Theory and Development of a Novel Collision Kernel Based on the Added Mass Force of Neighboring Particles

Modeling particle morphology in many high Reynolds number particle-laden flows requires an understanding of particle coagulation. Particle-to-particle collisions impact a broad range of problems, driving weather patterns through cloud droplet growth, evolution of soot in detonation and combustion, and cosmological phenomena for planet and star formation. While collision kernels have been formulated for modeling particles subjected to gravitational settling and Brownian motion, for example, there is a lack of understanding in collisions that arise due to rapid accelerations in shocked and high Reynolds number flows. While nanoscale particulates with sizes on the order of the mean free path in such flows can be modeled well based on Brownian motion, as size and inertia increase, particles may produce wakes that interact with neighboring particles, inducing net drifts of particles towards one another. Based on recent modeling developments in the added mass force in Briney et al. 2025 (DOI 10.1017/jfm.2024.1126), a system of partial differential equations was derived and solved over a particle’s surface to create a novel collision kernel. This model was written in FORTRAN for compatibility with ANSYS Inc. Chemkin, a commercially available off-the-shelf software for modeling particle coagulation. Verification of the new kernel’s implementation was performed against an already-established kernel in Chemkin for Brownian motion before being used to simulate collisions due to the added mass force in a highly simplified particle-laden flow. The observed magnitude of the added mass force with respect to particle size was compared to the Brownian and gravitational kernels to determine collision rates exhibited by particles undergoing high speed flow. These results will improve modeling fidelity of particle-laden flows subject to large local fluid accelerations.

DOI: https://doi.org/10.1017/S0022112005004568