Non-equilibrium flow of van der Waals fluids in nano-channels

The Enskog-Vlasov equation provides a consistent description of the microscopic molecular interactions for real fluids based on the kinetic and mean-field theories. The fluid flows in nano-channels are investigated by the Bhatnagar-Gross-Krook (BGK) type Enskog-Vlasov model, which simplifies the complicated Enskog-Vlasov collision operator and enables large-scale engineering design simulations. The density distributions of real fluids are found to exhibit inhomogeneities across the nano-channel, particularly at large densities, as a direct consequence of the inhomogeneous force distributions caused by the real fluid effects including the fluid molecules' volume exclusion and the long-range molecular attraction. In contrast to the Navier-Stokes equation with the slip boundary condition, which fails to describe nano-scale flows due to the coexistence of confinement, non-equilibrium, and real fluid effects, the Enskog-Vlasov-BGK model is found to capture these effects accurately as confirmed by the corresponding molecular dynamics simulations for low and moderate fluid densities.