Biological contamination is a real, perhaps inevitable, event aboard inhabited orbital vehicles. A major form of this contamination is fungal growth on exposed surfaces. While numerous models exist for microbial growth on air-water and surface-water interfaces, no models are available for fungal growth on air-solid surfaces and, evidently, none have been developed for a surface that is non-nutritive, e.g. a surface that not agar or a food stuff. We develop and present a model of fungal growth on air-exposed, non-nutritive solid surfaces. A unique feature of this testable model is that the development of a fungal mycelium can facilitate its own growth by condensation of water vapor from its environment directly onto fungal hyphae. The fungal growth rate is limited by the rate of supply of volatile nutrients and fungal biomass is limited by either the supply of non-volatile nutrients or by metabolic loss processes.