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In the course of the search for a flow pattern optimal for culture growth in vortex bioreactors, our experiments discovered striking flow structures that existing theoretical models cannot explain. Three immiscible liquids fill a vertical open cylindrical container whose sidewall is still while the bottom disk rotates driving a circulatory fluid motion. The centrifugal force pushes the lower liquid (L, aqueous glycerol) from the axis to the periphery near the bottom, creating its toroid circulation that in turn drives the middle liquid (M, sunflower oil) and the upper liquid (U, alcoholic glycerine). Under certain conditions with increasing rotation, counterflows develop near both interfaces LM and MU: the liquids move towards (away from) the axis below (above) the interface that seems paradoxical. At a small thickness of M, a stagnation zone arises where the axial and radial velocities vanish and the M liquid only rotates. As M thickness decreases, this stagnation zone expands and occupies the entire volume of the middle liquid. These counterintuitive results await their theoretical explanation and formulation of new contact conditions at the LM and MU interfaces.