**Conflict of interest**

*Vortex Dynamics Theories and Applications*

process [53, 54].

a more homogeneous distribution of local velocity gradients in comparison to the radial impeller. Also, high velocity gradients occur in the region around the impeller, which might significantly hamper the high rate activated sludge (HRAS) flocculation

An oscillator is a device whose action causes intermittent velocity gradients over time, space, and direction, and can be used for colloid removal based on physical flow manipulation. An oscillatory flow pattern is commonly found in reactors with an enclosed flow induced by an oscillator. Results from previous studies have shown that gentle oscillation can promote simultaneous flocculation and particle agglomeration over a relatively short periods of time [42]. This technique, whose implementation can result in reductions of the reactor sizes and process times, has a strong potential to improve conventional separation processes. It has also been observed that higher oscillating frequency promotes faster upward vertical velocities, resulting in different sedimentation patterns and removal efficiencies gener-

*5.5.2 Oscillatory flow vortex pattern (e.g., oscillatory reactor)*

ated by the different oscillation frequencies [43].

*Typical cross-sections of vortex patterns in fluid-particle reactors (a) rotatory-type flow field* 

*(b) oscillatory-type flow field (c) swirling-type flow field.*

**14**

**Figure 6.**

The authors declare no conflict of interest.
