1 Particle Size Analysis.pdf

Sub-Sieve Techniques Introduction and Stokes’ Law Russel M. Culibar METE 125 – MINERAL PROCESSING I Sub-Sieve Techniques • Sieving is rarely carried out on a routine basis below 38 µm; below this size the operation is referred to as sub-sieving. • The most widely used methods are sedimentation, elutriation, microscopy, and laser diffraction, although many other techniques are available. • Many concepts in use for designating particle size within the sub-sieve range, and is important to be aware particularly when combining size distributions determined by different methods. • For irregularly shaped particles, use combining factor when combining size distributions: Conversion Multiplying Factor Sieve size to stokes’ diameter (sedimentation, 0.94 elutriation) Sieve size to projected area diameter 1.4 (microscopy) Sieve size to laser diffraction 1.5 Square mesh sieves to roundhole sieves

1.2

Stokes’ Equivalent Diameter • Based on stokes’ law: a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient. • Assumptions for stokes law: • Laminar Flow • Spherical particles • Homogeneous (uniform in composition) material • Smooth surfaces • Particles do not interfere with each other. • Separation of particles based on the resistance of the particle to motion in a fluid. • The resistance to motion determines the terminal velocity which the particle attains as it is allowed to fall in a fluid under the influence of gravity. 𝑑2g(Ds − Df) v= 18ŋ v=terminal velocity d=diameter g=gravity Ds=particle density Df=fluid density ŋ=fluid viscosity (ŋ=0.001 Nsm-2 for water at 20oC)

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Because of the assumptions of stokes law, there is an upper size limit determined by the particles Reynolds number, a dimensionless quantity defined by: vdDf R= ŋ v=terminal velocity d=diameter g=gravity Df=fluid density ŋ=fluid viscosity (ŋ=0.001 Nsm-2 for water at 20oC) R=Reynolds number Reynolds number should not exceed 0.2 if the error in using stokes’ law is not to exceed 5%. In general, Stokes law will hold for all particles below 40 µm dispersed in water; particles above this size should be removed by sieving beforehand. The lower limit being 1 µm below which the settling times are too long, and also the effects on unintentional disturbances, are far more likely to produce serious errors.

PREPARED BY: Dayle Tranz R. Daño COURSE: METE 125 PROFESSOR: Dr. Vannie Joy Resabal TOPIC: Sedimentation Method GROUP NUMBER: 1 INTRODUCTION Sub-sieving techniques are used to determine the particle size of materials ranging below 38μm. The most widely used methods are sedimentation, elutriation, microscopy, and laser diffraction. DEFINITION AND PROCESS Sedimentation Methods are based on the measurement of the rate of settling of the particles uniformly dispersed in a fluid. This is well illustrated in the common laboratory experiment “beaker decantation”. The material being tested is uniformly distributed in low concentration in waiter, contained in a beaker or any similar container. The material concentration must be low to ensure that no interaction between materials will happen upon settling. A wetting agent may be added to ensure complete Figure 1. Beaker Decantation

dispersion of the particles. A syphon tube is immersed into the water to a depth of h below the water level, corresponding to about 90% of the liquid depth L. The terminal velocity v is calculated from Stokes' law for the various sizes of particle in the material, say 35, 25, 15, and 10 µ,m. For an ore, it is usual to fix D, for particles which are most abundant in the sample.

The time required for a 10 urn particle to settle from the water level to the bottom of the syphon tube, distance h, is calculated as

t = h/v

where t = time to settle h= immersion depth of siphon v= velocity calculated from Stokes’ law -------------stoke The pulp is gently stirred to disperse the particles through the whole volume of water and then it is allowed to stand for the calculated time from the equation above. The water above the end of the tube is syphoned off and all particles in this water are assumed to be smaller than 10 urn diameter However, a fraction of the -10 urn material, which started settling from various levels below the water level, will also be present in the material below the syphon level. In order to recover these particles, the pulp remaining must be diluted with water to the original level, and the procedure repeated until the decant liquor is essentially clear. In theory, this requires an infinite number of decantation, but in practice at least five treatments are needed, depending on the accuracy required. The settled material can be treated in a similar manner at larger separating sizes, i.e. at shorter decanting times, until a sufficient number of fractions is obtained.

