Locus of zero vertical velocities

The downward current is partially counterbalanced by an upward flow in the core region, depending on the underflow-to-throughput ratio. There is a well defined locus of zero vertical velocities (LZVV) which follows the profile of the cyclone. 

Figure 6.3 Vertical (axial) velocity distribution in a hydrocyclone. LZVV, the locus of zero vertical velocity...

Since the outer and the inner layers move in opposite vertical directions (i.e., the flow in the outer vortex moving down and the inner vortex moving up), there is a well-defined locus of zero vertical velocity between the two vortices. This locus forms an invisible boundary, which plays an important role in particle separa-... 

Equilibrium Orbit Theory. The general concept that particles of a given size reach an equilibrium radial orbit position in the hydrocyclone forms the basis of equilibrium orbit theory. The fine particles reach equilibrium at small radii where the flow is moving upwards and transports fines to the overflow, while the coarse particles find equilibrium position at large radii where the flow is moving downwards and carries these particles to the underflow outlet (apex). The dividing surface is the locus of zero vertical velocity (LZW). The size of the particles that find equilibrium radius on LZW will be the cut size that has an equal chance to finish in either overflow or underflow. 

A positive value iadicates vertical movement. Thea, moving from the outer wall to the air core, the axial velocity iacreases to positive values. Thus, the fluid motioa is dowa the wall of the cycloae to the apex and up the air core through the vortex finder. In the cylindrical section, the axial velocity goes negative again, approaching the vortex-finder wall. The fluid flow is then down the inner cyclone wall and the outer vortex-finder wall. There is a locus of zero axial velocity. 

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