The interaction of thin evaporating fluid films with solids is studied using the example of water on LiTaO3 (LTO). Adsorption energies are computed by ab initio density functional theory (DFT) and used to calculate the Gibbs free energy of adsorption of water on LTO. Integrating the disjoining pressure, consisting of molecular and structural components, with respect to film thickness gives an expression for the Gibbs free energy. In this way, parameters for the disjoining pressure can be calculated by fitting its integral to the Gibbs free energy computed by ab initio DFT. A combination of literature-known models for spin drying and evaporation is utilized to describe the temporal evolution of the water layer. The vapor above the water layer is modeled by diffusion and a mass balance is applied at the water-air interface. For thick initial layers, an analytical approximation is derived which only depends on fluid and ambient conditions but not on the substrate properties.