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Particle Size Analysis

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Particle Size Analysis PARTICLE SIZE ANALYSIS 1 CHARACTERIZATION OF SOLID PARTICLES • SIZE • SHAPE • DENSITY 2 SPHERICITY, 휑푠 Equivalent diameter, Nominal diameter 푆푢푟푓푎푐푒 표푓 푎 푠푝ℎ푒푟푒 표푓 푠푎푚푒 푣표푙푢푚푒 푎푠 푝푎푟푡푐푙푒 • 휑 = 푠 푠푢푟푓푎푐푒 푎푟푒푎 표푓 푡ℎ푒 푝푎푟푡푐푙푒 • Let • 푣푝 = 푣표푙푢푚푒 표푓 푝푎푟푡푐푙푒, 푠푝 = 푠푢푟푓푎푐푒 푎푟푒푎 표푓 푡ℎ푎 푝푎푟푡푐푙푒, • 퐷푝 = 푬풒풖풊풗풂풍풆풏풕 풅풊풂풎풆풕풆풓 = 퐷푎푚푒푡푒푟 표푓 푠푝ℎ푒푟푒 푤ℎ푐ℎ ℎ푎푠 푠푎푚푒 푣표푙푢푚푒 푎푠 푝푎푟푡푐푙푒푣 = 휋 푝 퐷 3 6 푝 2 6푣푝 • Surface area of the sphere of diameter Dp, 푆푝 = 휋퐷푝 = 퐷푝 푆푝 6푣푝 휑푠 = = 푠푝 푠푝퐷푝 It is often difficult to calculate volume of particle, to calculate equivalent diameter, Dp is taken as nominal diameter based on screen analysis or microscopic analysis 3 Sphericity of particles having different shapes Particle Sphericity Sphere 1.0 cube 0.81 Cylinder, length = 0.87 diameter hemisphere 0.84 sand 0.9 Crushed particles 0.6 to 0.8 Flakes 0.2 4 Sphericity, Table 7.1, McCabe Smith • Sphericity of sphere, cube, short cylinders(L=Dp) = 1 5 VOLUME SHAPE FACTOR 3 푣푝 ∝ 퐷푝 3 푣푝 = 푎 퐷푝 Where , a = volume shape factor 휋 휋 For sphere, 푣 = 퐷 3 or 푎 = 푝 6 푝 6 6 Commonly used measurements of particle size 7 Particle size/ units • Equivalent diameter : Diameter of a sphere of equal volume • Nominal size : Based on; Screen analysis and Microscopic analysis • For Non equidimensional particles Diameter is taken as second longest major dimension. • Units: Coarse particles – mm Fine particles in micrometer, nanometers Ultrafine - surface area per unit mass, sq m/gm 8 Particle size determination • Screening > 50 휇푚 • Sedimentation and elutriation - > 1 휇푚 • Permeability method - > 1 휇푚 • Instrumental Particle size analyzers : Electronic particle counter – Coulter Counter, Laser diffraction analysers, Xray or photo sedimentometers, dynamic light scattering techniques 9 Screening • Mesh Number = Number of opening per linear inch 1 • 퐶푙푒푎푟 표푝푒푛푛푔 = − 푊푟푒 푡ℎ푐푘푛푒푠푠 푚푒푠ℎ 푛푢푚푏푒푟 10 Standard Screen Sizes BSS= British Standard Screen IMM= Institute of Mining & Metallurgy U.S. Tyler mesh US. ASTM= American Institute for testing Materials • Ratio of aperture of two consecutive sieves= 2, 2, 4 2 [2, 1.41,1.18] 11 MIXED PARTICLE SIZE ANALYSIS: Differential and Cumulative Screen Analysis • 퐴푣푒푟푎푔푒 푝푎푟푡푐푙푒 푠푧푒, 퐷 푝 • Mass fraction, 푥 • Cumulative mass fraction , ϕ – Cumulative mass fraction bigger than a particle size – Cumulative mass fraction smaller than a particle size • Differential screen analysis curve – Plot Mass fraction vs Average particle size • Cumulative screen analysis curve – Plot Cumulative mass fraction vs Average particle size 12 13 Sl. Mes Screen Mass Mass Average , Cumulative No. h Opening retained on Fraction particle Cumulative Fraction No. a screen diameter fraction Dpi (cm) 푥= mi/M Smaller mi (gm) 퐷푝 Larger than than 퐷푝 퐷푝 1 1.00 2 3 ----- - Pan 1.00 0.00 푚 = 푀 푥 = 1 14 Differential and Cumulative Screen Analysis Curves 15 MIXED PARTICLE SIZES : Surface area, Specific Surface area, Volume surface mean diameter • 푣푝 = 푣표푙푢푚푒 표푓 푝푎푟푡푐푙푒, • 푠푝 = 푠푢푟푓푎푐푒 푎푟푒푎 표푓 푝푎푟푡푐푙푒, • 퐷푝 = 퐷푎푚푒푡푒푟 표푓 푝푎푟푡푐푙푒 • 휌푝 = 푑푒푛푠푡푦 표푓 푚푎푡푒푟푎푙 • Number of particles in a mass of “m” 푇표푡푎푙 푣표푙푢푚푒 푚 휌 • 푁 = = 푝 푣표푙푢푚푒 표푓 표푛푒 푝푎푟푡푐푙푒 푣푝 • Total surface area: 푚 6푣푝 6푚 6푣푝 • 퐴 = 푁푠푝 = = [휑푠 = ] 푣푝 휌푝 퐷푝휑푠 휑푠휌푝퐷푝 