The interplay of non-equilibrium effect, surface-confinement, and real gas phenomena significantly influences heat and mass transfer in nanoscale applications such as membrane technologies, thermal management of nano-systems, and gas separation. Despite their pivotal roles, addressing these factors concurrently poses a substantial challenge in theoretical and computational studies.

This talk will introduce an innovative kinetic model for van der Waals fluids confined in nano-spaces, which adeptly captures the heat and mass transfer behaviours over a broad range of fluid densities, spanning from the molecular to continuum scales. Derived from a self-consistent hierarchy addressing both gas-gas and gas-solid interactions at the nanoscale, this model takes into account the non-negligible sizes of both gas and solid molecules and the role of gas-gas and gas-solid attractions in phase change and gas adsorption. To account for the different efficiency of momentum and energy exchange between gas and solid molecules, a double distribution function model is further developed. This kinetic model assumes static and fixed solid molecules at an effective boundary location, where the evolution of momentum and energy is described by a velocity distribution function and a total energy distribution function, respectively, thus allowing for separate control over momentum and energy accommodations between gas and solid molecules. The Chapman-Enskog expansion validates the thermodynamic consistency of the present kinetic model as the Navier-Stokes equations with a van-der-Waals-type equation of state is recovered in the continuum limit. Additionally, correct transport coefficients, including shear and bulk viscosities and thermal conduction, are determined based on the relationship between these coefficients and the relaxation times of momentum and energy. The kinetic model is validated by molecular dynamics simulations.