend, in general, on the past history of the temperature and the kinematic variables. Full thermodynamical restrictions are deduced, and the theory is applied to the special case of a mixture of two ideal fluids.