ADVANTAGES AND DISADVANTAGES Sedimentation method has several advantages. Firstly, it is simple and cheap. Sedimentation method does not require equipment that are hard to look for and does not require an expert to perform. It also has the advantage over many other sub-sieve techniques in that it produces a true fractional size analysis, i.e. reasonable quantities of material in specific size ranges are collected, which can be analyzed chemically and mineralogically. This method is, however, extremely tedious, as long settling times are required for very fine parti•cles, and separate tests must be performed for each particle size. For instance, a 25 um particle of quartz has a settling velocity of 0.056cm per s ,and therefore takes about 3.5 min to settle at 12 cm h, a typical immersion depth for the syphon tube. Five separate tests to ensure a reasonably clear decant therefore require a total settling time of about

18 min. A 5 μm particle, however, has a settling velocity of 0.0022cm per s, and therefore takes about 1.5 hours to settle 12 cm. The total time for evaluation of such material is thus about 8 h. A complete analysis may therefore take an operator several days. Another problem is the large quantity of water which dilutes the undersize material, due to repeated decantation. Theoretically an infinite number of decantations are required to produce a 100% efficient separation into oversize and undersize fractions, and the number of practical decantations must be chosen according to the accuracy required and the width of the size range required in each of the fractions . EFFICIENCY In the system, after time t, all particles larger than size d have fallen to a depth below the level h. All particles of a size d1 , where d1 < d, will have fallen below a level h1 below the water level, where h1 « h. The efficiency of removal of particles of size d1 into the decant is thus:

since at time t = 0 the particles were uniformly distributed over the whole volume of liquid, corresponding to depth L, and the fraction removed into the decant is the volume above the syphon level, h-h1. Now, since t= h/v, and v is proportional to d2,

Therefore, by further derivation,

Where a = h/L

If a second decantation step is performed, the amount of -di material in the dispersed suspension is 1 - E, and the efficiency of removal of -d1 particles after two decantations is thus In general, for n decantation steps, the efficiency of removal of particles of size d1 at a separation size of d, is

The following table shows the number of decantation steps required for different efficiencies of removal of various sizes of particle expressed relative to d, the separating size, where the value of a= 0.9.

Table 1. Number of decantations required for required efficiency of removal of fine particles

It can be shown that the value of a has relatively little effect; therefore there is nothing to be gained by attempting to remove the suspension adjacent to the settled particles, thus risking disturbance and re-entrainment. Table 1 shows that a large number of decantations are necessary for effective removal of particles close to the separation size, but that relatively small particles are quickly eliminated. For most purposes, unless very narrow size ranges are required, no more than about twelve decantations are necessary for the test.

ANDREASEN PIPETTE TECHNIQUE A much quicker and less-tedious method of sedimentation analysis is the Andreasen pipette technique The apparatus (Figure 2) consists of a half-litre graduated cylindrical flask and a pipette connected to a 10 ml reservoir by means of a two-way stop cock. The tip of the pipette is in the plane of the zero mark when the ground glass stopper is properly seated. A 3-5% suspension of the sample, dispersed in the sedimentation fluid, usually water, is added to the flask. The pipette is introduced and the suspension agitated by inversion. The suspension is then allowed to settle, and at given intervals of time, samples are withdrawn by applying suction to the top of the reservoir, manipulating the two-way cock so that the sample is drawn up as far as the calibration mark on the tube above the 10 ml reservoir. The cock is then reversed, allowing the sample to drain into the collecting dish. After each sample is taken, the new liquid level is noted.

The samples are then dried and weighed, and the weights compared with the weight of material in the same volume of the original suspension. There is a definite particle size, D, corresponding to each settling distance h and time t, and this represents the size of the largest particle that can still be present in the sample. These particle sizes are calculated from Stokes' law for the various sampling times. The weight of solids collected, g, compared with the corresponding original weight, i.e. g/g0 then represents the fraction of the original material having a particle size smaller than D, which can be plotted on the size-analysis graph. The method is much quicker than beaker decantation, as samples are taken off successively throughout the test for increasingly finer particle sizes. For example, although 5 urn particles of quartz will take about 2.5 h to settle 20 cm, once this sample is collected, all the coarser particle-size samples will have been taken, and so the complete analysis, in terms of settling times, is only as long as the settling time for the finest particles. The disadvantage of the method is that the samples taken are each representative of the particles smaller than a particular size, which is not as valuable, for mineralogical and chemical analysis, as samples of various size ranges, as are produced by beaker decantation. Figure 2. Andreasen Pipette

