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

• The asymptotic behavior for particle coagulation over the entire size regime is analyzed.
• The analysis is based on the mathematical derivation rather than the physical assumption.
• The TEMOM has the same power law growth rate at long time for different kernel.
• The present results are consistent with the physical processes for particle coagulation.

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 Dahneke's solution. The results show that whether the collision kernel with Dahneke's 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.