퐷푝푠푝 16 Specific surface area, 퐴푤,area/mass 푚 6푣푝 6푚 6푣푝 • 퐴 = 푁푠푝 = = [휑푠 = ] 푣푝 휌푝 퐷푝휑푠 휑푠휌푝퐷푝 퐷푝푠푝 6푚1 6푚2 6푚푛 • 퐴푡표푡푎푙 = + + ⋯ … . + 휑푠휌푝퐷푝1 휑푠휌푝퐷푝2 휑푠휌푝퐷푝푛 퐴푡표푡푎푙 6푚1/푀 6푚2/푀 6푚푛/푀 • 퐴푤 = = + + ⋯ … . + 푀 휑푠휌푝퐷푝1 휑푠휌푝퐷푝2 휑푠휌푝퐷푝푛 6푥1 6푥2 6푥푛 • 퐴푤 = + + ⋯ … . + 휑푠휌푝퐷푝1 휑푠휌푝퐷푝2 휑푠휌푝퐷푝푛 6 푛 푥푖 • 퐴푤 = =1 휑푠휌푝 퐷푝푖 Volume surface mean diameter [also known as Sauter Diameter] 6 6 1 • 퐷 = = = 푠 휑 휌 퐴 6 푛 푥푖 푛 푥푖 푠 푝 푤 휑푠휌푝 푖=1 푖=1 휑푠휌푝 퐷푝푖 퐷푝푖 17 AVERAGE PARTICLE SIZE • Volume surface mean diameter: 6 1 퐷푠 = = 휑 휌 퐴 =푛 푥 푠 푝 푤 =1 퐷푝 • Arithmetic Mean Diameter: 푛 푛 =1 푁퐷푝 =1 푁퐷푝 퐷푁 = 푛 = =1 푁 푁푇 • Mass Mean diameter 푛 퐷푤 = 푥퐷푝 =1 • Number of particles: 푛 푛 푚 휌푝 1 푚 푁 = 3 푎푛푑 푁푇 = 푁 = 3 푎휌푝 푎퐷푝 =1 =1 퐷푝 18 VOLUME MEAN DIAMETER • Volume mean diameter: Diameter of a particle with average volume: 푇표푡푎푙 푣표푙푢푚푒 3 • 퐴푣푒푟푎푔푒 푝푎푟푡푐푙푒 푣표푙 = = 푎퐷푣 푁푇 푛 푛 푚 휌푝 1 푚 푁 = 3 푎푛푑 푁푇 = 푁 = 3 푎휌푝 푎퐷푝 =1 =1 퐷푝 3 푇표푡푎푙 푣표푙푢푚푒 푀 휌푝 1 휌푝 푎 퐷푣 = = = 푇표푡푎푙 푛푢푚푏푒푟 1 푛 푚 1 푛 푥 =1 3 =1 3 푎휌푝 푎휌푝 퐷푝 퐷푝 1 1/3 퐷 = 푣 푛 푥 =1 3 퐷푝 19 Number of particles Shape Factor a 3 • 푣푝 = 푎퐷푝 푛 푚푖 • 푁푇 = =1 3 푎휌푝퐷푝푖 • Number of particles per unit mass 푛 푛 푁푇 1 푚 1 푥 푁푤 = = 3 = 3 푀 푀 푎휌푝 =1 푎휌푝퐷푝 =1 퐷푝 1 푁푤 = 3 푎휌푝퐷푣 20 Sl. No. Mesh No. Screen Mass Mass Average , Cumulative Opening retained on Fraction particle Cumulative Fraction a screen diameter fraction Dpi (cm) 푥= mi/M Smaller mi (gm) 퐷푝 Larger than, 퐷푝 than퐷푝 4 0 6 25 8 125 10 325 14 250 20 160 28 50 35 20 48 10 65 8 100 6 150 4 200 3 pan 2 21 PROPTERTIES OF MASSES OF PARTICLES • Bulk density or apparent density, 휌푏, is defined as the weigh per unit volume of material including voids inherent in the material as tested. It is a measure of the fluffiness of the material. 푚 푚 푚 휌푏 = = and 휌푡 = 푉푇 푉푝+푉푣 푉푝 • Porosity, It is the ratio of the void volume and bulk volume. 푉 휀 = 푣 푉푇 푉푇 − 푉푝 푉푝 푚 휌 휀 = = 1 − = 1 − 푏 푉푇 푚 푉푇 휌푡 Pourabilityis defined as a measure of the time required for a standard quality of material to flow through a funnel of specified dimension. It characterizes the handling properties of fine particles 22 • Angle of repose,, is defined as the angle formed between sloping side of a cone shaped pile of material and the horizontal if the mass is truly homogeneous, would be equal to m, the angle of internal friction. In practice, the angle of repose is smaller than the angle of internal friction, of those inside the mass and are often drier and sticker. • Coefficient of internal friction is the measure of resistance present when one layer of solids over another layer of same particles. It is defined as: Coeff. Of internal friction =tan m 0 0 • For free flowing material m is between 15 to 30 23 • In solid masses the pressure is not the same in all directions. If pressure is applied in one direction it creates some pressure in other directions, but it is always smaller than the applied pressure. It is minimum I the direction at right angles to the applied pressure. The ratio of the normal pressure to the applied pressure in a mass of solid, is a material constant, generally denoted by K’ 푛표푟푚푎푙 푝푟푒푠푠푢푟푒 1 − 푠푛훼 퐾′ = = 푚 푎푝푝푙푒푑 푝푟푒푠푠푢푟푒 1 + 푠푛훼푚 K’ approaches zero for cohesive solids and free flowing material its value is between 0.36 to 0.6 • Coefficient of external friction is the measure of the resistance at an interface between particles and the wall of different material of