On the Link between the Langevin Equation and the Coagulation Kernels of Suspended Nanoparticles

Abstract

The ability of the Langevin equation to predict coagulation kernels in the transition regime (ranging from ballistic to diffusive) is not commonly discussed in the literature, and previous numerical works are lacking a theoretical justification. This work contributes to the conversation to gain better understanding on how the trajectories of suspended particles determine their collision frequency. The fundamental link between the Langevin equation and coagulation kernels based on a simple approximation of the former is discussed. The proposed approximation is compared to a fractal model from the literature. In addition, a new, simple expression for determining the coagulation kernels in the transition regime is proposed. The new expression is in good agreement with existing methods such as the flux-matching approach proposed by Fuchs. The new model predicts an asymptotic limit for the kinetics of coagulation in the transition regime.

Keywords

• Langevin dynamics
• coagulation kernels
• transition regime
• diffusive Knudsen number