Non-equilibrium evaporation of Lennard-Jones fluids: Enskog-Vlasov theory and Hertz-Knudsen model

TL;DR

The paper tackles non-equilibrium evaporation of Lennard-Jones fluids and limitations of classical Hertz-Knudsen and Enskog-Vlasov approaches for real fluids. It develops a simplified molecular kinetic model based on the Enskog-Vlasov framework with a calibrated equation of state $p = n k_{\rm B} T (1 + \rho b \chi) - a n^{2}$ and a collision term $\Omega = J_S + J_e$, enabling efficient simulations. The model reproduces the liquid–vapour coexistence curve, transport coefficients, vapour pressure, and surface tension for Argon with MD/experimental agreement, and reveals non-Maxwellian velocity distributions adjacent to the liquid–vapour interface under evaporation. This provides a practical computational tool for real-fluid non-equilibrium evaporation and can be extended to other noble gases and potentially to more complex fluids.

Abstract

Enskog-Vlasov equation is currently the most sophisticated kinetic model for describing non-equilibrium evaporative flows. While it enables more efficient simulations than the molecular dynamics (MD) methods, its accuracy in reproducing the flow properties of real fluids is limited by both the assumptions underlying the Vlasov forcing term and the approximation introduced by the Enskog collision term for short-range molecular interactions. To address this limitation, this work proposes a molecular kinetic model specifically designed for real fluids, with the Lennard-Jones fluids as an example. The model is first applied to evaluate the equilibrium characteristics of a liquid-vapour system, including the liquid-vapour coexistence curve, transport coefficients, vapour pressure, and surface tension coefficient. The results show excellent agreement with the MD simulation and experimental data. Furthermore, the model is used to investigate non-equilibrium evaporation, with a particular focus on the velocity distribution function adjacent to the liquid-vapour interface. The results confirm that deviations from the Maxwellian distribution persist in the vapour region, indicating limitations of the classical Hertz-Knudsen relation under pronounced non-equilibrium conditions. This work represents a critical step towards the development of an accurate and efficient computational framework for modelling non-equilibrium liquid-vapour flows for real fluids, with direct relevance to practical applications such as flow cooling.

Figures (5)

• Figure 1: Schematic of the simulation setup, with boundary conditions indicated in the figure. Periodic boundary conditions are applied for equilibrium cases, while absorbing boundary conditions are used for non-equilibrium cases.
• Figure 2: Equilibrium distributions of the number density at various temperatures.
• Figure 3: Comparison between the results obtained from kinetic model and experiment under different temperatures: (a) reduced number density; (b) shear viscosity and thermal conductivity; (c) vapour pressure; (d) surface tension coefficient. For better illustration, the liquid–vapour coexistence curve obtained from the original EV equation is shown in the figure 3(a). In figure 3(b), the results obtained from kinetic model are denoted by circles and squares, while the experimental data is denoted by solid lines.
• Figure 4: Comparison of transport coefficients (a, b) and pressure (c) at various temperatures and densities for the liquid bulk. The kinetic model results are shown by the symbols, while the experimental data are represented by the lines.
• Figure 5: (a) Profiles of number density, temperature, and bulk velocity during evaporation into vacuum; (b) Velocity distribution functions at different positions: $x = 11, 13, 14.5, 15$ and $17$. These positions are also denoted by black hollow stars in the figure (a).