Theoretical Derivation of Particle Collision Kernels from a First-Time-Passage Approach in the Diffusive Regime

JOSÉ MORÁN, Mohammad Reza Kholghy, University of Minnesota

     Abstract Number: 628
     Working Group: Aerosol Physics

Abstract
The collision kernels of suspended particles in the diffusive regime have been derived analytically based on a theoretical approach that describes the time between collisions as a stochastic variable modeled as a first-time-passage phenomenon. A numerical solution of the Langevin equation for a pair of suspended nanoparticles inspired in the work of Gopalakrishnan et al. (2011) reveals that such distribution is exponential with a parameter proportional to the particle collision kernel and number concentration. This observation is consistent with the theoretical derivation developed in the present work. Though it was not shown mathematically here, we also observe an exponential distribution for particle collisions in the particle-particle transition and ballistic regimes based on Langevin Dynamics simulations under diluted conditions.

The assumption of a diluted regime typically considered in the literature (Fuchs (1965); Friedlander, S. K. (2000)) is lifted and a concentration-dependent expression of the diffusive collision kernel of suspended nanoparticles is obtained analytically. This new expression is in good agreement with numerical simulations from the literature for moderately high levels of concentration (volume fraction < 10%). These new theoretical insights may lead to new venues in the theoretical modeling of aerosol coagulation along different regimes.

[1] Gopalakrishnan, R., & Hogan Jr, C. J. (2011). Aerosol Science and Technology, 45(12), 1499-1509.
[2] Fuchs, N. A. (1965). Physics Today, 18(4), 73.
[3] Friedlander, S. K. (2000). (Vol. 198). New York: Oxford university press.