Implementation of sorption hysteresis in multi-Fickian moisture transport

In the cellular structure of wood, bound-water diffusion and water-vapor diffusion interact via sorption in a complex moisture-transportation system. At low relative humidity, moisture transport may be modeled by a Fickian diffusion equation to a good approximation. At higher relative humidity, slow sorption and faster bound-water diffusion cause effects, which have been referred to as non-Fickian or anomalous, as they cannot be modeled by one Fickian diffusion equation. Previous research has demonstrated that a set of coupled diffusion equations, namely the multi-Fickian model, can represent this behavior. The multi-Fickian model describes the combined transport of bound water and vapor and their interaction through sorption. The bound-water concentration is also influenced by sorption hysteresis. In the worst case, sorption hysteresis may result in deviations of up to 30-35% in moisture content. Hence, for a precise moisture content computation, sorption hysteresis must be taken into account. The present paper explains the relation between sorption hysteresis and multi-Fickian moisture transport, and clarifies how models for the two phenomena are coupled. To illustrate the effects, a finite element simulation, which is based on the combined model, is presented.