Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.
The Helmholtz free energy is essential to the modelling of
multiphase flow with the diffuse interface formalism. In models
where it is a good approximation to let the temperature
be constant and uniform, a simplified calculation of the
Helmholtz free energy is performed, that leaves a number of
functions of temperature unspecified (one per chemical component,
in case of mixtures). If the model is to include the
energy balance equation, i.e., account for flow with variable
temperature, then the Helmholtz free energy must include
these temperature dependent terms. This paper is an exposition
of the determination of such terms, where three types
of molecules are considered: (i) single conformation, (ii) multiple
conformation, and (iii) polar. A specific example for
each case is included: methane, n-pentane, and water. The
Helmholtz free energy of fluid mixtures is also considered.