where NC is in rpm and D is the drum diameter in meters.

For both a static drum (0 rpm) and a drum rotating at the critical speed, there is no mixing action within the bed. For the slipping and slumping flow regimes, which occur when the rotational rate is less than 10% of the critical rotational speed, the bed moves essentially as a whole, meaning that the amount of mixing within the bed itself is negligible.

As the rotational speed increases through moderate rotational rates (from 10% to 60% of the critical rotational speed) the bed undergoes first rolling flow, characterized by a flat surface, and then cascading flow, characterized by a curved surface. There are no airborne particles. In both these flow regimes there is particle flow within the bed itself, although there may be dead zones. For rotational rates greater than 60% of the critical rotational speed, the flow changes to cataracting flow, in which particles are thrown into the air.

Most rotating-drum bioreactors are operated in conditions that give slumping flow, meaning that it is usually a good idea to attach baffles to the inner surface of the drum, in order to improve the mixing. However, it is also possible to operate unbaffled drums at high rotation rates. For example, the large-scale rotating-drum bioreactor reported by Ziffer (1988) had a diameter of 1.22 m, which gives a critical rotational speed of 38.3 rpm. During the period of peak growth rate the drum was rotated at 24 rpm, which represents 63% of the critical rotational speed, such that the bed must have been on the borderline between the cascading and cataract-ing flow regimes.

Schutyser et al. (2001) undertook studies of mixing in rotating drum bioreactors that give a greater insight into the radial mixing patterns that occur and how they are affected by baffles. They used a two-dimensional discrete-particle model, in which the predicted positions of a large number of individual particles are calculated by the model, with the change in the position of each individual particle during a time step depending on the sum of forces acting upon it as a result of collisions with other particles or with solid surfaces such as the bioreactor wall (Fig. 8.10(a)). They supported their modeling work with experimental validation in rotating drums containing cooked wheat grains.

They characterized the drum as being well mixed when the entropy of mixing was greater than 0.9 (see Fig. 8.10(b)) and compared the effectiveness of the mixing provided by a particular mode of drum design and operation on the basis of the number of drum rotations necessary to reach an entropy of mixing of 0.9.

initial positions and velocities

calculation of collisions

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