A thin liquid film drains radially off the surface of a horizontal, rotating substrate. Evaporation of solvent from the film increases the fluid viscosity and reduces the radial outflow. Governing equations are developed for the shape of the film interface as a function of space and time, as well as the axisymmetric solvent‐concentration distribution, for both unit order and large Peclet numbers. The numerical solution of these equations elucidates how a spinning film with either a corrugated or a flat free surface evolves over time in the presence of a time‐varying concentration (and viscosity) field. A correlation for the final film thickness in terms of the physical variables of the system is deduced from the governing equations, the result of which shows good agreement to published experimental results.