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Particle Size Definitions
Individual particle size terpconnect.umd.edu/~sehrman/particle-class/PSA-05-1-and2.ppt
• Sphere: diameter• Irregular particles
– Sieve equivalent diameter➢ Diameter equal to the diameter of a sphere passing through
the same sieve aperture as particle.– Surface area equivalent diameter
➢ Diameter equal to diameter of a sphere with same surface area as particle.
– Aerodynamic diameter➢ Diameter of a unit density sphere having the same terminal
settling velocity as particle.– Surface volume diameter
➢Diameter of sphere having same surface area to volume ratio as particle.
Assembly of particles• Particle size distribution
– Mass or mass fraction (%) of particles (i) above a given size or (ii) within a given size range.
– Cumulative size distribution➢ Mass or mass fraction (%) of particles below a given
size.
Sieve assembly
Sieve size (mm)
Mass fraction retained on each sieve
Cumulative mass fraction less than given sieve size
Size range (mm)
Mass fraction in given size range
4.76 0 1 >4.76 03.36 0.139 0.861 3.36-4.76 0.1392.38 0.24 0.621 2.38-3.36 0.241.68 0.189 0.432 1.68-2.38 0.1891.19 0.115 0.317 1.19-1.68 0.1150.841 0.08 0.237 0.841-1.19 0.080.595 0.063 0.174 0.595-0.841 0.0630.42 0.046 0.128 0.42-0.595 0.0460.297 0.034 0.094 0.297-0.42 0.0340.21 0.026 0.068 0.21-0.297 0.0260.149 0.021 0.047 0.149-0.21 0.0210.105 0.014 0.033 0.105-0.149 0.0140.074 0.009 0.024 0.074-0.105 0.0090.053 0.005 0.019 0.053-0.074 0.0050.037 0.006 0.013 0.037-0.053 0.006<0.037 0.013 <0.037 0.013
Size Reduction
Breakage Mechanism•Breakage originates at pre-existing “cracks” within particles.
–Resolved tensile and shear stresses propagate cracks.
•Modes–Slow compression
Larger cracks propagate faster.
–Fast compression/ImpactCompressive stress waves reflected from surface as tensile waves.Existing cracks extended and new cracks are formed.
–AbrasionHigh shear stresses due to rubbing of particlesFracture localized on the surface
• Specific energy consumption: Crushing versus grinding?
Unit Operations
• Crushing– Primary: Jaw crushers, Gyratory crushers.– Secondary: Cone crushers, roll crushers– Tertiary: Hammer mill
• Grinding– Rod mill– Ball mill– Autogenous
Jaw crusher Gyratory crusher
Gape: Opening at feed endSet: Opening at discharge end
Slow compression mode of breakageGyratory crusher crushes and draws in feed simultaneouslyJaw crusher works for only half cycle.Capacity of gyratory crushers greater than jaw crushers
Crushers
Roll Crushers• Sluggers increase
friction.• Mode of breakage
– Shear stresses.– Teeth tear into material.– Suitable for weak,
ductile materials.
Hammer Mill• Mode of breakage
– Impact.– Relatively weak, brittle
material (coal).
Crusher operating characteristicsJaw crusher
Gyratory crusher
Cone crusher
Grinding mills
Rod mill Ball mill
Autogenous mill• Larger Diameter/Length (?)
Characteristics• Grinding media
– Hard, good wear resistanceHigh C steel.
–Assorted sizes25 – 150 mmIncrease grinding surface area.Sufficient size to break largest feed particle.
• Speed– 65 – 80% of critical speed (Formula?)
• 30 – 50% mill filled with feed and grinding media.
•Wet grinding–Advantages over dry grinding. –Pulp density: 60 – 80% (wt.% solids)
Media coated with ore particles.Low density increases ball-to-ball contact.
•Product–Rod mill
Large sizes broken preferentially.Narrow size range.
•High energy consumption– Breakage by random “hits.”
Movement of charge in a ball mill
•Breakage Modes–Zones A & B
Abrasion & impact–Zone C
Impact
Specifications
Grinding kinetics
• Rate of breakage of size i,dMi/dt = -kiMi
• ki = Rate constant (t-1)
Grinding circuits
Work index (Wi, kWh/t)
• Coal: 13• Cement clinker: 5• Galena: 11• Glass: 3• Iron ore: 17• Limestone: 13• Quartz: 14