Scale-up of power consumption in agitated ball mills

Previous investigations have shown that the specific energy input is the overall parameter of influence on product size during communition in agitated ball mills, from laboratory up to industrial scale. The specific energy input is the introduced energy related to the amount of comminuted material. This parameter can be used for mill scale-up. Consequently, a method had to be found of introducing power into the mill so as to obtain a given specific energy input. For this purpose, stirring tests with purely Newtonian liquids were carried out in absence of solids and hence, without comminution. Mathematical models are presented which describe the power consumption in agitated ball mills in absence of grinding beads. In addition, tests with grinding beads filling were also performed, leading to scale-up guidelines with respect to power consumption. Finally, the influence of size and material of grinding beads was investigated.     

An explanation of abnormal breakage of large particle sizes in laboratory mills

Abnormal breakage in laboratory mills may be defined as departure from first-order kinetics, and occurs particularly for the larger particle sizes in the mill feed. The reason for this abnormal breakage is that all the particles within a size fraction do not have tire same strength, rather having a distribution of strengths which interacts with a distribution of applied loads on the part of the grinding media. The interrelation between these two distributions, of strengths and forces, is discussed statistically showing the conditions necessary for departure from first-order kinetics. Actual values of the distribution of strengths support the theory, and a final experiment on the grinding of the survival material from previous grinding tests validated the concepts presented.     

Empirical and scale-up modeling in stirred ball mills

Stirred ball mills are frequently used for ultrafine- and nanogrinding in food, pharmaceutical and chemical industry, but only few investigations have been published on empirical or scale-up modeling of stirred ball mills. Experiments have been carried out with a laboratory scale stirred ball mill. During the experiments the main technical parameters such as stirrer speed, grinding media, filling ratio, grinding time and the solid mass concentration have been systematically adjusted. The particle size distribution of mill products can be well estimated by empirical functions, so an empirical model has been prepared for the laboratory mill. The relation between the grinding fineness, grinding time and specific grinding work was represented for several materials such as pumice, andesite, limestone and tailings of ore mining industry. The power consumption of the stirred ball mill for scale-up was determined by a method based on the dimensional analysis. A new scale-up model has been presented as well by with industrial size stirred ball mills can be designed on the basis of the laboratory measurements.     

Application of grinding kinetics analysis of inorganic powders by a stirred ball mill

The need for ultra fine particles has been increasing in the preparation field of raw powders such as fine ceramics and high functional products. A series of wet grinding experiments were carried out on inorganic powders such as calcite, pyrophyllite and talc by a stirred ball mill. The grinding rate constant K’ in the equation of grinding kinetics was examined based on the grinding kinetics analysis as the same type of function of a previous paper on a vertical type planetary ball mill. The experimental particle size distribution of the ground products was obtained in various grinding conditions. The grinding rate constants K and K’ were expressed by empirical equation involving experimental conditions by a stirred ball mill. The empirical equation on the grinding rate constant was expressed in terms of a function involving the ball diameter of grinding balls, the median diameter of feed material, and Bond’s work index of material, in the experimental conditions. The values of empirical constants C1 and C₂ were 21.13 and 0.0109 on K, while C₁ and C₂ were 120.99 and 0.0192 on K′, respectively. And the particle size distribution of ground products of each test material for a given grinding time was found to be expressing the selection function (the specific rate of breakage) which was obtained from the grinding kinetics analysis. In this study, the grinding rate change on calcite and pyrophyllite was similar at the same experimental operation condition. However, in the case of talc, it was observed that the grinding rate was not increased compared with other samples.     

