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This paper describes a model for the penetration of fluid into a moving paper web in the application nip of a film coater. One-dimensional and two-dimensional solution methods are developed and compared. The two-dimensional model is solved using a Galerkin finite element method with a free surface algorithm. The depth of fluid penetration into the paper web increases with increase in applied pressure, paper permeability and exposure time. The fluid penetration depth decreases as the porosity or solution viscosity increases. The functional relationship among these variables depends on the profile of the pressure applied at the surface of the paper sheet. For the case of uniform paper permeability and no air compression in the web, the two-dimensional model gives similar results to the one-dimensional model.