(199b) Consequences of Non-Linear Particle Breakage: Falsified Breakage Kinetics and Delayed Attainment of a Self-Similar Particle Size Distribution

Comminution is an important unit operation in the production of raw materials, specialty chemicals, and value-added products. Population balance models (PBMs) have been used as a quantitative tool to model comminution. Most PBMs used in the last 60 years assumed the linearity of the breakage rate, i.e., first-order breakage kinetics. In this presentation, we organize key results from experimental studies that exhibit strong deviations from first-order breakage kinetics and present recent theoretical developments that address the complex phenomenon of non-linear particle breakage. The traditional linear model, the time-variant model, and the non-linear functional model [1] have been critically analyzed in view of experimental data. Extensive numerical simulations of dry ball milling systems [2,3] and particle bed breakage experiments [4] suggest that the non-linear functional model can serve as a unified framework by which non-linear particle breakage in a multitude of comminution systems can be systematically studied and quantified at the process length scale. Specifically, the presentation will focus on our recent efforts in exploring falsified breakage kinetics [5] and self-similarity of the milled particle size distributions [6]. We present how multi-particle mechanical interactions neglected by the traditional linear model can affect these phenomena and why elucidation of such complex phenomena entails rational, model-based design of particle breakage experiments, while indicating future research directions.

[1] E. Bilgili, J. Yepes, B. Scarlett, "Formulation of A Non-Linear Framework for Population Balance Modeling of Batch Grinding: Beyond First-Order Kinetics," Chemical Engineering Science, Vol. 61, 2006, pp. 33–44.

[2] E. Bilgili, B. Scarlett, "Population Balance Modeling of Non-Linear Effects in Milling Processes," Powder Technology, Vol. 153, 2005, pp. 59–71.

[3] M. Capece, E. Bilgili, R. Dave, “Identification of the Breakage Rate and Distribution Parameters in a Non-Linear Population Balance Model for Batch Milling,” Powder Technology, Vol. 208, 2011, pp. 195–204.

[4] E. Bilgili, M. Capece, “A Rigorous Breakage Matrix Methodology for Characterization of Multi-Particle Interactions in Dense-Phase Particle Breakage,” Chemical Engineering Research and Design, Vol. 90, 2012, pp. 1177–1188.

[5] M. Capece, E. Bilgili, R. Dave, “Emergence of Falsified Kinetics as a Consequence of Multi-Particle Interactions in Dense-Phase Comminution Processes,” Chemical Engineering Science, Vol. 66, 2011, pp. 5672–5683.

[6] M. Capece, R. Dave, E. Bilgili, “Influence of Non-Linear Breakage Kinetics on the Attainment of Self-Similarity for Dry Milling Processes,” Chemical Engineering Science, doi: 10.1016/j.ces.2013.04.017, 2013, in press.