Thermomechanical Approach to Calculating Mechanical Stresses in Inhomogeneous Fluids and Its Applications to Ionic Fluids

TL;DR

This paper introduces a thermomechanical method for calculating stress tensors in inhomogeneous fluids, including ionic fluids, offering a new perspective and applications to nanoscale confinement and fluctuating systems.

Contribution

It develops a thermomechanical approach based on thermodynamic potential invariance, providing an alternative to covariant methods and extending to fluids with vector order parameters.

Findings

Reproduces known results in inhomogeneous fluid theory

Derives new expressions for stress tensors in ionic fluids

Analyzes disjoining pressure in nanoscale slit pores

Abstract

This extended article presents a thermomechanical approach for calculating the stress tensor from the thermodynamic potential of inhomogeneous fluids and some applications to ionic fluids. The technique, based on the invariance of the fluid's thermodynamic potential with respect to spatial transformations of translation and rotation, offers an alternative to the general covariant approach developed by two of the authors. We apply this technique to both pure mean-field theories of fluids in general and a theory that includes thermal fluctuations of the order parameter, using the example of ionic fluids. Additionally, we apply the thermomechanical approach to fluid models with vector order parameters, such as liquid dielectrics. For this case, we obtain a general expression for the stress tensor. Furthermore, we discuss specific issues related to the calculation of disjoining pressure in ionic fluids confined in nanoscale slit-like pores with metal or dielectric walls, using the Coulomb gas model. To test the robustness of the proposed approach, we reproduce a number of known results from the statistical theory of inhomogeneous fluids and obtain several new ones.