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Roll-to-roll nanoimprint lithography (RTR-NIL) is a low-cost and continuous fabrication process for large-area functional films. However, the partial ultraviolet (UV) resin filling obstructs the ongoing production process. This study incorporates UV resin filling process into the nanopillars and nanopores by using RTR-NIL. A multiphase numerical model with a sliding mesh method is proposed in this study to show the actual phenomena of imprint mold rotation and feeding of UV resin on the polyethylene terephthalate (PET) substrate. The implementation of UV resin filling under environmental conditions was performed by utilizing the open-channel (OC) boundary conditions. The numerical model was solved by using the explicit volume of fluid (VOF) scheme to compute the filling on each node of the computational domain. The effects of different processing parameters were investigated through the proposed numerical model such as imprinting speed (IS), contact angles (CAs), viscosity, initial thickness of the PET, and supporting roll diameter. A good agreement was found between numerical simulations and experimental results. The proposed numerical model gives better insights of the filling process for the mass production of functional surfaces with nanopillars and nanopores patterns for different applications on an industrial scale.