Different approximate models of the sectional method for nanoparticle Brownian coagulation

Purpose - The original v(2)-based sectional method assumes that the selected property quantity of particles is uniformly distributed in each section, which makes particle size distribution (PSD) fluctuate dramatically in the entire size range. The number concentration in each section as well as the zeroth moment of PSD also cannot be correctly predicted in case there are not enough sections used in calculation. In order to provide a more appropriate representation of PSD, different approximate models are used to close the conservation equations. The paper aims to discuss these issues. Design/methodology/approach - The uniform distribution of the selected property quantity of particles in each section is not necessarily satisfied. Instead, the distribution is approximated using an expression with an approximation factor. Different models are investigated on recovering the initial size distribution and predicting the time evolution of size distribution as well as the first three moments so that the advantages and disadvantages of each model can be compared. Findings - The approximate model with an approximation factor of 0.8 is capable of predicting the time evolution of the zeroth moment accurately no matter how many sections are used in simulations. The original v(2)-based model is recommended to calculate the first and second moments as long as the section number is larger than 50, otherwise, the model with an approximation factor of 0.15 would be a preferred choice. Originality/value - Different approximate models can be used to improve the accuracy of the results supposing we know which moment is of great importance in calculation.