Impact breakage of spherical, cuboidal and cylindrical agglomerates

A numerical study of the micro-mechanics of breakage of agglomerates impacting with a target wall has been carried out using discrete element simulations. Three agglomerates of different shapes are examined, namely spherical, cuboidal and cylindrical. Each agglomerate consists of 10,000 polydisperse auto-adhesive elastic spheres with a normal size distribution. The effect of agglomerate shape and impact site on the damage of the agglomerates under an impact velocity of 1.0 m/s for an interface energy of 1.0 J/m² is reported. It is found from the simulations that cuboidal edge, cylindrical rim and cuboidal corner impacts generate less damage than spherical agglomerate impacts. The cuboidal face, cylindrical side and cylindrical end impacts fracture the agglomerates into several fragments. Detailed examinations of the evolutions of damage ratio, number of wall contacts and total wall force indicate that the size of the contact area and the rate of change of the contact area play important roles in agglomerate breakage behaviour. Internal damage to the agglomerate is closely related to the particle deceleration adjacent to the impact site. However, the local microstructure may not be a decisive factor in terms of the breakage mode for non-spherical agglomerates.     

The evolution of pellet size and shape during spheronisation of an extruded microcrystalline cellulose paste

The process by which cylindrical rods of soft solid paste extrudate are converted into round pellets on a spheroniser (Marumeriser™) plate was studied by interrupting spheronisation tests and measuring the size and shape of the pellets. Batches of 20 identical rods (20 mm long, 3 mm diameter) generated by ram extrusion of 47 wt% microcrystalline cellulose/water paste were spheronised at rotational speeds, ω, between 1200 rpm and 1800 rpm on a laboratory spheroniser. The time to complete spheronisation was found to scale with ω^−3.6, which was close to the ω⁻³dependency predicted by a simple collision model. Breakage occupied the first 10% of the process duration: rounding off was the rate-determining step. The evolution of pellet shape was classified into five stages, the duration of which was found to scale with spheronisation time. Pellet shape, quantified by aspect ratio, circularity, shape and angularity factors presented by Sukumaran and Ashmawy (2001), showed similar behaviour for all ω studied. A phenomenological model is proposed which identifies different routes for small and large rod breakage products.     

Scale-up procedure of parameter estimation in selection and breakage functions for impact pin milling

This paper presents a scale-up procedure of parameter estimation in the selection function and breakage function from single particle impact breakage to inform the predictions at the process scale of an impact pin mill. The selection and breakage functions used in population balance model (PBM) for particle breakage in the literature are briefly reviewed. Single particle breakage tests are conducted in a vertical impact tester subject to varying impact velocities. The single particle breakage results further serve to provide the database for the parameter estimation in Vogel and Peukert model (Vogel and Peukert, 2005). The estimated parameters in the particle level are upscaled in an impact pin mill using the population balance model, which is implemented in the software gPROMS (Process Systems Enterprise, UK) (gPROMS® 4.1 Release Notes, 2016). The impact milling tests were carried out in an impact pin mill UPZ100 subject to four feed rates, providing the dataset for model validation. The sensitivity analysis of the PBM parameters was conducted to help identify their leverage on the particle size distribution. The scale-up procedure by specifying the parameters from single particle level to the process level of PBM demonstrates an approach to help predict the size reduction process subject to the prevailing mechanism in an impact pin mill and other milling processes alike.     

A method to evaluate the overall breakage degree of pre-weakening processing and its applications

The product fineness indicator t₁₀ and the pre-weakening degree indicator percentage change of A * b value (C_Ab) were used to described the two aspects of the breakage result of processing with pre-weakening effect. However, there lacks a method to evaluate the ‘overall’ breakage degree with a single index. It was observed that when the high voltage pulse breakage (HVP breakage or HVPB) induced cracks inside pre-weakened particles were consumed during impact breakage, the breakage characteristics of the progeny particles are the same to raw ore particles. Based on this phenomenon, the concepts of equivalent size S_ie and equivalent size reduction t_10e are proposed. Raw ore particles of size S_ie is ‘equivalent’ to pre-weakened particles of size S_i in terms of their impact breakage product size distribution. Therefore the value of S_i and the consequently derived t_10e can be used to evaluate the overall breakage degree of pre-weakened particles. The calculation procedure of S_ie and t_10e is demonstrated in the context of HVP breakage. It is found that the impact breakage product of pre-weakened particles can be well predicted from S_ie. In addition to the evaluation of overall breakage degree of pre-weakening processing, this method also has potential to apply in the simulation of comminution circuits with pre-weakening processing and the development of breakage model for processing with pre-weakening effect.