Weber et al. (1999) quotes various values of the porosity ^for various different substrates: 0.31 for oats, 0.48 for hemp impregnated with a nutrient solution, 0.47 for impregnated bagasse, and 0.41 for impregnated perlite.
Note that the porosity of the bed is not constant during the fermentation, since the microorganism will tend to fill the inter-particle spaces. This is especially true in static beds during the growth of a mycelial organism, where aerial hyphae extend into the void spaces. Although this has received some attention (Auria et al. 1995), the phenomenon has not been sufficiently studied to incorporate these changes in porosity into bioreactor models. In any case, changes in porosity due to microbial growth will not be such a problem if the bed is agitated, since the movement of particles will tend to squash hyphae onto the surface, and rip apart any hyphae that do manage to span between particles during periods of static operation. In fact, in some cases intermittent agitation is used not to aid in heat transfer, but rather to restore the porosity of the bed and therefore reduce the pressure drop through the bed. Porosity can also change as the overall particle size and shape change due to consumption of dry matter.
The water activity of the solids is a key parameter in bioreactor models for two reasons. Firstly, microbial growth depends on the water activity of the solids (see Sect. 16.3.2) and, secondly, the driving force for evaporation is the difference be tween the water activity of the solid phase and the water activity that it would have if it were in equilibrium with the gas phase (see Sect. 18.5.1). Within a bioreactor there are many processes that affect the water content of the substrate and these changes will affect the water activity. Therefore it is necessary to have an equation relating the water content and water activity of the solids, or in other words, an equation describing the isotherm of the solids.
Typical isotherms for the types of solid materials used as substrates in SSF processes are shown in Fig. 19.4. For each particular substrate it will be necessary to determine the isotherm experimentally. A simple experimental method for doing this involves placing samples of the prepared but uninoculated substrate in several hermetically sealed containers, each container having a volume of a saturated salt solution (Fig. 19.4(a)). The containers are placed in a temperature-controlled incubator. Each sample is allowed to equilibrate with its salt solution. Once equilibrated, the fresh weights of the samples are determined, then they are dried and their dry weights are determined. This allows the construction of an isotherm, a plot of the water content of the sample at equilibrium against the water activity of the salt solution with which it was equilibrated (Fig. 19.4(b)). An empirical equation can then be fitted to the isotherm. For example, Nagel et al. (2001b) fitted the following equation to give the isotherm of autoclaved wheat at 35°C as a function of its moisture content (W, kg-water kg-dry-solids-1):
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