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

• A simplified kinetic model is developed to accurately simulate non-equilibrium evaporative flow of Lennard-Jones fluids. • The model successfully reproduces key equilibrium properties, including the liquid-vapour coexistence curve, transport coefficient, vapour pressure, and surface tension. • The velocity distribution function reveals significant non-Maxwellian features adjacent to the liquid-vapour interface, suggesting the breakdown of the classical Hertz–Knudsen relation under strong evaporation conditions. 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.