Optimization of variables in grinding brass particles for paint and pigment industry

Flaky metal powders commonly used as paint and pigments, are generally produced by grinding in ball mills or vibration mills. The key to good quality powder production is to optimize the processing parameters. In the present work grinding of brass particles is studied in detail in a laboratory size ball mill to determine the optimal levels of the ball to material ratio, type and amount of additives, mill speed, ball load, etc. The quality of the powder is assessed on the basis of water coverage, degree of flattening and luster by visual inspection. Preliminary results in a 35 cm diameter ball mill with 30% ball load show that a material to ball ratio of 0.067 with a 0.1% dosage of stearic acid is required for good quality powder. For determining optimal mill speed and ball size a 2² factorial design of experiment has been followed. It has been determined that to achieve best powder quality the mill must run at 70% critical speed and the ball size must not exceed 20 mm. The quality of the powder assessed through SEM study for surface morphology and particle size analysis compares very well with the industrial samples.     

Flow of particulate solids through tumbling mills

The transport behavior of particulate solids flowing through tumbling mills depends strongly on the mill operating conditions. This paper presents the results of a detailed study to delineate the effect of the important operating variables on the hold-up, mean residence time and residence time distribution of particulate solids flowing through ball mills and rod mills. The effects of feed rate, media load, and mill speed on these transport parameters are discussed, emphasizing the fundamental differences between particulate transport in ball mills and rod mills. Under identical dimensionless operating conditions over the range of the investigation, the material hold-up and the Peclet number of the flow regime in the rod mill were always higher than those in the ball mill. Mechanistic interpretations of the observed transport phenomena are presented, and their implications in the context of tumbling mill analysis and design pointed out.     

Effects of concentration of dispersions on particle sizing during production of fine particles in wet grinding process

Stirred media milling is a prospective technology for producing colloidal dispersions by means of wet grinding process. In the past, many researchers have studied the effects of different operating parameters such as size, shape, nature and quantity of grinding medium, the speed of agitator in grinding chamber, the feed rate of dispersions, etc. in stirred media mills. However, it is still less known how particle sizing which generates valuable information of particle size of the product to interpret, control and optimize the grinding process, is influenced by the concentration of the dispersion during stirred media milling where particles change their size from micron to colloidal range rapidly. One of the reasons of this lack had been our incapability in the past to study the particle size distribution of dispersions without dilution. The recent advent of acoustic attenuation spectroscopy is known to be capable of studying dispersions without dilution, under real process conditions and on line. The study employs acoustic attenuation spectroscopy to investigate the effects of concentration of dispersions of CaCO₃ on its particle sizing during size reduction process in a stirred media mill (LabStar manufactured by NETZSCH). The dispersions of CaCO₃ at 5%, 10%, 20% and 30% (m/m) were studied about six hours under a selected set of operating conditions. Contrary to the existing knowledge obtained through other techniques of particle sizing that are based on the principle of dilution, acoustic attenuation spectroscopy shows that, under certain grinding time at given operating conditions, increase in concentration of dispersion results in better grinding results yielding smaller particles. The causes behind the differences in results of acoustic attenuation spectroscopy and dynamic light scattering have been thoroughly investigated. We find certain limitations of acoustic attenuation spectroscopy in particle sizing. A typical phenomenon which causes misleading trends in particle sizing is multiple scattering in acoustic measurements. Multiple scattering, particularly, influences acoustic results when particles approach to fine size range during size reduction process.     

Experimental investigations and modelling of the ball motion in planetary ball mills

Planetary ball mills feature attractive properties, like the possibility of dry or wet operation, straightforward handling, cleanability and moderate costs. Consequently they are very well suited for lab scale process development in diverse industries, including pharmaceuticals and new materials. A number of questions still remain unanswered regarding this mill type. These include the stress conditions as well as transfer of the grinding results to other types of mills with free moving balls, such as stirred media mills, which can be built in large scales and operated continuously.In order to measure the ball motion and, thus, the stress conditions, a planetary ball mill was equipped with a high speed video camera, so that the grinding ball motion during the comminution process can be recorded and analysed. The influence of important process parameters on the ball motion pattern was assessed in this study, namely speed ratio, ball filling ratio and friction conditions, the latter by applying different mill feeds. The experimental results show considerable influences of the ball filling ratio and friction conditions. The measured ball motion patterns differ significantly from ball trajectories which were calculated using kinetic equations proposed in older publications.In addition to the measurements the ball motion was simulated using a three dimensional Discrete Element Model (DEM). An attempt was made to account for mill feed via altered friction coefficients. Correlations of the DEM results and experimental findings at different operating conditions show a good agreement. Based on simulation data the frequency distribution of the stress energies in the mill could be calculated and compared for different operating conditions.     

