Analytical solution of TEMOM model for particle population balance equation due to Brownian coagulation

•The analytical solution for particle balance equation based on TEMOM is proposed.•The analysis is based on the mathematical derivation rather than the physical assumption.•The analytical solutions for TEMOM model provide a basic framework to approximate PBE.

In the present study, we have derived the analytical solutions of particle coagulation due to Brownian motion in the free molecule and continuum regime, based on the Taylor-series expansion method of moment (TEMOM). The derivation is rigorous, and the accuracy of the analytical solution is fully dependent on underlying approximations in an expanded Taylor series. The analytical solutions for TEMOM model provide a basic framework to approximate the population balance equation. The analytical results together with the previous asymptotic analysis of TEMOM model will benefit for the understanding of Brownian coagulation mechanism.