Theoretical analysis of acoustic and turbulent agglomeration of droplet aerosols.

[Display omitted] • The theoretical analysis is applied to investigate acoustic agglomeration of aerosol particle. • Droplet agglomeration induced by acoustic waves and turbulent flow is considered. • The probability of collision and agglomeration of particles is investigated. • The rapid refilling process of aerosols after an orthokinetic motion is considered. • Effects of environmental parameters on aerosol agglomeration are conducted. This study meticulously explores the agglomeration mechanisms in microscale droplet aerosols, specifically focusing on acoustic and turbulent agglomeration mechanisms. Our theoretical analysis reveals a significant impact of orthokinetic and hydrodynamic processes on acoustic agglomeration. The acoustic wake effect elucidates the swift replenishment of small particles subsequent to an orthokinetic phase. An optimal frequency, varying for different droplets, was identified in orthokinetic agglomeration within the 50–250 Hz range. Hydrodynamic agglomeration remained relatively stable at an acoustic frequency exceeding 1000 Hz. The aggregation kernel function, denoted as K ij , exhibited a significant increase with increasing sound pressure levels, reaching up to 10−8 s−1. Environmental temperature had a predominantly positive effect on orthokinetic and Brownian agglomeration, although it exhibited an inhibitory effect on hydrodynamic agglomeration. For raindrops, a correlation was identified between particle spacing and K ij ; a larger particle spacing corresponded to a smaller K ij. Despite an increase in particle spacing to 50 times the particle diameter, the hydrodynamic effect persisted. The aggregation kernel function linked to Brownian thermal motion was found to be 3–4 orders of magnitude lower than that of orthokinetic and hydrodynamic interactions. Additionally, the turbulent agglomeration kernel function for fog, cloud, and rain droplets with corresponding parent nuclei of 100 μm was of the same order of magnitude as the acoustic agglomeration kernel function. [ABSTRACT FROM AUTHOR]