title: Destructive aggregation: aggregation with collision-induced breakage.
abstract: Mean-field population balance equations are used to describe the evolution of particle size distributions in a wide variety of systems undergoing simultaneous aggregation and breakage. In this paper we develop a population balance that includes aggregation combined with collision-induced particle breakage for arbitrary fragment distribution functions, provided that this distribution function depends only on the total mass of the particles undergoing a collision. We then develop a specific distribution function for arbitrary two-body collisions by postulating that each collision produces a transition-state aggregate having the morphology of a linear polymer. The behavior of the resulting equation is then analyzed for the case in which the collision kernel is a constant, and partial analytical solutions are derived and compared to corresponding Monte-Carlo simulation results. The computer simulations are then used to validate a proposed scaling law for the steady-state particle size distribution. Lastly, the behavior of the aggregation with collision-induced-breakage population balance equation is compared and contrasted with the behavior of an analogous aggregation with linear-breakage population balance equation.
authors.affiliation: Department of Chemical & Biological Engineering, 2114 Sweeney Hall, Iowa State University, Ames, IA 50011-2230, USA. vigil@iastate.edu
authors.forename: R Dennis
authors.initials: RD
authors.lastname: Vigil
authors.forename: Isaac
authors.initials: I
authors.lastname: Vermeersch
authors.forename: Rodney O
authors.initials: RO
authors.lastname: Fox