EXPLAINING A HYDORCYCLONE PARADOX

In this note I had answered a practical question (posed by Dale Larson of Chevron at a mathematics--industry workshop at RPI in May 1992).  The question was to explain the following  puzzling effect.  

A  centrifuge used to separate oil droplets from water consists of a tube, around 3ft long and 2in  in diamater; the water polluted with droplets of oil is injected at the top end of this vertical tube. The tube, together with the mixture inside,  rotates around its axis, and the oil gravitates towards the axis, forming a thin core. At the bottom end of the vertical tube the oil is sucked out through a hole in the center of the endcap, while the purified water is removed through a hole near the wall of the tube. The mixture travels downwards through the tube at the speed of about 10 ft/sec. It is surprising, therefore, that the oil core actually rises (due to buoyancy) against the downward fast flow. 

The note [30] explains this phenomenon and  gives some estimates of the effects of various changes in the   design of the centrifuge.