A new steady-state icing model is presented Which explicitly takes into account the dynamics and thermodynamics of a liquid film on the ice accretion surface under high liquid fluxes. The film is generated by excess unfrozen impinging liquid, is set in motion by the aerodynamic shear stress, and is eventually shed. In order to keep the model simple, it is formulated for a rotating cylinder subjected to a continuous supercooled freshwater spray. The model is used to explore the physics of the liquid film, and confirms that the film is thin and laminar except possibly under extreme liquid fluxes. It predicts supercooling of several degrees at the film surface, in agreement with recent observations. Further, the model is used to investigate the dependence of the icing rate on the following parameters: liquid water content, air temperature, wind speed, spray temperature, cylinder diameter, and heat transfer coefficient.