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Graphical abstract Highlights • Liquid permeability through a nanopore was calculated via molecular dynamics. • The permeability was affected by the interaction between molecules and pore wall. • A new viscous flow model in nano-scale pore was proposed. Abstract Liquid-phase permeation was simulated in nano-scale pores via non-equilibrium molecular dynamics (NEMD). Two virtual cristobalite membranes were prepared with pore diameters of 1.7 and 2.4 nm. NEMD simulation system was employed as an ideal experimental system to calculate the affinity between liquid argon molecules and membrane materials during permeation. When argon-membrane interactions decreased, permeation flux increased. With a smaller interaction the permeation flux exceeded the value posited by the Hagen-Poiseuille theorem, while a lower-than-expected level of permeation flux was observed when the interactions with the pore surface became greater. We focused on the viscosity change of liquid in a nano-scale pore due to attractive or repulsive interactions with the pore surface, and a mathematical model for describing the liquid permeation flux in a nanopore was proposed by solving the Navier-Stokes equation by considering the viscosity distribution of a liquid confined in a pore. The local viscosity of a liquid confined in a pore was calculated from the total potential distribution in the pore based on the Andrade equation. The predicted level of permeation flux, the velocity profiles of different pore sizes, and the interactions of the pore models all showed good agreement with the NEMD simulation results. [ABSTRACT FROM AUTHOR]