## Info

water content (kg-H2O kg-dry-solids-1)

Fig. 19.4. Moisture isotherms. (a) Hermetically sealed container in which the substrate is allowed to equilibrate with a saturated salt solution. "♦" represents a salt crystal. (b) Isotherms of some substrates used in SSF processes: (---) Desorption isotherm of autoclaved wheat grains at 35°C as determined by Nagel et al. (2001b), reproduced with kind permission from John Wiley & Sons, Inc.; (—) Isotherm of corn as described by Eq. (19.8) at 20°C (lower curve), 35°C (middle curve), and 50°C (upper curve) (Canada 1998)

### 19.3 Air Density 273

Likewise, Calgada (1998) fitted the following equation to give the water activity of corn (aws) as a function of the moisture content (W, kg-water kg-dry-solids-1) and the temperature:

aw = (1 - exp (- W(L275-0 0029rs) exp (2.9 + 0.004Ts. (19.8)

Note that this equation can be rearranged to be explicit in the solids water content and can be used to calculate the water content necessary to give a desired water activity of the corn at a given temperature:

Microbial growth on the substrate could potentially change the isotherm significantly. That is, for the same water content, uninoculated substrate and fermented substrate could have quite different water activities. However, this point has received relatively little attention. In the development of bioreactor models it has been assumed that the fermenting solids have the same isotherm as the uninoculated substrate. However, Nagel et al. (2001b) did develop a mathematical model in which the water in the particle was segregated into intracellular and extracellular water, and such an approach could be incorporated into bioreactor models.