Papers by Elias Stamboliadis
A Measure of Separation
Science, Jun 16, 2011
Journal of the Mechanical Behaviour of Materials, 2012
The relationship of the energy required to break a particle or a particulate material vs. particl... more The relationship of the energy required to break a particle or a particulate material vs. particle size has been studied by many researchers. On the one hand, mineral processing engineers, who are interested in the specific energy (in joules per cubic meter or joules per kilogram) required for grinding, almost agree that it is inversely proportional to the particle size, although they might disagree on the type of the relationship. On the other hand, building and structural engineers, who are mainly interested in the strength of materials (in newtons per square meter or pascals), they almost agree that at the size range of the elements used, their strength depends on the quality of the material rather than its size. The present article shows that both groups of engineers are right about the size range of the bodies used by each one. However, there is a critical size that determines the fracture behavior of a brittle material. The definition of the critical size can be used to unders...
Mining, Metallurgy & Exploration, 2003
The present work assumes that all the molecules that make a particle of a brittle material share ... more The present work assumes that all the molecules that make a particle of a brittle material share its suiface energy. This energy is the area of the particle times its suiface tension. The specific suiface energy of the particle, energy per unit mass or per mole, is also used as a potential that characterizes the energy state of its molecules. It is assumed that the energy for the breakage of a brittle particle is usedfor the creation of new suifaces. It is also assumed that this energy is distributed among the molecules according to the classical theory by Maxwell-Boltzman. Given the correspondence between the specific energy of a particle and the number of its molecules that share it, one can find the size of a particle and consequently the size distribution of the material produced after breakage. The parameters necessary to complete the task are the energy input, the initial mass of the material, its molecular weight, the shape factors, the density and the suiface tension. The last one is a difficult parameter to assess due to the fact that solid materials have structural defects that can cause variation of their suiface tension. The present approach also allows the calculation of an equivalent temperature that can be used as an index of the energy state of the system.
Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis
Particulate Science and Technology, 2016
ABSTRACT It is known that the single linear Gates–Gaudin–Schuhmann (GGS) model is in some cases u... more ABSTRACT It is known that the single linear Gates–Gaudin–Schuhmann (GGS) model is in some cases unable to fully describe the particle size distribution of comminution products. In order to overcome this shortcoming, piecewise regression analysis was used to predict the size distributions derived, after grinding for various periods four mono-sized fractions of quartz and marble in a laboratory ball mill. The single line was divided into two straight lines, which indicate the presence of two domains of particle sizes and therefore the involvement of two distinct breakage mechanisms. The obtained GGS model parameters were used to determine the evolution of particle size distribution as a function of the energy input. In addition, the existing relationships between energy input and particle size distribution were improved, by taking into account the effects of the feed size and material type. The new relationships obtained can be used for a more accurate estimation of the required energy for breakage.
Journal of the Mechanical Behavior of Materials, 2007
In mono-axial tests of the strength of materials under tensile or compressive load the behavior o... more In mono-axial tests of the strength of materials under tensile or compressive load the behavior of the materials is studied by varying the stress, which is measured as the force over the cross section area of the specimen tested, usually a cylinder of initial length L(0). The force F is the independent variable and the length L(F) is a function of the variable F and the properties of the material as well. The deformation L(0)-L(F) =AL is usually taken into consideration. In a previous paper, "The Fracture of Brittle Materials as an
Journal of the Mechanical Behavior of Materials, 2005
It is known that the tensile strength of glass fibers of the same length increases as their diame... more It is known that the tensile strength of glass fibers of the same length increases as their diameter decreases. At the same time it is also known that the specific fracture energy of mineral particles increases as their size is reduced as well. This evidence has been used to support the theory for the existence of structural defects in the matter. The number of cracks and their size decrease with the size of the particle and the material becomes stronger. The present work presents a model that can explain the increased strength of finer fibers or smaller mineral particles as a result of energy balance at the moment of fracture without the assumption of structural defects in the matter. According to the proposed mathematical model the energy consumed for the fracture of a brittle material, like glass or mineral particles, is partly used to deform the specimen and increase its surface area and partly is stored in the matter as internal potential energy. At the moment of fracture the internal energy exceeds the cohesion energy of the matter and the specimen breaks. A useful implication of the proposed model is that it also provides the means to measure the surface tension and the specific cohesion energy of solid materials. The deviation of the specific cohesion energy from the theoretical strength of the material shows the existence of defects in the matter.
