Toward a logistic model of dynamic mold growth on wood

Abstract

This paper deals with mathematical modeling of mold growth on wood. The logistic growth equation is used to model mold growth phenomena in changing environmental conditions. Microscopic mold coverage fraction is used in the logistic equation to represent mold development on a material surface over time. The current state-of-the-art dynamic Finnish mold growth model is used as the reference model for development of the logistic mold growth model. The optimal values of mold growth coefficient are estimated by simulations of mold growth under constant environmental conditions and by finding the best agreement with the Finnish mold growth model using mathematical optimization methods. It is shown that the mold growth coefficient can be approximated as a function of relative humidity, temperature, wood species and the quality of the surface. The model parameters are then verified by a comparison with the Finnish mold growth model. In this case, cyclic step changes of constant relative humidity are used. Finally, the logistic mold growth model is compared with published experimental observations of mold growth. The discrepancy of mold growth models and experimental mold growth data, and possible improvements are discussed.