# Influence of Acoustic Streams on the Efficiency of Ultrasonic Particle Agglomeration
## 1 Introduction  
The main efforts of environmental services are aimed at ensuring high-quality purification of ambient air polluted by industrial production and man-made natural phenomena. This is due to the fact that the presence and uncontrolled distribution of aerosols of various substances in the air has a negative impact on humans, flora and fauna [1, 2]. It is generally accepted that the most dangerous particles are those measuring 2.5 microns or less, since the respiratory system introduces such particles into the bloodstream and accumulates toxic material in human organs [3, 4]. The extremely dangerous nature of fine aerosols has been confirmed by numerous studies, in particular those conducted by [PERSON], [PERSON], [PERSON] and others. As a result of these studies, a connection has been established between long-term exposure to fine aerosols and sudden deaths of healthy children and young people [5]. The proof of such a correlation explains the exceptional importance of finding ways to protect people and developing systems for purifying air from fine aerosols. All existing cleaning systems (separators) based on the inertial collection method practically do not capture particles smaller than 2.5 microns [6, 7, 8, 9], and systems capable of capturing such particles (filters and electric precipitators) are characterized by low dust capacity or operate with the formation of very harmful particles. environment and human health nitrogen oxides and ozone. The most effective way to solve the problem is the use of high-intensity ultrasonic vibrations, the effect of which on aerosols causes processes of convergence and agglomerationof small particles into large ones. This process is called ultrasonic agglomeration [10; 11]. Fine particles combined due to ultrasonic action can subsequently be easily captured by conventional gas cleaning devices [12; 13]. However, as follows from results of studies by various authors ([PERSON], [PERSON], [PERSON]), ultrasonic agglomeration loses its advantages when aggregating particles smaller than 2.5 \(\upmu\)m for their subsequent removal, while providing a significant increase in efficiency (up to 99%) in the removal of particles larger than 2.5 \(\upmu\)m, as per [14; 15; 16]. The reason for this lies in the very physical principles underlying the sonic agglomeration process. It is known that the impact of ultrasonic vibrations on gas media generates two types of nonlinear effects affecting dispersed particles in gases:  
1. Effects arising due to the phenomena of momentum transfer of the gas phase between particles;
2. Effects arising due to oscillatory motions of solid particles of different sizes relative to each other. The first group of effects contributes to the hydrodynamic mechanism (first described by [PERSON] in 1891) of particle agglomeration, when equivalent forces of hydrodynamic interaction (arising as a result of mutual distortion of flow fields around particles) bring particles closer to each other and promote their agglomeration. In this case, the probability of collision of particles is proportional not only to the interaction force of particles, but to their concentration, primarily (and, in fact, to the distance between particles) [17]. The second group of effects is realized in the orthokinetic mechanism (first described by [PERSON], [PERSON], [PERSON]), which consists of the fact that the particle does not oscillate with the gas phase synchronously, while it slides relative to the gas phase and oscillates with a smaller amplitude of displacement than the gas itself. The sweep effect is related to the inertia of the particle [18]. The ratio of the particle oscillation amplitude to the gas oscillation amplitude is called the drag coefficient. The drag coefficient depends on the particle size, and particle collision occurs due to the fact that particles of different sizes oscillate with different amplitudes (with non-zero amplitude relative to each other) and randomly collide and aggregate.