Minerals Engineering, 2007
The present paper is a partial theoretical approach to the comminution process. A general theory ... more The present paper is a partial theoretical approach to the comminution process. A general theory of comminution should consist of two parts, one that deals with the energy required to break mineral particles and another that examines how this energy is distributed to the particles generated after breakage. The present approach deals with the second part that examines how the energy invested for comminution is distributed to the mill product. It uses the generally accepted concept, which assumes that the useful part of comminution energy is consumed to create new surfaces and finds the relationship between a characteristic particle size of the mill product and the energy consumed for grinding. The paper introduces the concept of potential energy and provides the means to give a value to the energy state of a material produced by a specific type of equipment. The energy efficiency is also taken into consideration and is used to calculate the energy actually invested for comminution. The main conclusion is that the specific surface energy is a physical property of materials and can be used as a universal index characterizing their grindability, regardless of the mill type or the mill efficiency. The physical dimensions of this index are energy per unit surface area (J/m 2) compared to energy per unit volume or unit mass, which are the dimensions of the indices proposed so far.
KONA Powder and Particle Journal, 2017
It is known that ball milling is an energy intensive process and great efforts have been made ove... more It is known that ball milling is an energy intensive process and great efforts have been made over the years to improve energy efficiency. The use of population balance models (PBMs) can assist in the design of mineral processing circuits and the scale-up of laboratory mill results to full-scale. However, since each model has its own capabilities and limitations, it is believed that a combined use will provide more accurate information for the reliable description of the process. In this study, the simulation of grinding of quartz is investigated in order to identify the optimal mill operating parameters. With the use of population balance modeling the specific rate of breakage and the cumulative breakage parameters can be determined from mono-size, short grinding time batch tests. The determined breakage parameters were back calculated by minimizing the residual error between experimental and reproduced size distributions. By combining two software packages the back calculated breakage parameters were used for the prediction of the optimum ball filling volume. The proposed procedure can be also applied for the identification of optimal mill operating parameters for other minerals.
Bulletin of the Geological Society of Greece, 2017
During recent decades many studies have be done on the rocks that developed in the area of Wester... more During recent decades many studies have be done on the rocks that developed in the area of Western Greece and especially in Epirus, known in geoscientific literature as Ionian Zone of External Hellenides. These rocks have undergone geological research (basic geological mapping, research for hydrocarbons, metals and inert materials) and exploitation (inert materials). Recently, within the sedimentary succession of the Ionian zone submarine fans, in the region of Peta–Kompoti, in the prefecture of Arta, have been identified positions where sedimentary gold is present. Recently, positions where sedimentary gold is present, within the sedimentary rocks of the submarine fans, in the region of Peta–Kompoti, prefecture of Arta, have been identified. For the continuation and the practical application of these positive results, it was necessary to obtain a documented reference of geological parameters. After a series of new sampling and detailed analysis of the samples, this work presents th...
Bulletin of the Geological Society of Greece, 2013
In Epirus, Western Greece, there exist extensive low quality phosphate rock deposits. Although ph... more In Epirus, Western Greece, there exist extensive low quality phosphate rock deposits. Although phosphate fertilizers are extensively used in agriculture and Greece imports about 200.000 ton/y, of phosphate ore in addition to ready to use phosphate fertilizers, these deposits are not yet exploited.This work examines the possibility to upgrade this type of ore using different methods of mineral processing. The results obtained are poor and unsatisfactory for commercial exploitation. The main reasons are the type of P2O5 bearing mineral and mainly it’s intergrowth with the associated gangue ones.The present work examines the mineralogy and chemistry of the ore, the energy size relationship in crushing using a centrifugal crusher, its behavior in grinding, its behavior to heavy liquid treatment and its floatability using oleic acid as well as dialkyl-orthophosphate collectors. The later were specially prepared for this purpose. Finally the ore was calcined at 950 oC in order to dissocia...
