Effects of more realistic single-particle rate laws in the Eulerian population-balance equation

Abstract

Considerable insight has been obtained by introducing deliberately (over-) simplified rate laws (for suspended particle nucleation, coagulation, growth/dissolution, sintering, breakage,…) into the generally nonlinear integro-partial differential equation called the ‘population balance’ equation (PBE). This approach has been justified by the complexity of this equation, and the need to satisfy it along with many other local PDE-balance principles in multi-dimensional transient flow environments. However, current requirements for process design, and the practical need to infer meaningful physicochemical parameters based on accessible measurements on large populations rather than individual ‘particles’, make the introduction of more accurate rate laws an essential ingredient for the next generation of such process models. Following up on our earlier analyses of the effects of more accurate collision frequency rate laws for fractal-like aggregates, we further demonstrate this claim here by examining two further instructive linear.