On the growth rate of particle surface area for Brownian coagulation

The surface area of fine particles corresponds to the Gibbs free energy, and the particle number density corresponds to the entropy of particle system. In this study, the growth rate of particle surface area is given quantitatively for Brownian coagulation both in the free molecule and continuum regime based on the moment method. The results show that the relative growth rate for particle surface area is one-thirds of that for particle number density. The relationships together with the second law of thermodynamics form a kind of physical constraints for Brownian coagulation, which will be helpful to understand the population balance equation from point of view of thermodynamics.