(167a) Interpretation of Breakage Data via Moment Models

This paper presents a methodology for solving the inverse problem related to particle breakage, i.e., for extracting model parameters from breakage data. The method is rooted in similarity solutions for breakage when the rate is power-law in particle size and the daughter distributions are self-similar. The daughter distribution employed contains two terms, each of which follows Hill-Ng statistics and has parameters with mechanistic meaning. Overall, this results in a six-parameter model: two parameters (exponent and prefactor) to describe the breakage rate and four parameters to describe the daughter distribution. Once the model parameters are in hand, solution of the forward problem via the quadrature method of moments (QMOM) is shown to reproduce the data from which the parameters were extracted. Distributions reconstructed on basis sets of modified gamma functions are shown to reasonably represent the observed product distributions. This full treatment is illustrated for five data sets from the literature, and data requirements for application of the model are discussed. For a number of additional data sets, the inverse problem is solved to begin the compilation of a database of model parameters cross-referenced against mills, materials and conditions with the aim of beginning a systematic mapping of model parameters for a priori modeling of breakage processes.