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