Thermomechanical Approach to Calculating Mechanical Stresses in Inhomogeneous Ionic Fluids

This extended article presents a thermomechanical approach for calculating the stress tensor from the thermodynamic potential of ionic fluids. Our technique, which is based on the invariance of the thermodynamic potential with respect to spatial transformations of shear and rotation, offers an alternative to the general covariant approach recently developed by two of us. We apply this technique in both pure mean field theories of ionic fluids and in a theory that includes thermal fluctuations of the electrostatic potential, using variational field theory. We also apply the thermomechanical approach to fluid models described by vector order parameters, such as liquid dielectrics, and obtained for this case a general expression for the stress tensor. Additionally, we discuss specific issues related to the calculation of disjoining pressure in ionic fluids confined in nanoscale slit-like pores with conductive or dielectric walls.