Removal of phenols from the water effluents of olive presses
Environmental and Climate Technologies, Nov 9, 2012
Abstract The water effluents of olive presses contain a number of phenols that are hardly biodegr... more Abstract The water effluents of olive presses contain a number of phenols that are hardly biodegradable and therefore constitute an environmental hazard, mainly in the Mediterranean countries. The present work presents the results obtained from the study of artificial solutions containing one kind of phenol, namely gallic acid that consists of the main type of phenols present. According to the experimental procedure, the phenol is removed from the water solution by absorption on different naturally occurring raw rock materials. The first material is caustic magnesia produced after the calcination of a magnesite sample from Macedonia, Greece, the second is a sample of sedimentary psammitic marl from the area of Chania, Crete, Greece, and the third solid absorbent is a bentonite sample from the island of Milos, Greece. According to the results obtained, magnesia seems to be by far the best absorbent, with an absorbing capacity of 3500 mg of phenol per gram, followed by the psammitic marl. The absorbing capacity of bentonite is almost negligible
Geomaterials, 2013
The energy size relationship is examined, either as the specific energy required breaking a parti... more The energy size relationship is examined, either as the specific energy required breaking a particulate material from an initial size d 1 to a final size d 2 , where d is usually the d 80 size, or as the specific energy required to break a single particle. The present work uses the results obtained using a controlled frequency centrifugal crusher to crush particles of a predetermined size class under different rotation frequencies related to the kinetic energy of the particles at the moment of crushing. The paper calculates the relationship between the rotation frequency and the kinetic energy of the particles before crushing and examines the size distribution of the products. The study results allow presenting the relationship between the kinetic energy of the particles and the mass of particles produced below the initial size class. The work also produces the optimum mathematical model that describes this relationship among three proposed ones. According to this model one can calculate the energy required breaking half of the initial mass below the initial size class and the corresponding specific energy is appointed to the average size of the class. The parameters of the mathematical model can be used to compare the grindability of the different materials. The process can be used as an alternative to the drop weight technique used so far for the study of the breakage energy of minerals and rocks.
European Scientific Journal, Jan 14, 2014
A closed circuit crushing consists of a crusher that breaks the feed material, a screen that clas... more A closed circuit crushing consists of a crusher that breaks the feed material, a screen that classifies the material and a conveyor system that returns the over size back to the crusher. The capacity of a centrifugal crusher with a given motor power depends on its rotation frequency. The lower the rotation frequency the lower the specific energy, or breakage intensity, that the particles obtain before breakage and hence the greater the capacity of the crusher to provide a low specific energy to the feed particles On the other hand, according to the breakage model the fraction of the feed that breaks below the feed size class is greater as the kinetic energy given to the particles increases. The combination of these two parameters has two effects: a) the energy cost per mass of the material broken by the crusher decreases as the breakage intensity decreases and b) the circulating load that has to be returned to the crusher increases as the breakage intensity decreases. This paper shows how to calculate the optimum crusher breakage intensity, or rotation frequency, in order to minimize the energy cost per ton of the product broken below size.
Removal of arsenic from water solutions by naturally occurring limonite
Arsenic is a pathogenic element and its presence in drinking water is undesirable. It is well kno... more Arsenic is a pathogenic element and its presence in drinking water is undesirable. It is well known that arsenic reacts with iron to form insoluble substances and it is absorbed from water by iron compounds. This work examines the possibility to remove arsenic from water solutions by naturally occurring limonite. Limonite samples were collected from an old iron ore mining area in the district of Hania in the island of Crete and one of them was selected for the experimental work. Two series of absorption tests were performed in order to develop an efficient procedure of arsenic removal from artificial water solutions of different concentrations. In the first series of tests a constant amount of limonite is used in each case to remove arsenic from water solutions of the same volume that differ in the initial concentration of arsenic. For high initial concentrations of arsenic up to 2000 ppb the remaining arsenic is still high and the efficiency of the process is low. This problem is o...
The surface chemistry of the flotation millerite, pyrrhotite and pentlandite with dialkyl-dithiophosphates [microform] /
Seventy-four leaves inserted. Includes abstracts in English and French. Thesis (Ph. D.)--McGill U... more Seventy-four leaves inserted. Includes abstracts in English and French. Thesis (Ph. D.)--McGill University, 1977. Includes bibliographical references (leaves 245-249). Microfiche of typescript.
Developments in gold recovery equipment and their use in Greece
Gravity separation techniques were used in the early years to extract native metal nuggets and fl... more Gravity separation techniques were used in the early years to extract native metal nuggets and flakes from placer gold deposits. This was relatively easy for visible metal grains. As the size of the grain becomes smaller traditional gravity separation techniques become inadequate to recover native gold. Cyanidation was invented as a solution to the problem. According to it, gold and other precious metals are dissolved in water by sodium cyanide. The result was a drastic increase of world gold production but at the same time environmental issues were raised. In Greece gold mining has become equivalent with the absolute destruction of the environment and is under extinction. In the last years a new type of gravity equipment have been produced which create a gravitational field up to 200 G and can separate gold from gangue minerals at sizes below 50 μ m. The strong gravitational field is created by centrifugal forces and the separation occurs in a fluidized bed, formed by water flow. A...
