A thermodynamic framework for the thermal conductivity of dense fluids

TL;DR

The paper addresses predicting transport coefficients in dense fluids, focusing on thermal conductivity. It develops a thermodynamic transition-rate framework that generalizes lattice-based ideas to continuous space and yields the ratio $\lambda/\lambda_{\rm id}$ as a function of equilibrium properties, including non-extensive Massieu corrections $\Delta S$. The main result is the explicit formula $\lambda/\lambda_{\rm id} = \frac{4 T^2}{15 k_B^2 T_{\rm id}^2}(C_V \mu_{TN} + T^2 \mu_{TT}^2)$, together with explicit expressions for $\mu_{TN}$, $\mu_{TT}$, and $T_{\rm id}$, and its validation for hard-sphere and Lennard-Jones fluids, plus argon data. This provides evidence for a universal link between dense-fluid transport and equilibrium thermodynamics, enabling predictions from an equation of state without empirical transport-modeling parameters and suggesting extensions to viscosity and diffusion.

Abstract

A thermodynamic framework that predicts the thermal conductivity $λ$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in continuous space, an expression for the ratio $λ/λ_{\rm id}$ is derived, where $λ_{\rm id}$ is the dilute-gas value; the ratio depends solely on equilibrium thermodynamic properties and is therefore directly computable from any equation of state. The resulting formula quantitatively reproduces simulation data for hard spheres throughout almost the entire fluid range, and captures the behavior of Lennard-Jones fluids in the supercritical region where thermodynamic fluctuations remain moderate. Comparison with experimental data for argon, reported by other authors, also shows good agreement. These results provide evidence that transport coefficients of dense fluids can be expressed as their dilute-gas values multiplied by a universal function of equilibrium thermodynamic properties.

Figures (3)

• Figure 1: Relative thermal conductivity $\lambda/\lambda_{\rm id}$ for a hard-sphere fluid as a function of density $\rho$. The concentration units are $d^{-3}$, with $d$ the particle diameter. Data points: numerical results from Ref. pieprzyk3. Curve: Eq. \ref{['e.lambdaHS']}. The vertical dotted line marks the fluid phase limit at $\rho=0.939$.
• Figure 2: Thermal conductivity $\lambda$ of the LJ fluid as a function of density $\rho$ for several temperatures $T$ (LJ units). Symbols: simulation data from Ref. galliero. Curves: Eq. \ref{['lambda']} evaluated using the EoS of Ref. pieprzyk.
• Figure 3: Thermal conductivity $\lambda$ of supercritical Argon as a function of density $\rho$. Symbols: experimental data from Ref. mardolcar ($T =$ 378 K and 429 K) and Ref. sun ($T=$ 300 K, 320 K and 340 K). Curves: Eq. \ref{['lambda']} evaluated using the LJ EoS of Ref. pieprzyk.