General analytical solution to coagulation problem with homogeneous collision kernel

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.

Keywords:

• Coagulation
• homogeneous collision kernel
• log-normal moment method
• analytical solution
• degree of homogeneity

Additional information

Funding

This research was supported by the National Strategic Project-Fine particle of the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (MSIT), the Ministry of Environment (ME), and the Ministry of Health and Welfare (MOHW) [NRF-2017M3D8A1092022].