Geomaterials, 2011
The work index W i was defined by F. Bond as the specific energy (kWh/ton) required to reduce a p... more The work index W i was defined by F. Bond as the specific energy (kWh/ton) required to reduce a particulate material from infinite grain size to 100 microns. The calculation is based on the size-energy relationship 1,2 2 1 1 1 n n e C x x , which for n = 0.5, x 1 = ∞ and x 2 =100, by definition gives e ∞,100 = W i and consequently C = 10W i. In theory, for a given material the value found for W i should be constant regardless of the measured sizes x 1 and x 2 used to calculate the constant C by measuring the energy e 1,2. In practice this is not so due to the fact that n ≠ 0.5 and many correction factors have been proposed to overcome this inadequacy experienced by accepting n = 0.5. The present paper proposes a simple way to calculate the appropriate exponent n using conventional grinding procedures. The same calculation can be used to calculate the true value of W i and attribute a potential energy state to a material at any size.
Geomaterials, 2014
The Nome nickel laterite deposit is located in the North East of Albania. The ore deposit, develo... more The Nome nickel laterite deposit is located in the North East of Albania. The ore deposit, developed between ultramafic rocks and limestones during Early Cretaceous to Eocene, represents part of the Albanian Mirdita ophiolite zone. The lateritization of the deposit was observed mainly in three separate areas, the Has-Kukes-Lure in the North, Pogradec-Librazhd in the center and Devoll in the South. The main mineralogical components of the ore are goethite, hematite and quartz, while the secondary ones are chlorite (clinochlore, Ni-chlorite), kaolinite and lizardite. Nickel is mainly found in chlorite. The ore is characterized by the presence of spheroid particles, such as oval, pisoid, peloid and composite spheroid. According to the microscopical examination the ore is characterized in general as allotriomorphic, inequigranular and the texture is oolitic-pisolitic. For the mineral processing gravimetric and magnetic separation are used in the size fractions −8 + 4 mm, −4 + 1 mm, −1 + 0.250 mm and −0.250 + 0.063 mm. The chemical and mineralogical analyses, as well as the microscopic examination have shown that mineral processing by magnetic separation gives the most satisfactory results for the size fractions −1 + 0.250 mm and −0.250 + 0.063 mm.
Crushing of Mineral Particles by Control of Their Kinetic Energy
Material Science and Applied Chemistry, 2013
Minerals Engineering, 2002
The contribution of this paper on the relationship of energy-particle size in the comminution of ... more The contribution of this paper on the relationship of energy-particle size in the comminution of brittle particulate materials is based on two concepts: (a) the potential energy of a single particle and (b) the size distribution of particles in a particulate material. The potential energy Q x of a single particle of size x is defined as the energy required to create this particle. By definition Q x ¼ q x M x , where q x is the specific energy per unit mass and M x the mass of the particle. The relationship, which relates the energy to the size of the material, is assumed to be an empirical one: ðdq x =dxÞ ¼ ÀCð1=x m Þ, where C and m are constants. For particulate materials, the particle distribution is assumed to be the Gates, Gaudin, Schuhmann: P x ¼ W 0 ðx=yÞ a , where P x is the cumulative particle mass finer than x, W 0 is the total mass of the assembly, y is the maximum particle size (size modulus) and a is a constant (distribution modulus). The potential energy E y of a particle assembly is defined as the total energy of its particles. It is shown that for m > 1 and a À m 6 ¼ À1 then E y ¼ ðCW 0 =ðm À 1ÞÞða=ða À m þ 1ÞÞy 1Àm and for a À m ¼ À1 then E y ¼ ðCW 0 =ðm À 1ÞÞðln y a =y a Þ. For m ¼ 1 and a 6 ¼ 0 then E y ¼ ÀCW 0 ðln y À 1=aÞ. For a ¼ 0, which is practically impossible, then E y is not defined. The case for m < 1 is not realistic because it gives negative values for the potential energy. The conditions for the application of the formulae above are presented in the text.
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Papers by Elias Stamboliadis