Numerical Method for Modeling Nucleation and Growth of Particles that Prevents Numerical Diffusion

Abstract: State-of-the-art models for aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method to numerically solve particle growth kinetics. In this method, particles that are smaller than the critical size are omitted from consideration, because they are thermodynamically unfavorable. This omission is based on the assumption that most of the newly formed particles are above the critical size and that the subcritical-size particles are not important to take into account. Due to the nature of the nodal method, it suffers from the numerical diffusion, which can cause an artificial broadening of the cluster size distribution leading to significant overestimation of the number of large-size particles. To address these issues, we propose a more accurate numerical method that explicitly models particles of all sizes, and uses a special numerical scheme that eliminates the numerical diffusion. We extensively compare this novel method to the commonly used nodal solver of the General Dynamics Equation (GDE) for particle growth and demonstrate that it offers GDE solutions with higher accuracy without generating numerical diffusion. Incorporating small subcritical clusters into the solution is crucial for: 1) more precise determination of the entire shape of the particle size distribution function and 2) wider applicability of the model to experimental studies with non-monotonic temperature variations leading to particle evaporation. The computational code implementing this numerical method in Python is available upon request.