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

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 42; no. 10; p. 136
• Main Author: Farago, Oded
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V
• Subjects: Biological and Medical Physics; Biophysics; Complex Fluids and Microfluidics; Complex Systems; Condensed matter physics; Fluxes; Heat transmission; Nanotechnology; Osmosis; Physics; Physics and Astronomy; Polymer Sciences; Reciprocity; Regular Article; Soft and Granular Matter; Surfaces and Interfaces; Temperature gradients; Thin Films; Transport properties; Soft Matter: Interfacial Phenomena and Nanostructured Surfaces
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2019-11898-3

. 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-Hückel) regime. Graphical abstract