Radial mixing of particles in a dry batch ball mill

Poor mixing in dry ball mills can lead to insufficient presentation of fine particles to the classifying air, overgrinding of particles and wastage of energy in a ball mill. A video capture method has been used to study radial mixing kinetics in a dry batch ball mill. Experiments were conducted in a ball mill with PVC plastic powders being used as particles so that the effect of size reduction could be neglected. Radial mixing in ball mills was studied at typical industrial speeds of 75%, 80% and 90% of critical. The rate of particle mixing was observed to increase with increasing mill speed. A simplified mathematical model is presented that can be used to predict the radial mixing of particles in a ball mill. A parameter, k, was used to quantify the kinetics of mixing as affected by the mill's speed.     

Agglomeration and breakage of nanoparticles in stirred media mills—a comparison of different methods and models

The increasing industrial demand for nanoparticles challenges the application of stirred media mills to grind in the sub-micron size range. It was shown recently [Mende et al., 2003. Mechanical production and stabilization of submicron particles in stirred media mills. Powder Technology 132, 64-73] that the grinding behavior of particles in the sub-micron size range in stirred media mills and the minimum achievable particle size is strongly influenced by the suspension stability and thus the agglomeration behavior of the suspension. Therefore, an appropriate modeling of the process must include a superposition of the two opposing processes in the mill i.e., breakage and agglomeration which can be done by means of population balance models. Modeling must now include the influence of colloidal surface forces and hydrodynamic forces on particle aggregation and breakup. The superposition of the population balance models for agglomeration and grinding with the appropriate kernels leads to a system of partial differential equations, which can be solved in various ways numerically. Here a modified h-p Galerkin algorithm which is implemented in the commercially available software package PARSIVAL developed by CiT (CiT GmbH, Rastede, Germany) and the moment methodology according to [Diemer and Olsen, 2002a. A moment methodology for coagulation and breakage problems: Part I—analytical solution of the steady-state population balance. Chemical Engineering Science 57 (12), 2193-2209; Diemer and Olsen, 2002b. A moment methodology for coagulation and breakage problems: Part II—moment models and distribution reconstruction. Chemical Engineering Science 57 (12), 2211-2288] are used and compared to explicit data on alumina. This includes a comparison of the derived particle size distributions, moments and its accuracy depending on the starting particle size distribution and the used agglomeration and breakage kernels. Finally, the computational effort of both methods in comparison to the prior mentioned parameters is evaluated in terms of practical application.     

A short-lived radioactive tracer method for the measurement of closed circuit ball mill residence time distributions

This paper describes an extension of the short-lived radioactive tracer method to the on-stream measurement of residence time distributions of ball mills in closed circuit with a classifier. In essence, the method calls for tracing a size of irradiated circuit feed particles for which the classifier behaves as a simple splitter. By assuming that the mill RTD is particle size independent and that there is negligible tracer dispersion in the classifier, tracer data obtained in the mill product are mathematically treated to give the mill RTD. The extended method is derived, developed and demonstrated on a closed circuit test loop and on a pilot-plant scale ball mill in closed circuit with a hydrocyclone.     