Sedimentation techniques tend to be very tedious, due to the long settling times required for fine particles ( up to 5 h for 3 urn particles) and the time required to dry and weigh the samples. The main difficulty, however, lies in completely dispersing the material within the suspending liquid, such that no agglomeration of particles occurs. Combinations of suitable suspending liquids and dispersing agents for various metals are given in BS ISO 13317-1. Although the Andreasen pipette is perhaps the most widely used method of sizing by sedimentation, various other techniques have been developed, which attempt to speed up testing. Examples of these methods, which are comprehensively reviewed by Allen ( 1997), are the photo-sedimentometer, which combines gravitational settling with photo-electric measurement, and the sedimentation balance, in which the weight of material settling out onto a balance pan is recorded against time, to produce a cumulative sedimentation size analysis. REFERENCES Wills B.A, Napier-Munn T.J (2006). Will’s Mineral Processing Technology. Elsevier Science & Technology Books

Isabela Psalm C. Torcende (Group 1) 2013-0330

MetE 125- Mineral Processing I Dr. Vannie Joy Resabal

WRITTEN REPORT: ELUTRIATION TECHNIQUES Elutriation is a process of sizing particles by means of an upward current of fluid, usually water or air. The process is the reverse of gravity sedimentation and the Stoke’s law applies. In sedimentation, the material to be sized is dispersed in a fluid and allowed to settle under carefully controlled conditions. Meanwhile, in elutriation, samples are sized by allowing the dispersed material to settle against a rising velocity. Both techniques separate the particles on the basis of resistance to motion in a fluid. Resistance to motion determines the terminal velocity which the particle attains as it is allowed to fall in a fluid under the influence of gravity. Classification is a method of separating mixtures of minerals into two or more products on the basis of the velocity with which the grains fall through a fluid medium. The fluid being either air or water, usually water in mineral processing. Wet classification is applied to minerals that are too fine to be sorted efficiently by screening. The velocity of the particles in the fluid medium is dependent of the size, shape, and specific gravity of the particles. Principles of classification are important in mineral separation utilizing gravity concentrators. When a solid particle falls freely in a vacuum, it is subject to constant acceleration and its velocity increases indefinitely, being independent of size and density. Hence a lump of lead and a feather fall together at exactly the same rate. In a viscous medium, there is resistance to this movement and the value increases with velocity. When equilibrium is attained between the gravitational and fluid resistance forces, the body reaches its terminal velocity and thereafter falls at a uniform rate. The nature of resistance depends on the velocity of the descent. At low velocities motion is smooth because the layer of fluid in contact with the body moves with it, while the fluid a short distance away is motionless. Between these two positions is a zone of intense shear in the fluid all around the descending particle. Effectively all resistance to motions is due to the shear forces or viscosity of the fluid and is hence called viscous resistance. At high velocities the main resistance is due to the displacement of fluid by the body, and viscous resistance is relatively small; this is known as turbulent resistance. Whether viscous or turbulent resistance predominates, the acceleration of particles in a fluid rapidly decreases and the terminal velocity is quickly reached. All elutriators consist of one or more “sorting columns” (Figure 4.10) in which the fluid is rising at constant velocity. Feed particles introduced to the sorting column will be separated into two fractions, according to their terminal velocities, calculated from Stoke’s law. 𝑑2 𝑔 (𝐷𝑠 − 𝐷𝑓 ) 𝑣= 18ƞ

Those particles having terminal velocities less than that of the velocity of the fluid will report to the overflow, while those particles having a greater terminal velocity than the fluid velocity will sink to the underflow. Elutriation is carried out until there are no visible signs of further classification taking place or the rate of change in the weights of the product are negligible. This involves the use of much water, involving dilution of the undersize fraction, but it can be shown that this is not as serious as in beaker decantation. Consider a sorting column of depth h, sorting material at a separating size of d. If the upward velocity of water flow is v, then by Stoke’s law, 𝑣 ∝ 𝑑 2 . Particles smaller than the separating size d will move upwards in the water flow at a velocity dependent on their size. Thus, particles of size 𝑑1 , where 𝑑1 < 𝑑, will move upwards in the sorting column at a velocity 𝑣1 , where 𝑣1 ∝ (𝑑 2 − 𝑑12 ). The time required for a complete volume ℎ change in sorting column is 𝑣 , and the time required for particles of size 𝑑1 to move from the bottom to the top of the sorting column is

ℎ

𝑣1

. Therefore the number of volume changes

required to remove all particles of size 𝑑1 from the sorting column ℎ/𝑣1 𝑑2 1 = = 2 = 2 ℎ/𝑣 𝑑 − 𝑑1 1 − (𝑑1 )2 𝑑

Comparing these figures with those in Table 4.5, it can be seen that the number of volume changes required is far less with elutriation than it is with decantation. It is also possible to achieve complete separation by elutriation, whereas this can only be achieved in beaker decantation by an infinite number of volume changes.

