Separation in the Periodic Pump-out Regime

Let Us be the Stokes velocity of free motion of a bubble with completely frozen surface, which under the obvious condition pq pi equals 

To these equations, one must add the expression (24.3) for f W) and the relation for the volume concentration of bubbles  

As a boundary condition, we should take the condition of absence of bubbles at the bottom wall of the separator  

Since the diameters of bubbles range from Di to D2, at t 0 there are three regions in the considered volume (Fig. 24.1), divided by flat surfaces of contact discontinuities (these surfaces are already familiar to us from the similar problem of suspension sedimentation (Section 8.5)). Consider a plane (z, t) (Fig. 24.2) and straight lines 

The region corresponds to a single-phase area I, which is free from bub- 

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