Transfer Between Subsystems When the Substrate Bed Is Treated as Two Separate Phases

In some cases the substrate bed is not treated as a single pseudo-homogeneous phase, but rather as two separate phases. In fact, this is necessary in those cases in which it is not reasonable to assume that the substrate particles and inter-particle air are in thermal and moisture equilibrium.

Oxygen transfer between the solid and inter-particle gas phase has received some attention. Until recently, kLa was used as the transfer parameter, in analogy to SLF (Durand et al. 1988; Gowthaman et al. 1995). However, the two systems are different (Thibault et al. 2000a) (Fig. 4.5). In SLF, the major barrier to O2 transport resides in a thin liquid film around each bubble, and there is no biomass

Fig. 4.4. The difference in bed-to-headspace heat and mass transfer for unaerated and forcefully aerated beds. The regions shown here correspond to areas at the surface of the bed (see the dashed boxes within the Group I and Group II bioreactors in Fig. 4.2). In the left-hand diagram the dotted line represents the boundary between the static gas phase and the flowing gases within the headspace in this case much of the transfer from the solids occurs within the bed in this case much of the transfer from the solids occurs within the bed and therefore no O2 consumption within this film. Rather, the biomass is located within a well-mixed bulk phase. In SSF, the limiting step is diffusion within the static biofilm at the substrate surface, and simultaneous diffusion and consumption occur in this biofilm. Therefore kLa is not the appropriate parameter to characterize O2 transfer in SSF. Instead the biofilm conductance, kFa, should be used. It takes into account the diffusivity of O2 within the biofilm and the thickness of the aerobic part of the biofilm, and therefore will very likely change during the fermentation (Thibault et al. 2000a). The biofilm conductance (kFa) might be able to be used to compare the influence of various operating parameters on the O2 mass transfer in a given system, but it cannot be used to compare the performance of different microbe/substrate systems (Thibault et al. 2000a). This contrasts with SLF, in which kLa can be used to compare the efficiency of O2 transfer in quite different systems. The question of O2 transfer is further complicated by the fact that aerial hyphae, that is, hyphae exposed directly to the air within the inter-particle gas phase, can in some cases make a significant contribution to overall O2 transfer (Rahardjo et al. 2002).

Static liquid film

• O2 transfer limited to diffusion

• assumed not to have any biomass in it, therefore O2 not consumed in this region

• O2 transfer limited to diffusion

• ki_a depends on the liquid film thickness, the diffusivity of O2 in the film and the area of the film (total bubble surface area)

Well-mixed bulk liquid region

• all O2 consumption occurs here

Static gas layer

• simultaneous diffusion and consumption of O2

Biomass layer (static)

Flowing gas

• kFa depends on the diffusivity of O2 in the film, the thickness of the aerobic part of the biofilm and the overall biofilm area

• simultaneous diffusion and consumption of O2

Biomass layer (static)

Flowing gas

Fig. 4.5. Comparison of the situations for O2 transfer in (a) SLF and (b) SSF

The substrate particle, the biofilm, and the static gas layer will contribute to the overall resistance to heat and water transfer. In the case of water transfer, note that the water changes phase as it leaves the solid, taking the energy of evaporation from the solid. This represents a combined heat-and-mass-transfer process. Heat and mass transfer from the particle to the inter-particle air has received little attention in SSF, although the literature about the drying of foods is relevant. At the high water activities typically encountered in SSF, there will typically be a film of liquid water at the surface and, for evaporation of this water, the major barrier is the static gas film that surrounds the particle.

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