Direct extraction of the orthokinetic coagulation kernel reveals particle-scale physics of acoustic agglomeration

Acoustic agglomeration is a particle-laden flow process in which oscillatory gas motion induces size-dependent particle entrainment, generating differential particle velocities that govern interparticle collisions and aggregate growth. However, the physical origin of the orthokinetic coagulation kernel that links particle-scale dynamics to aerosol-scale evolution remains insufficiently quantified. In this study, a multiscale discrete element method (DEM)–population balance model framework is employed to resolve this particle-flow interaction and directly extract the orthokinetic coagulation kernel from particle-resolved simulations without empirical calibration. A decorrelated size-pair matrix with ensemble averaging over 54 independent DEM simulations yields the kernel K = K0 (di + dj)α |di − dj|β, with α = 1.97 ± 0.10 and β = 0.99 ± 0.05 (R2 = 0.981), providing direct particle-scale evidence for the classical orthokinetic scaling governed by collision cross section and differential acoustic entrainment. Independent Brownian coagulation simulations yielded a mean ratio of 0.975 ± 0.118 relative to the Smoluchowski solution, indicating good agreement with the theoretical prediction. Without parameter tuning or rescaling, the extracted kernel predicts a 67.8% reduction in particle number concentration over 10 s while maintaining a mass drift below 2%. The simulations reveal that the orthokinetic kernel arises from the combined effects of geometric collision cross section and size-dependent acoustic entrainment, while the macroscopic particle size distribution evolves through preferential sweeping of smaller particles by larger ones. The results establish a direct physical connection between oscillatory flow-induced particle motion and aerosol-scale agglomeration, providing new insight into the multiscale dynamics of acoustic particle-laden flows.