Evaporation can be important in various instances within SSF bioreactors:

• at the surface of a bed exposed to the air (for example, the surface of a tray);

• between the air and solid phases in a forcefully-aerated bed.

The equations used to describe evaporation in the various circumstances will have many similarities with the equations used to describe heat transfer, as will become apparent in the subsections below. Note that the diffusion of liquid water or water vapor is not described here, since bioreactor models typically assume that it is negligible. If it were to be included in a model, the diffusion term would have a mathematical form similar to Eq. (18.9).

18.5.1 Evaporation from the Solids to the Air Phase

The rate of evaporation from the solids to the gas phase within the bed depends on

• the difference between the water activity that the solid actually has (awsoUd, di-mensionless) and the water activity that it would have if it were in equilibrium with the gas phase (aw,/);

• the area of contact between the solid and gas phases (A, m2);

• the mass transfer coefficient (kw), which is the mass of water transferred per unit of time per unit of area per unit of driving force. Since the driving force is expressed in terms of water activity, which is dimensionless, the units of kw are simply kg-H2O m-2 h-1.

Flowing air removes water (Eq. (18.19))

Flowing air removes water (Eq. (18.19))

air flux (G) across a cross-sectional area normal to the flow of Ab

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