Abstract
Entrainment in selective withdrawal occurs when both the top and bottom phases are withdrawn through a capillary tube oriented perpendicular to a flat gravitationally separated liquid-liquid interface. The tube introduces two distinct features to the conditions for fluid entrainment. First, the ratio of the two phases being withdrawn is affected by the region of influence of the flow upstream of the tube's orifice. Second, a minimum withdrawal flow rate must be reached for entrainment regardless of the distance between the interface and the tube. We show that these phenomena can be understood based on the Reynolds number that governs the external flow field around the capillary tube and the capillary number that regulates the effect of the viscosity and capillarity.
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