Implementation of sorption hysteresis in multi-Fickian moisture transport

Henrik Lund Frandsen, Staffan Svensson

Research output: Contribution to journalJournal articleResearchpeer-review


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 humidities, moisture transport may be modeled by a Fickian diffusion equation with a good approximation. At higher relative humidities, 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.
Original languageEnglish
Issue number6
Pages (from-to)693-701
Publication statusPublished - 2007


  • Hysteresis
  • Moisture transport
  • Multi-Fickian
  • Multi-phase
  • Non-Fickian
  • Sorption


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