# Modeling particle-particle binary coagulation rate constants for spherical aerosol particles at high volume fractions using Langevin Dynamics simulations

## Abstract

Effect of volume-fraction and particle-particle hydrodynamic interactions on the coagulation rate of particles are investigated. Particle coagulation is modeled using Langevin Dynamics (LD) based trajectory simulations of N mono-sized spherical particles in a periodic domain. The extended Kirkwood-Risemann approach (J. Fluid Mechanics 855, 535 (2018)) is invoked to compute particle-particle hydrodynamic interactions whose effect is parameterized as a function of the momentum Knudsen number (Kn). The results are summarized as a model for coagulation rate constant (βij) that depends on the diffusive Knudsen number (KnD) used in prior work to parameterize coagulation in the dilute regime (Aerosol Sci. Tech. 45, 1499 (2011)), Kn and particle volume-fraction ηv. In the absence of hydrodynamic interactions, it is observed that the coagulation rate constant in the continuum limit for mass transfer (KnD→0) is significantly enhanced by a factor of ∼80 at ηv∼0.3 due to particle crowding. While considering hydrodynamic interactions for ηv≥0.05, we use a screening distance around each particle that scales inversely with ηv beyond which the contribution of farther neighbors is neglected owing to the rapid decay of hydrodynamic interactions with distance. We also present new LD calculations of βij and elucidate the dependence of the same on Kn1 and the particle radii ratio θr for the coagulation of two particles in the dilute limit ηv→0. It is observed that the reduction of βij becomes significant as Kn1→0: at the lowest momentum Knudsen number considered (Kn1=0.1): βij is reduced by a factor of ∼10 for equally sized particles (θr=0.5). At high KnD,Kn1, the particle size disparity is not significant, and it is seen that βij matches hard sphere predictions, indicating the insignificant contributions by hydrodynamic interactions. A series of animations of 2-particle simulations are presented as part of the Supplemental Information to illustrate the role of hydrodynamic interactions in particle coagulation. Computational results are summarized as regressions for convenient incorporation into particle/droplet growth sectional models.

## Publication Title

Journal of Aerosol Science

## Recommended Citation

Suresh, V., Liu, Z., Perry, Z., & Gopalakrishnan, R.
(2022). Modeling particle-particle binary coagulation rate constants for spherical aerosol particles at high volume fractions using Langevin Dynamics simulations.* Journal of Aerosol Science**, 164*
https://doi.org/10.1016/j.jaerosci.2022.106001