Gianfranco Ferrara

The influence of particle shape on the dynamic dense medium separation of plastics

Abstract The separation of post-consumer plastics of different polymeric compositions is becoming an important topic for the reduction of waste and promotion of recycling. The comminution of plastics creates variable particle shapes which cause difficulties in the separation by a cyclone. To study the influence of particle shape, tests have been performed to determine how the partition curve changes with particle shape in cylindrical cyclones. The test results give a complete picture on the influence of particle shape and size on the cut density d 50 and the probable error E p . Coupled with a mathematical description of the partition curve, these parameters can assist in process simulation, selection and design of dense medium separation (DMS) systems devoted to plastic recycling.

Inclusion shape, mineral texture and liberation

Abstract The effect of an ores texture on liberation was explored using simplified texture models composed by a continuous phase and an inclusional phase with different geometric aspects of the inclusions. Unexpectedly, a parameter called the “textural rank” was developed that may be useful for a quantitative characterization of the rocks textures. Among the conclusions: the shape of the inclusions leads to the definition of a measurable textural rank, τ, that ranges continuously from 1, for predominantly platy inclusions, to 3, for predominantly blocky inclusions. When the reduction size is small compared to size of the inclusions the values for different textures of the degree of liberation of the two phases practically coincide while, as the reduction size increases, these values differ becoming dependent on the textural rank. The textural rank is a prime predictor of the degree of liberation of a given mineral in an ore. Finally, in the special case of cubic inclusions (as well as other regular polyhedra and spheres), the derived equation for calculating the degree of liberation of the inclusive phase reduces to Gaudins equation.

Liberation — Volume and mass lockedness profiles derived — Theoretical and practical conclusions

Abstract For the first time the shape of the lockedness profile, the frequency distribution of the fraction of the particle locked, is derived for spherical particles. Equations for both the volume and mass lockedness profile are derived. From this analysis eleven new theorems are presented which relate to the eight theorems derived previously. The deep U-shaped curves for the lockedness profile reveal that the amount of near density material is unexpectedly large. In addition, at the midpoint of the lockedness profile is the invariant Ferrara point that characterizes the shape of the lockness profile.

Comminution of porous materials

Abstract The behaviour of porous materials in comminution processes differs substantially from that of non-porous materials. It is strongly affected by the type of porosity, which may be characterized by different void shapes and interconnection degrees. This paper discusses the comminution of porous materials having voids of compact shape (like spheres) and not interconnected. For such materials different behaviours can be expected for the two comminution ranges above and below the mean voids interspace. In fact, for the coarser sizes the mechanical behaviour of the material is that of the porous material defined by its bulk mechanical properties; below the mean voids interspace down to very fine sizes the mechanical behaviour of the material is that of the non-porous material constituting the matrix. Therefore, a transitional region should exist, with the result of bi- or trimodal size distributions for comminuted porous materials. To verify the above mentioned theory, tests were performed on two types of materials, artificial and natural: (a) perforated bricks with 20 mm voids; (b) natural pumice stone. The resulting size distributions differ in slope above and below the mean voids interspace, and the two parts of the distribution are connected by a transition curve. The results may be of interest in studying the comminution of different types of materials, particularly secondary materials and scraps.

Modelling of screening operations

Abstract This paper reviews the Ferrara-Preti screening model and shows that recent laboratory and pilot plant data validate this approach. The model successfully predicts the partition curve (selectivity function) and therefore the product size distributions, given the feed size distribution. Some improvement in the application of the model, concerning numerical solution of the equations and parameter estimation, are indicated. Information is then given on the influence of some operating conditions on the screen performance studied through the modification of the model parameters, a way that could be useful for a more complete approach to modelling of screening operations. Some applications of the model to improvement of screening operations, sizing of screens, simulation of screening and of integrated plant operations are discussed.

Rheology of Low Density Suspensions in Dense Medium Separation of Post-consumer Plastics∗

Abstract The aim of this paper is to investigate the feasibility of using clay suspensions in dynamic dense medium separation of post-consumer plastics. The Theological behavior of suspensions formed with different commercial clay samples was studied to ascertain that both viscosity and stability could be maintained in the range required by dense medium separation systems. Suspensions made with a selected clay sample were used in a laboratory test rig equipped with a conical cyclone and a cylindrical cyclone with peripheral underflow discharge. Preliminary separation tests were carried out using different density plastic tracers. The results with both separators demonstrated that the separation of two plastics of different densities can be obtained.

Liberation of voids by comminution : its influence on apparent density of porous materials

Abstract For the first time, the concept of liberation of voids in a porous material is defined. A simple model has been developed for calculating the degree of liberation of voids for different sizes of the particles resulting from comminution. Void liberation affects the apparent density of the particles, i.e. the most important particle characteristic in gravity separation processes. This paper shows to what extent the porous material should be reduced in size to obtain an adequate liberation for the process requirement.

Influence of particle shape on liberation

While particle shape affects the probability of a particle being locked, some of the extant liberation models assume that the fragmentation particles are spherical. Using cylinders and bicones as models of a particle shape, and considering all possible positions and orientations in three-dimensional space, it was concluded that as long as the particles are blocky this assumption of particle sphericity is correct. For elongated particles, however, the assumption of sphericity leads to large errors in calculating the degree of liberation. A new particle shape factor is proposed to obtain an equivalent sphere diameter Dp which permits accurate liberation evaluations.

Size distribution of comminuted porous materials: the oops region

Abstract This theoretical paper examines the expected shape of the size distribution curves of comminuted porous materials. A transitional region is predicted in the size distribution of the fragments from porous materials called the ‘oops’ region. Also predicted is a change in fragment shape before and after the particle size passes through the size region of the voids—the Swiss cheese effect. The problem of void liberation and characterizing or measuring void volumes is discussed.

Locked particle standard deviation for two-phase systems

Abstract In many industrial applications, solids composed of a matrix and an inclusion phase are size reduced. For the first time, this monograph derives equations that describe the frequency distribution and standard deviation of the inclusions in the large locked particles. For large locked particles, the important variables in determining the volume and thus compositional frequency distribution are the ratio of inclusion to particle size, the volume fraction and the size distribution of the inclusional phase. In the size range where the particle size is large compared with the inclusion size, the reduced number standard deviation equation is derived for both a mono size and a size distribution of inclusions. Even for large locked particles, the random compositional variations are significant until the ratio of particle to inclusion size approaches 100. Beside the mineral industry, this work has strong implications for the ceramic, electronic, fertilizer, food and other industries using blending followed by compaction.