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

The direct expansion method of moments for nanoparticle Brownian coagulation is investigated in the entire size regime. The exact Dahnekeʹs 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.