Multiphase model for nanoimprint lithography

Abstract Reynolds’ lubrication theory is extended to capture two-fluid dynamics based on relative permeability concepts used for multiphase flow in porous media. A reduced-order model of gas dissolution is constructed by combining two-phase lubrication theory with Henry’s law and analytic approximations of surface area and diffusion length. The governing equations are solved as a thin-shell, finite-element model that can be used to investigate process sensitivities to a variety of technologically important parameters. Results are compared to those from related computationally intensive alternative formulations and to experimental flow visualizations to demonstrate its efficacy in modeling large area, many-drop processes and capturing the gas dissolution behavior observed in practice.