燃烧法和固相法所制备的红褐色陶瓷颜料ZnFe1.2Cr0.8O4的研磨效果研究

本文以燃烧法和固相法分别制备的红褐色陶瓷颜料ZnFe_1.2Cr_0.8O₄(燃烧法：C-ZnF;固相法：S-ZnF)为研究对象,采用正交试验的方法对颜料颗粒的研磨最优参数进行分析探讨。使用激光粒度仪表征研磨前后颜料颗粒的粒度及其分布,通过极差分析法来分析研磨的最优参数。结果表明,上述两种颜料颗粒的最优研磨条件均为：添加5wt%的分散剂WF211,研磨时间为100min,研磨转速为2000rpm。在相同的研磨条件下,对比固相法制备的颜料颗粒S-ZnF,燃烧法制备的颜料颗粒C-ZnF可以得到颗粒粒度细且分布窄的颜料颗粒产品。另外,采用一种粒数衡算模型(PBM)来模拟颜料颗粒的研磨过程破碎行为,计算颜料颗粒在研磨过程中的选择函数矩阵。通过模拟分析表明,颜料颗粒C-ZnF的研磨效果要优于颜料颗粒S-ZnF。     

OPTIMIZATION OF OPERATING VARIABLES FOR PRODUCTION OF NANOPARTICLES USING RESPONSE SURFACE MODELING

The objective of this study is to investigate the effect of operating parameters such as ball loading (J), solid mass fraction (C_m), pH of the suspension, and grinding time (t) on particle size distribution for the production of nano mineral particles in a stirred ball mill using response surface modeling. The particle size is arrived at by the method of Rosin-Rammler-Bennett distribution rather than by the average diameter method. Box-Behnken design is employed to arrive at the number of trials required. The results obtained show that particle size decreased with the increase in ball loading, pH, and grinding time, but not solid mass fraction. Moreover, optimum (i.e., minimum particle size) value of pH and solid mass fraction is found to be 12 and 0.3 respectively for the studied material, silica.     

Continuous grinding in a small wet ball mill. Part IV. A study of the influence of grinding media load and density

TXX influence of changes in grinding media load and density on the grinding behaviour of trace quantities of quartz within an environment of calcite in a small continuous wet ball mill have been studied using (a) ball loads ranging from 45% to 100% of the standard load of 1-in. balls, (b) a standard load of 1-in. pebbles and (c) standard loads of equicylinders with specific gravities ranging from 2.82 to 9.49. A mill overload condition (125% ball load) has also been studied using a feed comprising 5% by weight of full-size-range quartz and 95% standard calcite.The results show that variations in breakage behaviour were best followed by a comparison of the adjusted breakage rate constants (k′) for individual sizes corresponding to a standard hold-up-weight. The changes in k′ with ball load could be explained in terms of changes in number of impacts per unit time and in the environmental size distribution. A reduction in the density of the grinding media caused a disproportionate decrease in k′ for the coarse sizes compared with the fine sizes, and breakage rates tended to zero for all sizes as the density of the medium approached that of the pulp.Whilst under some of the test conditions the flow of tracer solids behaved anomalously, under most conditions there was an approximately linear relationship between average residence time and total weight of media charged to the mill.Media density per se had no effect on breakage function, but there was a distinct change due to change in media shape.     

Effect of media size in stirred ball mill grinding of coal

As a prerequisite to producing super-clean coal with any physical coal-cleaning process, such as microbubble flotation, the feed coal must be micronized to liberate finely disseminated mineral matter. The stirred ball mill is regarded as one of the most efficient devices for micronizing coal. Using a 13.4 cm batch mill, the optimum operating conditions have been determined in terms of media size, feed size and media type. The rate of breakage determined with monosized feeds are compared on the basis of specific energy consumption. It has been found that a 20:1 ball size/particle size ratio gives optimum grinding conditions.     

Residence time distributions in a stirred ball mill and their effect on comminutionVerweilzeitverteilung in einer rührwerkskugelmühle — bedeutung für die zerkleinerung

Experimental investigations concerning the residence time distributions of both the solid and the liquid phase have been carried out for a continuously operated stirred ball mill. It is admissible to consider the suspension as a single-phase fluid.Residence time distributions are found to be well described by an axial dispersion model. The dimensionless transport parameter, the Peclet number, is shown to be dependent on operating conditions of the mill.Comparisons between grinding results obtained during continuous operation and during batch operation under comparable conditions reveal the effect of residence time distributions. The particle size distribution of the continuously ground product can be calculated using batch grinding data and residence time distribution information.     

