High-accuracy method for modeling nucleation and growth of particles
State-of-the-art numerical models describing the kinetics of aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method, in which 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 newly formed particles are above the critical size, so that subcritical-size particles are not important to take into account. Due to the nature of the nodal method, it suffers from numerical diffusion, which can cause an artificial broadening of the cluster size distribution leading to a 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 substantially reduces the numerical diffusion and provides high solution accuracy and numerical stability. We extensively compare this novel method to the commonly used nodal solver of the general dynamic equation (GDE) for particle growth and demonstrate that it offers GDE solutions with higher accuracy with low numerical diffusion. Incorporating small subcritical clusters into the solution is crucial for: 1) more precise determination of the entire 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.