Population balance in confined comminution using a physically based probabilistic approach for polydisperse granular materials

Abstract

SUMMARYA novel, simplified approach is presented in order to compute variations of grading in granular assemblies during confined comminution under quasi-static compression. The method is based on a population balance equation and requires a breakage probability, considered here as a probabilistic phenomenon that takes into account the particle strength and the loading condition of individual grains. Under basic assumptions, a simple breakage probability can be defined in order to get a valuable result for engineering applications and powder technology. The size effect in the strength of individual particles is introduced according to Weibull's theory. The particle loading and the cushioning effect in the granular packing are accounted for by considering the orientations of the contact forces obtained from 3D discrete element method simulations of highly polydisperse materials. The method proposed could have a value for engineering purposes in powder technology and geomechanics and gives a general framework for further research developments based on population balance.

A micro‐macromechanical compression model of crushing in granular materials based on a probabilistic approach and energy aspects

“…measures the difference of the distribution of the contact force between different size fractions. Our simulation results in Figure 10A, as well as the results from Ovalle et al, 13 show that the suggested range of is 0-0.4. The distribution of the contact force of the largest particle size fraction of each gradation is extracted and compared in Figure 10B.…”

“…The parameter controls the shape of the distribution of the normalized contact force. Comparing Equation (11) and Equation (12), is positively related to the particle size and Ovalle et al 13 found the empirical expression ∝ ( ∕ max ) , where = 0.36, through DEM simulations. The DEM simulations also reveal that the value of the maximum size fraction max decreases with the increase of the particle size range.…”

“…Marketos and Bolton 11 proposed a linear relationship between the average contact force and particle size. Ovalle et al 13 further proposed that the relationship between the average contact force and particle size was a quadratic function.…”

Quantification of particle crushing in consideration of grading evolution of granular soils in biaxial shearing: A probability‐based model

“…This is not consistent with what was observed by most researchers that compressed granular assemblies tend toward fractal grading . Mathematical models such as Markov chain model and population balance model were also used recently to estimate grading evolution in granular materials. In addition, Marketos and Bolton developed a probabilistic model to estimate particle crushing in the 1‐dimensional compression of a granular assembly based on data derived from discrete element method (DEM) simulations, making use of the contact force information in the model, as had been increasingly used by others .…”

“…This assumption is reasonable for many granular materials, such as Quartz sands, Quiou limestone sand, Leighton Buzzard silica sand, and Biotite gneiss . For strongly heterogeneous materials, Weibull theory may be invalid after significant breakage …”