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Fig. 6.5. Predictions of the model of Rajagopalan and Modak (1994). Key: (-) 20 h;

(---) 60 h; ( ) 100 h. Note that the top of the tray is represented by zero bed depth and the center plane corresponds to a bed depth of 3.2 cm. The fractional modifiers of the specific growth rate constant (pFT and /uFO) are explained in the text (see Eq. (6.5)). Adapted from Rajagopalan and Modak (1994), with kind permission from Elsevier region, the rate of O2 consumption in the biofilms within this region is sufficiently low that the O2 transfer from void space to biofilm can maintain a high O2 concentration in the biofilm. In other words, in the center of the bed, temperature is the most important factor limiting growth. In fact, the temperature limitations are so severe in the middle of the bed that even after 100 h (when the organism would easily have reached its maximum concentration if it had been growing at the maximum possible specific growth rate), much of the bed has a biomass concentration significantly lower than the maximum biomass concentration (Fig. 6.5(e)).

The work of Smits et al. (1999) confirms that O2 levels in the inter-particle spaces will generally not be a limiting factor. They used a heat and mass transfer model to investigate how the relative importance of O2 limitation and temperature limitation depends on the thermal conductivity of the bed and the effective diffu-sivity of O2 within the pores of the bed. For the growth of Trichoderma reesei in a tray, their model predicted that O2 diffusion within the inter-particle spaces would only become limiting at a 10-cm bed depth if the effective diffusivity of O2 in the bed was less than 4x10-6 m2 s-1 and the thermal conductivity was greater than 0.45 W m-1 °C-1. The effective diffusivity of O2 in a bed with biomass at its maximum density is actually of the order of 4x10-6 m2 s-1 (Auria et al. 1991) meaning that O2 supply to a 10-cm bed depth can potentially become limiting, although this will only happen if there is a combination of high biomass concentration and high growth rate.

Smits et al. (1999) also modeled the diffusion of water vapor in the void spaces of the bed. When it was assumed that the air surrounding the tray was maintained at a high humidity, then the combination of metabolic water production with the relatively slow water vapor diffusion meant that the predicted water content of the substrate remained above the initial value. Under such conditions there will be no danger of the growth rate being limited by low water activities of the solid substrate. Of course, as Smits et al. (1999) point out, water could become limiting if the trays were incubated in an environment of low relative humidity. This would complicate operation since it would be necessary to periodically spray water onto the bed and to mix it in.

Rajagopalan and Modak (1994) used their model to investigate the effect of the height of the bed and the temperature of the surroundings on the average biomass concentration in the bed after 100 h of cultivation. For bed heights of 1.6 cm and less, the average biomass content reached its maximum possible value (i.e., 30 kg-dry-biomass m-3) within 100 h only when incubated at temperatures near the optimum temperature of 38°C, namely at 35°C and 40°C (Fig. 6.6). This was because with these small bed thicknesses the bed temperature remained near the incubation temperature.

At a bed height of only 3.2 cm, the maximum biomass concentration was achieved by 100 h only when the bed was incubated at temperatures below the optimum temperature (i.e., between 30-35°C). Of course this lower outside temperature, combined with the metabolic heat production, combined to maintain the whole of the bed near the optimum temperature of 38°C.

For a bed height of 6.4 cm it was impossible to maintain the majority of the bed near the optimum temperature for growth, as evidenced by the fact that the highest value for the average biomass content at 100 h was only 16.6 kg-dry-biomass m-3, obtained with incubation at 30°C. Incubation at lower temperatures controlled the temperature in the interior of the bed at values near the optimum, but cooled the surface to values at which growth was very slow. The problem of adequate temperature control became worse still at a bed height of 12.7 cm.

Fig. 6.6. Results obtained by Rajagopalan and Modak (1994) when they used their model to investigate the effect of the height of the bed and the temperature of the surroundings on the average biomass concentration in the bed after 100 h of cultivation. Adapted from a table presented by Rajagopalan and Modak (1994), with kind permission from Elsevier

Incubation temperature (°C)

Fig. 6.6. Results obtained by Rajagopalan and Modak (1994) when they used their model to investigate the effect of the height of the bed and the temperature of the surroundings on the average biomass concentration in the bed after 100 h of cultivation. Adapted from a table presented by Rajagopalan and Modak (1994), with kind permission from Elsevier

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