Implications of Shear on Agglomerates in Solution

Now that we have a means for estimating the shear, it is of interest to see how often and for what duration, agglomerates will be subject to high levels of shear. The chamber has a throughflow of Q . The radial or impeller stream discharge Qr can be approximated by  

The ratio Rq = Q /Qr will determine how often particles recirculate and pass through the high shear impeller zone. For large values of R the inflow will dominate and relatively few particles will recirculate. If the density difference between the particles and fluid is sufficiently small and the particles themselves are small they will follow the fluid motion. 

The fraction of particles which will travel directly to the outlet without being recirculated in period T will be % = Rq/(1+Rq) where T = V/Qi and V is the volume of the chamber. The firaction of the particles in the inflow left to recirculate one or more times is simply l-%. In the next period T, of the l-X particles recirculating, / wiU be the fraction removed. Thus the fraction of particles that recirculate once is can be generalised to give the fraction f of particles that have been exposed to the 

The duration of exposure tcxp to the high shear on each passage through the impeller can be estimated from  

The Kolmogoroff length in the peak dissipation region is estimated to be around 9 (im. Thus, as long as particle agglomerates are larger than this in size, the preceding analysis will be valid. The Reynolds number Re is well above the required value of 400. 

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