Asymptotic behavior of TEMOM model for particle population balance equation over the entire particle size regimes

In the present study, the asymptotic behavior of TEMOM model for particle population balance equation over the entire particle size regime has been analyzed mathematically with harmonic mean and Dahnekeʹs solution. The results show that whether the collision kernel with Dahnekeʹs solution or harmonic mean method in the transition regime, the relative growth rates for particle moments have the same power law as that in continuum regime at long time. The result is consistent with the physical processes in particle coagulation due to the Brownian motion. The asymptotic analysis is just based on the mathematical formulation rather than the physical assumption, and the accuracy of asymptotic solution is fully dependent on the expanded Taylor series. The results can be used to model the evolution of particle coagulation over the entire size regime at a long time, and it will reduce the computational cost greatly.