Characterization of media mills based on mechanical energy applied to particles

This paper deals with the evaluation of characteristics of media mills having a different milling mechanism based on the mechanical energy applied to the particles to be processed during a milling treatment. Spherical copper powder was used as a stress-sensitive material and the milling treatment of the copper powder was carried out under various operating conditions using three types of media mills, a horizontal tumbling ball mill, vertical agitating ball mill and bead mill. The size distributions of copper powder before and after the milling treatment were measured and the deformation of copper particles was determined experimentally. The net energy applied to the copper powder was estimated from the plastic deformation of copper particles. It has been clarified that the applied energy depends strongly on the motion of media in the mill. By introducing two dimensionless parameters, which express the energy transfer efficiency from the kinetic energy of media to the particles and the motion of media in the mill, respectively, the media mills could be characterized on a uniform scale based on the applied energy regardless of milling mechanism.     

Regrinding sulphide minerals — Breakage mechanisms in milling and their influence on surface properties and flotation behaviour

Changes in surface properties with grinding and regrinding play a key role in mineral flotation performance. Different particle breakage mechanisms in grinding mills may change the mineral surface properties in different ways, possibly leading to different mineral floatabilities depending upon the predominant breakage mechanism. The Magotteaux Mill^® and IsaMill were selected as representations of a tumbling and a stirred mill, respectively. The latter has a greater contribution to particle size reduction from the abrasion mechanism than the former which also has contributions from impact breakage.Mineral recovery decreased with size reduction through stirred mill regrinding (i.e., the IsaMill) employing ceramic media from 90%, achieved before regrinding (d₈₀ 80 μm regrind feed), to 71, 58, 20 and 5% achieved after regrinding to d₈₀ values of 60, 40, 20 and 10 μm, respectively. A similar trend of decreasing recovery was also observed with regrinding in the tumbling mill (i.e., Magotteaux Mill^®). Changes in mineral flotation behaviour were investigated with respect to (i) particle size, (ii) increase in surface area, and (iii) surface contamination with size reduction in the two different mills. The flotation of pyrrhotite with additional reagents illustrated that the total change in recovery through regrinding results mainly from the increase in surface area of the pyrrhotite afforded by size reduction. The effects of the predominating particle breakage mechanism on the change of mineral surface properties were studied through regrinding in the two different mills. In particular it was observed that the hydrophobicity/floatability of the coarse particles decreased to a greater extent with stirred mill regrinding than with tumbling mill regrinding at coarser regrind product sizes (d₈₀ 70 and 60 μm) presumably due to the greater contribution of the abrasion mechanism to size reduction afforded by the stirred mill. It was also observed that the difference in recovery for the same regrind product size from the two different mills decreased when approaching finer regrind sizes, which indicated that the particle breakage mechanisms of the different mills for fine regrind product size were not as influential as for coarse regrind product sizes.     

The influence of grinding technique on the liberation of clinker minerals and cement properties

This paper describes a study of the relationship between the physical, chemical and mineralogical parameters of cement products obtained by different grinding mechanisms namely high pressure grinding rolls (HPGR) and ball milling, and their effects upon the properties of cements prepared from the ground clinker. Samples were prepared as narrow size fractions and also as distribution samples. Characterization parameters were ascertained by using XRF, laser sizing, Blaine and BET surface area and image analysis methods. HPGR grinding resulted in higher degrees of liberation of clinker phases arising from the intergranular breakage along the grain boundaries compared to ball mill grinding. As for service properties, water demand of HPGR products was higher than ball mill products resulting from high micro fissured structure. Despite high liberation of particularly alite mineral in HPGR grinding, the compressive strength of ball mill products was slightly higher than HPGR products for narrow size samples. Finally, particle size distribution effect on strength was more obvious for distribution samples; generally ball milling gave higher strength values.