Solid-state fermentation is different from the more well known process of liquid fermentation because no free flowing water is present. The technique is primarily used in Asia. Well-known products are the foods tempe, soy sauce and saké. In industrial solid-state fermentation, the substrate usually consists of loose substrate particles, although in research situations agar like substrates are also common. Solid-state fermentations cannot be mixed as easily as liquid fermentations. Because of this, it is difficult to maintain the temperature in the fermentation at an acceptable level and to prevent differences in substrate availability throughout the solid material. An advantage of solid-state fermentation is that the process is cheap, and that products are in some cases easier to separate from the substrate than in liquid. Because of this, the technique is economically interesting. The process has not been studied as extensively as liquid fermentation. This thesis extends the available knowledge by providing several mathematical models for both biological and physical processes that occur in aerated packed beds.In aerated packed beds, the metabolic heat that is released in the microbial process is removed by blowing air through the packed material. The effectiveness of the aeration is the result of both the heat uptake capacity of the air itself and of the evaporation of moisture to the air. In fact, the evaporation contributes more to the heat removal than the air itself. A side effect of the evaporation is that the decreasing moisture level in the substrate can become limiting for the microbial process.In this thesis, the growth of Aspergillus oryzae and Aspergillus sojae, two related species of fungi, in an aerated packed bed of moist wheat kernels is studied. The study deals with both the microbial and physical aspects of the system.Many different types of substrate have been used in studies on solid-state fermentation. Prior to starting the work on the mathematical models, we checked if the fermentation results of A. oryzae on several types of wheat matched, The check was done by matching respiration profiles for several types of wheat and two pretreatment methods. It turned out that considerable differences between the pretreatment methods can exist, which indicated the importance of using the exact same type of substrate and pretreatment in experiments that are to be compared.No accurate model description of the microbial aspects of SSF is available yet. Because the focus of the major part of the thesis is on deriving model descriptions for the physical aspects of cooling and drying-out in aerated packed beds, it was decided that using a temperature-response model for the description of heat development would incorporate too many uncertainties in the overall packed-bed model. The heat development in the further studies presented was therefore based on fitted oxygen consumption profiles instead of on modelled microbial growth.For the validation of the physical models in this thesis, experiments were carried out in a packed bed of approximately 50 cm height. This packed bed was insulated thermally, and offered the possibility of taking online temperature measurements and sampling the moisture content. The models that were derived to describe the changes in growth conditions in the packed bed in time and space were based on well-known physical relations. All physical models are composed of heat- and mass balances. As described above, the temperature dependence of the fungus was neglected, and the metabolic heat development was incorporated in the balances by means of fitted respiration profiles. This way, inaccuracies in the heat production in the physical model were prevented, allowing the focus on the correct description of heat and mass transfer.The first model presented was based on an existing model, which overestimated the drying out of the solid material. This overestimation was due to the assumption of constant saturation of the gas phase with water vapour. The overestimation of the drying out meant that the assumption of vapour saturation needed to be adjusted. Heat and mass transfer coefficients were determined for the substrate involved, and besides this water activity was introduced as a factor that limited the evaporation of water from the substrate. The addition of water activity was of great influence on the model results.The insight in the effect of local water activity on the fermentation was the onset for a study on the response of fungi to changing water activity. A system was designed that allowed the dynamic response of the fungus on decreasing water activity to be measured. The experimental set-up was based on isothermal experiments that were slowly dried out by blowing dry air through them, with simultaneous experiments carried out at aw ~ 1 for comparison with the response to the drying out. Considering the fact that all studies on water activity that preceded this approach were based on static and artificial conditions, this set-up is more similar to the actual conditions in a packed-bed fermentation.Contrary to the expectations, the system that was dried out showed a decreased fungal growth rate when the water activity in the substrate was still the same as it was in the reference experiment. We checked two possible causes for this phenomenon. Moisture gradients in the particle were ruled out, because these were too small to be able to cause the difference in growth rate. We found that there is most likely a region of very cold substrate material due to wet-bulb cooling. Wet-bulb cooling is a phenomenon in which the evaporation of water from a system to a passing airflow allows the system to cool to temperatures below the temperature of the air. Because we used dry air in our experiment, the effect was too large to be compensated through conduction. An estimated 5% of the bed could not be fermented because of the low temperature. For a successful series of experiments, we need to obtain drying with a 100% constant bed temperature. For such a series, a good comparison of the effect of drying on fungal behaviour will be possible.During the experiments in the packed-bed involving Aspergillus oryzae strong shrinkage of the packed-bed occurred because the fungus tied the substrate particles together. Because of the shrinkage, the aeration lost effectivity and the fermentation results were suboptimal. A model was designed to describe the amount of shrinkage, based on the decrease in water content in the bed. The validation of this model could not be performed with A. oryzae, because it was impossible to carry out controlled fermentations with this fungus. Therefore, A. sojae was used, which has the same growth characteristics as A. oryzae, except for the formation of substrate ties. The model on shrinkage offers a good prediction of the shrinkage that is expected with the combined effect of fungal growth and dehydration. 1f in industrial fermentations a different shrinkage pattern is observed, this is an indication that there is channel formation somewhere in the bed. This observation can be than followed by for instance a mixing event, improving the overall performance of the fermentation.In the final chapter of this thesis, an overview of the work that could possibly offer further improvements to the present models is given. It was concluded that the modelling of the microbial aspects offer the biggest chances for success in this respect, since this aspect has of yet been modelled less accurately than the physical part.