Thermodynamically Admissible Diffuse Interface Model for Nanoscale Transport of Dense Fluids

TL;DR

This paper introduces an improved diffuse interface model for nanoscale fluid transport that accurately captures interfacial heat and mass transfer by incorporating higher-order corrections and density-gradient-dependent properties.

Contribution

The work develops a thermodynamically consistent diffuse interface model with enhanced interface resistance representation, fitting parameters to kinetic theory solutions for better nanoscale transport predictions.

Findings

Accurately models interfacial heat transfer and evaporation.

Improves upon conventional NSK models with higher-order corrections.

Validates model against kinetic theory solutions.

Abstract

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to accurately capture transport phenomena across extremely thin interfaces due to underestimation of interface resistances. In this work, we improve the NSK model by adding a production term in the momentum equation based on higher-order corrections. To enhance interface resistances, viscosity and thermal conductivity are made dependent on the density gradient, increasing resistance only within the interface region. The gradient-based coefficients are determined by fitting to solutions of the Enskog-Vlasov equation for Couette flow (see Struchtrup and Frezzotti, 2022). Applying these fitted equations to pure heat conduction and planar evaporation problems shows that the model accurately captures interfacial transport, making it a useful tool for studying nanoscale evaporation, thermal management, and droplet dynamics on solid surfaces.