Conservation Equations for Chemical Elements in Fluids with Chemical Reactions

It is well known that when chemical reactions occur, the masses of the participating molecules are not conserved, whereas the masses of the nuclei of the chemical elements constituting these same molecules, are conserved. Within the context of non-equilibrium thermodynamics, the first fact is expressed by the differential balance equations, for the densities of the chemically reacting molecules, having a non zero source term. At the same time the conserved quantities like the total mass, charge and energy obey differential conservation equations, i.e with zero source term. In this paper, we show that in fluids with chemical reactions occurring in them, there are additional conserved quantities, namely densities associated to the fact that the masses of the chemical elements are conserved. The corresponding differential conservation equations are derived. The found out conserved densities, one for each involved chemical element are shown to be linear combinations of the densities of those reacting molecules containing the element, weighted with the number of atoms of the element in the species. It is shown that in order to find the conserved densities, it is not necessary to know explicitly the reactions taking place. Some examples are provided.