# Influence of Acoustic Streams on the Efficiency of Ultrasonic Particle Agglomeration
## 3 Results
### Particle Path Analysis  
At the first stage, the paths of particles in the agglomeration chamber were analyzed using the developed test bench. Particle paths were tracked on the basis of frame-by-frame tracking of tracer particles filmed with a camera. The output power of the generator was set so that the sound pressure level for both types of disks used was at least 165 dB. The resulting frame images are shown in Figure 5.  
Figure 5: Particle distribution in the agglomeration chamber: (**a**) flat radiator; (**b**) step-function radiator. Based on the analysis of the obtained particle path data, diagrams of paths travelled by particles in the agglomeration chamber using both types of radiators were plotted (Figures 6 and 7). When using a flat radiator (at distances of 7.5 and 15 mm), a standing wave is generated with two and three nodal planes of particle velocity, respectively, into which solid particles move, agglomerate and where they are contained. Herewith, intense vortex flows generated due to adjacent regions of the ultrasonic field oscillating in counter-phase originate. As a result, the particles are captured by the vortex motion both within one node areas and between them through the low sound pressure level zones located in the vicinity of (opposite to) the zeros of oscillations of the disk radiator. In this case, in addition to  
Figure 6: Diagram of particle paths in the agglomeration chamber when using a flat radiator: 1—chamber body; 2—radiator; 3—reflector; 4—inlet tube; 5—annular domain for emission of the sounded gas-disperse flow; 6—areas of agglomerates formation; 7—gas-dispersion flow; 8—distribution of amplitudes of vibrations of the disk radiator; 9—zeros of vibrations of the radiator; 10—areas of maximum vibration amplitudes; 11—vortex areas. Figure 7: Diagram of particle paths in the agglomeration chamber when using a step-function radiator: 1—chamber body; 2—radiator; 3—reflector; 4—inlet tube; 5—annular domain for emission of the sounded gas-disperse flow; 6—areas of agglomerates formation; 7—gas-dispersion flow; 8—distribution of amplitudes of vibrations of the disk radiator; 9—zeros of vibrations of the radiator; 10—areas of maximum vibration amplitudes. the agglomeration of particles in the node areas of vibrational velocity their additional reciprocal vortex movement and interaction with each other take place, which further results in an increase in the efficiency of agglomeration  
Changing the distance to a greater or lesser extent, relative to the resonance distance, results in origination of a traveling wave and disappearance of node areas. At the same time, vortex flows are practically not generated, reducing the efficiency of agglomeration. It is also established that at a distance equal to \(\lambda\), the intensity of vortex flows is higher than at a distance equal to \(\lambda_{G}/2\). At the distances equal to \(\
icefrac{{1}}{{4}}\)\(\lambda_{G}\) and \(\
icefrac{{3}}{{4}}\)\(\lambda_{G}\), conditions at which the sound pressure level reaches its minimum value become effective. For comparison, Figure 7 shows a flow diagram for a radiator generating a uniform ultrasonic field. As in the previous case, when a step-function radiator is used, a standing wave with two and three nodal planes of vibrational velocity into which the solid particles travel, agglomerate and are retained, respectively, is generated when the distance between the radiator and the reflector is 7.5 mm, as well as when the distance is 15 mm. Further particle agglomeration does not occur due to containment of already formed particles in the standing wave nodes. At the same time, there is no mutual movement of particles within the nodal zone without any additional forced gas flow. Continuous supply of aerosol results in additional increase in the size of particles retained by the ultrasonic field in the node areas. At the same time, the vortex flows are not observed.