A new thermodynamic function for binary mixtures: the co-molar volume

We have developed a new theory relating partial molar volumes of binary mixtures to the specific (Voronoi) volumes. A simple relation gives new insight into the physical meaning of partial molar volumes in terms of the actual volumes occupied by the molecules. Partial molar quantities are defined through the use of the Euler theorem for homogeneous functions. These properties have been in use for a long time, despite the fact that they do not give an intuitive picture of the properties they are to represent. For instance, the partial molar volume of a given component in a mixture is the change in the total volume with a change in composition, hence it represents the derivative of a volume. The molar volume is a measurable property in the laboratory, and as such a body of thermodynamics, but the derived partial molar volume is not a direct measure of the physical volume occupied by the added component. On the other hand, the physical volume can be computed using e.g. molecular dynamics simulations by Voronoi tesselation. We shall call this volume the specific volume. To bridge the partial molar volume and the specific volume, we define a single new thermodynamic variable - the co-molar volume - thus bringing the latter into thermodynamics. We demonstrate this bridge through molecular dynamics simulations. The co-molar volume is closely related to the co-moving velocity defined in immiscible two-phase flow in porous media.