The problem of of the use of fly ash still constitutes a research and exploration area for scientists. This is due to the fact that, 6,000,000 Mg of coal combustion by-products (CCB) are storage on landfills yearly in Poland alone. One of the potential directions of using fly ash is to use it as a substrate in hydrothermal syntheses of mesoporous materials (synthetic zeolites). Zeolites are aluminosilicates with a spatial structure. Due to their specific structure they are characterized by a number of specific properties among others molecular-sieve, ion-exchange and catalytic that can be used in engineering and environmental protection. So far, the synthesis has been carried out using coal combustion by-products such as fly ash or microsphere. The article analyzes whether separation from the fly ash of the appropriate fraction (below 63 μm) will affect the formation of zeolite grains. The syntheses were carried out using class F fly ash and the fraction separated from it, which was obtained by sieving the ash through a 63 μm sieve. Chemical (XRF) and mineralogical (XRD, SEM-EDS) analyzes were carried out for substrates as well as the obtained reaction products. In the case of substrates, the analysis did not show any significant differences between the ash and the separated fraction. However, in products after synthesis (Na-X zeolite with a small amount of Na-P1 zeolite, and small amounts of quartz and unreacted aluminosilicate glass - mullite) higher aluminum and sodium contents were observed from the separated fraction, with a lower calcium and potassium content. A small proportion of illite was observed on the diffraction curve of the zeolite from the fraction. Observations of grain morphology showed no differences in formation. Based on the conducted analyzes, it can be stated that, considering the economics of the synthesis process, the separation of fine fractions from the fly ash does not affect the quality of the synthesis process.

Nickel slag has a high-content iron and is a secondary utilization resource with great development potential. The coal-based direct reduction is an innovative technology that can be used to utilize the iron resources in nickel slag. The effect of the particle size of nickel slag on the strength and the reduction of nickel slag-coal composite briquettes were investigated. Four samples with particle size of 75~106 μm, 106~150 μm, 150~270 μm, and >270 μm were selected. The drop strength increased 9.4 times and the compressive strength reached 281.1 N when the nickel slag particle size decreased from >270 μm to 75~106 μm. The reduction degree determined by the data from the thermogravimetric experiment indicated that its maximum was 79.545%. The reduction experiments performed at 1200°C for 45 minutes indicated that the nickel slag with particle sizes between 75~106 µm were appropriate for the reduction of the nickel slag-coal composite briquettes.

In this study, lead-free 0.94 Na0.5Bi0.5TiO3-0.06BaTiO3 (NBT-BT) compositions at morphotropic phase boundary were successfully synthesized by solid-state reaction method. The effects of the particle size for various milling time (12-24-48 hours) and sintering temperatures (1100-1125-1150-1175oC for 2h) on the electrical properties of the NBT-BT ceramics were evaluated. Experimental results showed that particle size and sintering temperatures significantly affect the electrical properties of NBT-BT ceramics. The particle size of the ceramic powders decreasing while milling time increases to 48 hours. Particle size values for 0, 12, 24 and 48 hours (h) milled powders were measured as nearly 1.5 µm, 1 µm, 700 nm, and 500 nm respectively. The bulk density enhanced with increasing sintering temperature and showed the highest value (5.73 g/cm3) at 1150oC for 48h milled powder. Similarly, the maximum piezoelectric constant (d33) = 105 pC/N, electromechanical coupling coefficient (kp) = 25.5% and dielectric constant (KT) = 575 were measured at 1150oC for 48 h milled powder. However, mechanical quality factor (Qm) was reduced from 350 to 175 with decreasing particle size. Similarly, remnant polarization was dropped by decreasing powder particle size from 56 μC/cm2 to 45 μC/cm2.

