Relevance list and pi space

When different criteria for describing the suspension state are in use, these must also be taken into consideration in the formulation of the suspension characteristics. Depending on which criterion is used in the determination of the critical stirrer speed Wx , which can be represented by x for the 1-s criterion, for the particle layer height criterion h = 0.9 or by a required distribution quality the process numbers are correspondingly designated e.g. Re or Fr.  

In the early investigations of suspension in stirred tanks, there were no deep technical insights in the flow behavior in this complicated phenomenon and there 

In the research studies in the 196O s and 197O s the average particle size dp was taken to be the characteristic dimension of length of the solid particle in the relevance list and the geometrical number dp/d was thus formed. It was evident, however, that the pi spaces, which is addition to gAp only took this particle number into consideration, differentiated too strongly and led to contradictory scale-up rules. A cause for this circumstance could, however, not be identified (see Section 5.3.2.5). 

On the basis of the analogy between no.9 and dp (Fig. 5.5), on the one hand, and the sinking velocity of the particle swarm Wss and dp, on the other, the sinking velocity of the swarm u gs was later incorporated into the relevance list. This consciously took account of the fact, that this property of the particle swarm is calculated from the sinking velocity Wg of a single particle in a liquid at rest and thus strictly speaking only applies to a liquid at rest. 

Wss is thus preferably incorporated into the relevance list, because the process can be physically better interpreted with it. From the standpoint of dimensional analysis it must be examined which consequences result from the incorporation of this quantity. Two possibilities must be taken into consideration  

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