Direct expansion method of moments for nanoparticle Brownian coagulation in the entire size regime

• We investigate the previously proposed method of moments on Brownian coagulation in the entire size regime.
• Quadrature method of moments is used to compare with the investigated method and sectional method is used as a reference.
• The exact Brownian coagulation kernel for the entire size regime can be used in this new method.
• The investigated method can provide better results of the zeroth and second moments suppose the initial geometric standard deviation is small.

The direct expansion method of moments for nanoparticle Brownian coagulation is investigated in the entire size regime. The exact Dahneke's formula is used as the coagulation kernel. After comparing the results predicted by the direct expansion method of moments with those provided by the quadrature method of moments, the direct expansion method is proved to be qualified for predicting the time evolution of the lower order moments such as the zeroth and second moments. For relatively small initial geometric standard deviation, the results predicted by the direction expansion method of moments are more accurate than those provided by the quadrature method of moments. The partial derivatives of the coagulation kernel that appear in the direction expansion method of moments are calculated numerically due to the complicated form of the selected kernel, and the computational time can be reduced by means of parallel computing.