Abstract
Since the pioneering work of Lee was published, the log-normal moment method (LNMM) has been applied in order to obtain approximate analytical solutions to the coagulation problem with several different types of collision kernels. In this study, the coagulation problem with an arbitrary homogeneous collision kernel is solved using LNMM. The new analytical solution is used to analyze the ways in which the error of the log-normal analytical solution varies depending on the functional form of the collision kernels, which could not be discussed in detail with the previous individual analytical solutions for specific collision kernels. The log-normal analytical solution tends to underestimate the particle size distribution width due to the symmetric assumption, leading to the underestimation of the polydispersity effect. This increases the error of the analytical solution as the particle size dependency of the collision kernel increases.