Elutriation thus appears more attractive than decantation, and has certain practical advantages in that the volume changes need no operator attention. It suffers from the disadvantage, however, that the fluid velocity is not constant across the sorting column, being a minimum at the walls of the column, and a maximum at the centre. The separation size is calculated from the mean volume flow, so that some coarse particles are misplaced in the overflow, and some fines are misplaced into the coarse underflow. The fractions thus have considerable overlap in particle size and are not sharply separated. Although decantation method never attains 100% efficiency of separation, the lack of sharpness of the division into fractions is much less than that due to velocity variation in elutritation (Heywood,1953). Elutriation is limited at the coarsest end by the validity of Stoke’s law, but most materials in the sub-sieve range exhibit laminar flow. At the fine end of the scale, separations become impractical below 10µm, as the material tends to agglomerate, or extremely long separation times are required. Separating times can be considerably decreased by utilization of centrifugal forces, and one of the most widely used methods of sub-sieve sizing in modern mineral processing laboratories is the Warman cyclosizer (Finch and Leroux, 1982), which is extensively used for routine testing and plant control in the size range 8-50µm for materials of specific gravity similar to quartz (sp.gr. 2.7), and down to 4µm from particles of high specific gravity, such as galena (sp.gr. 7.5).

Figure 4.1 Warman cyclosizer

The cyclosizer consists of five cyclones, arranged in series such that the overflow of one unit is fed to the next unit. The individual units are inverted in relation to conventional cyclone arrangements, and at the apex of each, a chamber of is situated so that the discharge is effectively closed. Water is pumped through the units at a controlled rate, and a weighed sample of solids is introduced ahead of the cyclones. The tangential entry into the cyclones induces the liquid to spin, resulting in a portion of the liquid, together with the faster-settling particles, reporting to the apex opening, while the remainder of liquid, together with the slower settling particles, is discharged through the vortex outlet and into the next cyclone in the series. There is a successive decrease in the inlet are and vortex outlet diameter of each cyclone in the direction

of the flow, resulting in a corresponding increase in inlet velocity and an increase in the centrifugal forces within the cyclone, resulting in a successive decrease in the limiting particle-separation size of the cyclones. The cyclosizer is manufactured to have definite limiting separation sizes at standard values of the operating variables, viz. water flow rate, water temperature, particle density, and elutriation time. To correct for practical operation at other levels of these variables, a set of correction graphs is provided. Complete elutriation normally takes place after about 20min, after which the sized fractions are collected by discharging the contents of each apex chamber into separate beakers. Reference: Wills, B.A. & Napier-Munn, T. (2005). Mineral Processing Technology. Publisher: Elsevier Science & Technology Books.

Prepared by Subject Professor Group #

: Jonel A. Quitiquit : MET E 125 : Engr. Vannie Joy T. Resabal :1

Objectives: - To know what is Micropic Sizing and Image Analysis. - To know the function and uses in the industry. I.

Introduction A microscope examination should always be carried out whenever a sample is prepared for particle size analysis. Such an examination allows an estimate of the particle size range of the powder under test and its degree of dispersion. If the dispersion is incomplete it can be determined whether this is due to the presence of agglomerates or aggregates and, if agglomeration is present, may indicate the need for an alternative dispersing procedure Microscopy is often used as an absolute method of particle size analysis since it is the only method in which the individual particles are observed and measured.

It is useful not only for particle size measurement but also for particle shape and texture evaluation, collectively called morphology, with sensitivity far greater than other techniques. The images may be viewed directly or by projection. Binocular eyepieces are preferred for particle examination but monoculars for carrying out a particle size analysis since, by using a single eyepiece, the tube length can be varied to give stepwise magnification. II.

Microscopic Sizing The image of a particle seen in a microscope is two dimensional and from this image an estimate of particle size must be made. Microscopic sizing involves comparing the projected area of a particle with the areas of reference circles, or graticules, of known sizes, and it is essential for meaningful results that the mean projected areas of the particles are representative of the particle size. This requires a random orientation in three dimensions of the particle on the microscope slide, which is unlikely in most cases.

III.

Analysis Method Manual methods of obtaining data from images are slow and tedious and this can give rise to considerable error. The introduction of fully automated image analysis systems has virtually eliminated manual methods and also supplanted semiautomatic systems. All image analysis systems use scanning techniques for converting images into electrical signals that are processed to yield data on the images.

IV.