construction. Coefficient of External friction = tan S – Where S is the angle of external friction of solid and material.24 SOLIDS CONVEYING 25 • Screw conveyors • Belt conveyors • Bucket elevators • Spaced-Bucket Centrifugal-Discharge Elevators • Spaced-Bucket Positive-Discharge Elevators • Continuous-Bucket Elevators • Super-capacity Continuous-Bucket Elevators • V-Bucket Elevator-Conveyors • Skip Hoists • Vibrating or oscillating conveyors • Continuous flow conveyors • Apron Conveyors • Pneumatic conveyors • Hydraulic Conveyors 26 SELECTION OF CONVEYORS • Capacity requirement : Belt for larger capacity and screw cannot handle large capacity • Length of travel : belt conveyors ; miles, Pneumatic convey 300m, vibrating conveyor even less • Lift or lift and horizontal shift : single or mixed • Material characteristics – chemical and physical, size, friability, flowability abrasiveness, moisture or oxidation effect • Processing requirement; dewatering, heating cooling 27 Screw conveyor • Helicoid ( helix rolled from flat steel bar) or sectional flight mounted on a pipe or shaft rotating in a U shaped trough – Horizontal of slight incline upto 20ofinely divided solids, sticky material, semisolid materials, boiler ash. Etc. – Continuous spiral for dry granular free flowing material – Discontinuous spirals for wet, muddy and thick materials. – Short distance upto about 40m – Types of flow : • Archemedian flow or • Plug flow – Unit operation – mixing, heating & cooling with hollow shaft 28 29 BELT CONVEYORS • Continuous belt passing around two large pulleys at two ends, one drive pulley other tail pulley. – Universal application – Very long distances several km – Speed up to 300m/min 5000tons/hr – Slope upto 30o – Material – neoprene, Teflon, natural rubber, vinyls, cotton, asbestos fibre, etc. – Various designs of idlers – May require cleaning by revolving brush, metal or rubber scraper, taut wire 30 31 Idlers and Plate support arrangements: (a) Flat belt on idler (b) flat belt on continuous plate (c)troughed belt on 20 deg idler (d) troughed belt on 45 deg idler (e) Same as d but with rolls of equal lengths (f) troughed plate on continuous plate 32 33 Feeders to Belt conveyors- Vibratory and Star Feeder 34 BELT CONVEYOR DISCHARGE ARRANGEMENTS: (a) over end pulley (b) over end pulley by reversible shuttle conveyor (c) through travelling tripper(d) through fixed trippers 35 www.bakerybelting.com 36 BUCKET ELEVATOR • Bucket elevator consists of a number of buckets attached to a continuous double strand chain which passes over two pulleys • Solids fed directly to bucket and also scooped up from the bottom. • Emptied from the top by turning of the bucket. • Line speed 1-2m/s 37 BUCKET ELEVATORS (a)Spaced-Bucket Centrifugal-Discharge Elevators (b)Spaced-Bucket Positive-Discharge Elevators (c)Continuous-Bucket Elevators (d)Supercapacity Continuous-Bucket Elevators 38 • Spaced bucket ; Centrifugal discharge – free flowing, fine or small lump material like grain, coal, sand or dry chemicals • Spaced bucket positive discharge- buckets are for sticky materials which tend to lump, inverted for positive discharge, knockers can also be used • Continuous – finely pulverized or fluffy materials, the back of the preceding bucket serves as a discharge chute for the bucket.
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