Equilibrium centrifugation

Transport equations. When centrifugal equilibrium is disturbed, as by establishment of counterflow or injection of feed and removal of effluents, flow of the gas mixture and of its individual components takes place relative to the rotating centrifuge. The analysis to be given has the following restrictions. 

Design studies for a commercial plant by Geppert and associates [Gl] indicate that optimum conditions are feed composition f = 0.042 mole fraction UF5 in hydrogen, pressure ratio pjp = 2.1, and a cut 0 = 3, at which a — 1 = 0.0148, still four times that in gaseous diffusion, and somewhat higher than what would be predicted for centrifugal equilibrium at the speed attainable from expansion through this pressure ratio. The cut of 3 necessitates use of a three-up, one-down cascade, as shown in Sec. 14.2 of Chap. 12. 

The flow geometry assumed is illustrated in Fig. 14.21. The gas mixture is assumed to be rotating at uniform angular velocity co in a semicircular groove of radius a. Centrifugal equilibrium is established where the mixture is separated by the flow divider at radius c into an iimer, light fraction enriched in hydrogen and Fs and an outer, heavy fraction depleted in these components relative to UF. ... 

Figure 14.27 Variation of separative capacity with peripheral speed and cut for centrifugal equilibrium at constant angular velocity.

Pure UF is expanded isentropically from 313 K through a Becker nozzle to sonic speed. Assuming centrifugal equilibrium in wheel flow and a cut of 5, find the separation factor. Cp for UFs = 31.3 cal/(K-g-mol). 

The mathematical expressions used so far for liquid systems subjected to a centrifugal field have assumed that the solvent density Ms/ Vsf) was essentially constant across the centrifuge. In general, it will vary in the radial direction due to the variation of pressure which influences VIt is particularly true when there is at least one solute species present in the system at a substantial concentration. Under such a condition, we use expression (3.1.58) for centrifugal equilibrium and expression (3.3.17) for d/i,j j. at any location. This leads to... 

Although this profile exists under centrifugal equilibrium, we may assume that the actual radial proffle will be somewhat different In the countercurrent gas centrifuge, we can expect that the radial diffusive flux - C(Dab dxy(r)/dr will be superimposed on that due to the equilibrium profile, leading to the following expression for Jl/. 

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