Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Particle-vapor molecule (condensation) and particle-particle (coagulation) collision kernels are critically important parameters for the description of particle size distribution evolution in aerosols. We use mean first passage time calculations to find a dimensionless form of the collision kernel that applies in the limit where the ratio of the masses of colliding entities (aerosol particles or vapor molecules) to gas molecule mass, Z, approaches infinity, and the colliding entities are dilute in concentration. In these calculations, the motion of colliding entities is monitored with Langevin dynamics, and the collision kernel is inferred from the time required for collision. The presented analysis reveals that the dimensionless collisional kernel (H) is a function solely of the diffusive Knudsen number (Kn(D), the square root of the product of kT and the reduced mass divided by the product of the reduced friction factor and collision radius), and a number of commonly used expressions for the collision kernel also collapse to the functional form H(Kn(D)), irrespective of whether they were derived for Z -> infinity or Z -> 0 conditions. The examined collision kernel expressions are further found to agree within 10% of our calculations as well as with each other across the entire Kn(D) range. This result suggests that a single collision kernel can be used to describe all transition regime collision rates, i.e., both condensation and coagulation rates, with reasonable accuracy, and establishes that Langevin-equation-based mean first passage time calculations can serve as a simple approach to examine transition regime collision phenomena.