How Does it Work? Image analysers accept samples in a variety of forms - photographs, electron micrographs, and direct viewing- and are often integrated in system software. Figure shows the grayscale electron backscatter image of a group of mineral particles obtained with a scanning electron microscope; grains of chalcopyrite (Ch), quartz (Qtz), and epidote (Epd) are identified in the image. On the right are plotted the size distributions of the "grains" of the mineral chalcopyrite (i.e, the pieces of chalcopyrite identified by the instrument, whether liberated or not) and the "particles" in which the chalcopyrite is present. The plots are based on the analysis of several hundred thousand particles in the original sample, and are delivered automatically by the system software. Image analysis of this kind is available in many forms for the calculation of many quantities (such as size, surface area, boundary lengths) for most imaging methods, e.g. optical, electron.

V.

Uses in the industries -

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VI.

Determination of particle size distribution Particle shape e.g. aspect ratio (ratio between breadth and length) which gives valuable extra information -complementary to laser diffraction – about particle characteristics. Overview of particles dispersed in liquid or air. Measurement of object sizes e.g. mesh size of sieves.

Advantages and Disadvantages of Microscopic Sizing and Image Analysis

The advantages of using semi or fully automated methods are the accuracy of the examined particle. It is also available in many forms for the calculation of many quantities such as size, surface area, boundary lengths for most imaging methods. The disadvantages of manual method are that the operator were over estimating/under estimating and badly biased on the sample. In the semi/fullyautomated machine depends on the input setup by the operator. Errors may be directly made by erroneous inputs of operator. VII.

References: Wills, B.A. & Napier-Munn, T. (2005). Mineral Processing Technology. Publisher: Elsevier Science & Technology Books.

Written Report Electrical Impedance Method (Coulter) 2014 – 0145 Kristelle Mae P. Sanoy The Coulter method of sizing and counting particles is based on measurable changes in electrical impedance produced by nonconductive particles suspended in an electrolyte. A Coulter counter is a machine used for counting and sizing particles suspended in electrolytes. A typical Coulter counter has one or more microchannels that separate two chambers containing electrolyte solutions. As fluid containing particles or cells is passes through each microchannel, each particle causes a change to the electrical resistance of the liquid. This machine detects these changes in resistance. The Coulter principle states that particles pulled through an orifice, simultaneous with an electric current, produce a change in impedance that is proportional to the volume of the particle passing through the orifice. This change in impedance or pulse is caused by the displacement of the electrolyte due to the particle. The pulses are electronically amplified, scaled and counted. The volume may be represented as the equivalent spherical diameter. The measured particle sizes can be channelized using a height analyzer circuit and a particle size distribution is obtained. The instrument measures particle volume, the equivalent diameter is calculated from that of a sphere of the same volume. The instrument is applicable in the range of 0.4 – 1200 µm. The electrical response of the instrument is essentially independent of the shape of particles with the same volume, an exception to this may occur with some extreme shapes. Color or refractive index of the particles does not affect the results.

Report On Laser Diffraction Instruments By: Advent Fel R. Bañez Laser Scattering Technology Low angle light scattering or Laser Diffraction has been known as a laboratory technique since 1960 specially when wide range of distribution need to be analyzed. With a dynamic range of 0.1-3000 microns. The Size Analysis is based on the theory of intensity distribution measurement of coherent laser light scattered by the particles describe by Mie theory. And the width of the pattern is dependent on size. The process can be described as the laser light meets a population of particles, volumetric size distribution can be determined from the scattered light distribution. Based on this observation that large particles scatters light at low angle and intensity of light scattered is high and small particles scatters light at high angle and the intensity of light scattered is low. Two important Theory governs the function of laser light diffraction the Mie Theory and the Franhaufer theory. The Mie theory assumes the particles are spherical in nature. And Franhaufer theory states that the intensity of light scattered is proportion to the particle size. Repeatability and precision are the most important feature of light scattering technology over a wide particle size range. Also the speed, non-contact nature and robustness of the method to ambient condition make laser diffraction suitable for on line particle size analysis applications. Which also does not require external calibration. Instruments 1. Malvern Specifications: Particle size range = 0.01 – 3500 microns Accuracy = Better than 0.6% Precision = Better than 0.5% variation

2. CILAS 1090 Specifications: Particle Size range: 0.04 – 500 microns Multi Laser Design

2. Microtac S3500 Specifications: Particle size range = 0.02 – 2800 microns Precision = 0.6% variation

Loopholes Although Laser Diffractometry is the most popular particle size analysis used today with its ease and proven precision. It has also some drawbacks that needs to be address such as False Assumptions of random particle orientation. And the Distortion measurement in which a ghost particle caused by sharp edge can be interpreted by the laser diffraction instruments to be small particles. Conclusion: Laser Diffraction Instruments selection based on the above specifications depend on what size the particle are to be analyzed. and based on the address loopholes the use laser diffraction instruments is reliable due to its precision and speed.