Population balance diffusion terms

The basic objective of the theoretical analyses is to obtain the effective rate constant for bimolecular reaction between rodlike polymers when the reaction is limited by slow diffusion, in terms of the polymer diffiisivities. The latter are dependent on the concentration and polymer length, and consequently the rate constant is obtained as a function of these variables. This is then useful for predicting the time evolution of the molecular weight distribution using a population balance analysis [48-50]. 

In the approach adopted in my first edition, the derivation and use of the general dynamic equation for the particle size distribution played a central role. This special form of a population balance equation incorporated the Smoluchowski theory of coagulation and gas-to-panicle conversion through a Liouville term with a set of special growth laws coagulation and gas-to-particle conversion are processes that take place within an elemental gas volume. Brownian diffusion and external force fields transport particles across the boundaries of the elemental volume. A major limitation on the formulation was the assumption that the panicles were liquid droplets that coalesced instantaneously after collision. 

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