The process of enrichment in a jig has usually been described and analysed using particle density as a separation feature. However, a degree of particle loosening in the jig bed is affected by, inter alia, the terminal particle free settling velocity which in turn is affected by the size, density and shape of a particle. Therefore, the terminal particle settling velocity clearly characterises the feed transferred to a jig for the enrichment process. Taking the comprehensive particle geometric (particle size and shape) and physical properties (particle density) into account comes down to the calculation of the terminal particle settling velocity. The terminal particle settling velocity is therefore a complex separation feature which comprises three basic particle features (particle density, size and shape). This paper compares the effects of enrichment of coal fines in a jig, for two cases: when the commonly applied particle density is separation feature and for the particle settling velocity. Particle settling velocities were calculated in the selected three particle size fractions: –3.15+2.00, –10.00+8.00 and –20.00+16.00 mm based on the industrial testing of a jig for coal fines and detailed laboratory tests consisting in determining particle density, projective diameter and volume and dynamic particle shape coefficient. The calculated and drawn partition curves for two variants, i.e. when particle density and particle settling velocity were taken into account as the separation argument in selected particle size fractions, allowed to calculate and compare separation precision indicator. With the use of a statistical test, the assumption on the independence of random variables of the distribution of components included in the distribution of the particle settling velocity as a separation feature during enrichment in a jig was verified.

Complex circuit of milling-classify systems are used in different branches of industry, because the required particle size distribution of product can seldom be reached in a single-stage grinding on the same device. The multistage processes of comminution and classification make possible suitable selection of parameters process for variables graining of fed material, mainly through sectioning of devices or change of their size and the types. Grinding material usually contains size fractions, which meet the requirements relating finished product. Then profitable is preliminary distributing material on a few size fractions, so to deal out with them demanded fraction of product, whereas remaining to direct alone or together with fed material to the same or different device. If the number of mills and classifiers in a circuit is large enough, building the model of particle size distribution transformation becomes rather complicated even for the circuit of a given structure. The situation becomes much more complicated, if we want to compare characteristics of all possible circuits, that can be constructed from these mills and classifiers, because the number of possible circuits increases greatly with the increase of number of devices being in the milling-classify system. The method creating matrix model for transformation of particle size distribution in a circuit of arbitrary structure of milling-classify system is presented in the article. The proposed model contains the mass population balance of particle equation, in which are block matrices: the matrix of circuit M, the matrix of inputs F and the matrix of feed F0. The matrix M contains blocks with the transition matrix P, the classification matrix C, the identity matrix I and the zero matrix 0 or elements describing the transformation of particle size distribution in the circuit. The matrix F is the block column matrix, which elements describing all particle size distributions at inputs to the circuit elements. The matrix F0 is the block column matrix, which elements describing particle size distributions in all feeds to the circuit. In paper was discussed this model in details, showed algorithm and three examples formatrix construction for the closed circuit ofmilling-classify systems. In conclusion was affirmed, that presented model makes possible to forecasting particle size distribution of grinding product, which leaving chosen the unit of system. The matrix model can be applied to improving modeling of mineral processing in the different grinding devices.

The mathematical modeling of mineral processing is a very complex task because of random character of comminuted materials. However, it allows applying of standard laws of mass preservation and mass transport. The basic method of description of comminution processes is determination of particles size distribution curves for products. In the paper, the concept of applying so-called censored distribution functions was presented, what means equations of exponential, Weibull, log-normand logistic distribution functions as the basis of crushers work description (formulas 1, 2, 3 and 4). The censoring of distribution functions is being realized through acceptation of maximum particle size dmax and the shape of them depends on shape and scale parameters. The joining of technical parameters of comminuting devices with parameters of equations describing distribution functions of products allows creating of satisfying models of comminution processes. After application of general forms of separation curves the description of sieving processes is possible (equations 6a and 6b) and then also of comminution systems. The optimization of aggregates production may be based on introduction of goal function determining profit dependably on amount of individual assortments. In case of analysis of comminution systems (formulae 10) in preparation of feed to beneficiation the goal function should be based on levels of useful minerals exposure in individual fractions. The paper shows the possibility of simulation of comminution processes course leading to determination of optimal conditions of systems containing comminution and sieving processes. Furthermore, the necessity of creation of empirical models for grinding processes was shown as they would be the compensation of models being result of heuristic analysis of phenomena. Also, the elementary rules of selection of models forms and their modifications based on justification of relations between distribution function parameters and basic technical parameters of devices as well characteristics of comminuted materials were discussed. The paper is the introduction to further research of general approach to joining grained materials characteristics with comminution effects.