A simple statistical-mechanical interpretation of Onsager reciprocal relations and Derjaguin theory of thermo-osmosis

TL;DR

This paper uses statistical mechanics to derive and interpret the Onsager reciprocal relations and Derjaguin theory of thermo-osmosis at a molecular level, providing new insights into interfacial heat and particle fluxes.

Contribution

It offers a molecular-level derivation and interpretation of thermo-osmotic and mechano-caloric transport coefficients, connecting macroscopic thermodynamics with microscopic models.

Findings

Derived expressions for transport cross-coefficients using statistical mechanics.

Demonstrated the equality of thermo-osmotic and mechano-caloric coefficients.

Provided a simple interpretation linking interfacial heat and particle fluxes.

Abstract

The application of a temperature gradient along a fluid-solid interface generates stresses in the fluid causing "thermo-osmotic" flow. Much of the understanding of this phenomenon is based on Derjaguin's work relating thermo-osmotic flows to the mechano-caloric effect, namely, the interfacial heat flow induced by a pressure gradient. This is done by using Onsager's reciprocity relationship for the equivalence of the thermo-osmotic and mechano-caloric cross-term transport coefficients. Both Derjaguin theory and Onsager framework for out-of-equilibrium systems are formulated in macroscopic thermodynamics terms and lack a clear interpretation at the molecular level. Here, we use statistical-mechanical tools to derive expressions for the transport cross-coefficients and, thereby, to directly demonstrate their equality. This is done for two basic models: (i) an incopressible continuum solvent containing non-interacting solute particles, and (ii) a single-component fluid without thermal expansivity. The derivation of the mechano-caloric coefficient appears to be remarkably simple, and provides a simple interpretation for the connection between interfacial heat and particle fluxes. We use this interpretation to consider yet another example, which is an electrolyte interacting with a uniformly-charged surface in the strong screening (Debye-H\"uckel) regime.