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What is Comminution

From Wikipedia:

Comminution describes the movement of the particle size distribution (grains, drops, bubbles) into a range of finer particle sizes

From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982

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grinding

Product can be shippedand used Directly in BF

From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982

Comminution Critical in Mineral Processing

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Glacial abrasion

Debris FlowSaltation

Sklar and Dietrich

weathering

Comminution in Landscape Dynamics

x

Down Stream Fining

2/17

From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982

x0eDD Sternberg’s law

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A Thing to Know

For a Given EnergyWhat is the Reduction in Particle Size—

The Comminution Laws

From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982

Main Result Suggest How

Sternberg law for down streamFining could be modified byMineral Engineering Results

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From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982

The Comminution Laws

Consider a simplistic comminution operationthat for each event reduces the particle sizeby a factor of 1/2

Rittinger (1867): NewSurfaceE FP x4Nx4

FP x

1

x

1CE

xF After q events

21

ln

xx

ln

q2

1

x

x F

Pq

F

P

2P

2F

x

xN

Kick (1885): Energy for each event

E=Constant

After q events

E = q E

F

P

x

xlnCE

6/17

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Rittinger (1867): NewSurfaceE

FP x

1

x

1CE

Kick (1885): Energy for each event

E=Constant

P

F

x

xlnCE

A general Law For general case x—an average part. size

Log Particle Size

Log E

nerg

y Inpu

t

Grind Limit Kick

Ritt

enge

r

CrushingAbrasion

After Hukki

Instructive to look at energy asA function of size reduction for quartz Ritinger works best at describing

Abrasion-

Kick at describing crushing

Rittinger2,Kick1

2n1,x

dxCdE

n

7/17

Walker suggested a two parameter law

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x

To Down Stream Fining

x0eDD Sternberg’s Law

Question: What is relation of

FP x

1

x

1CE

P

F

x

xlnCE

Kick Rittinger

Set E = x (distance down stream) and x = D particle size

0C D

DlnKxKick

x0eDD Is Sternberg

0R D

1

D

1KxRitinger

1

0D

1xD

wear

An alternative

Could it make a difference

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Log-log plot of representative particle size (mm) vs. distance downstream, reproduced from Fig 2 in Adams (1979).

Sternberg-Kick Law Finding in river headwaters

Modified LawSuggested by AdamsWear –1/Distance

Rittinger Law

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0.01

0.1

1

10

100

0.1 1 10 100 1000

Rittinger Law

Modified LawSuggested by AdamsWear –1/Distance

Sternberg-Kick Law

Quartz/Schist Ratio

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1n2,D

1

D

1KE

1n0

1nR

0C D

DlnKE

0R D

1

D

1KE

Mineral Laws of Comminution

1n2,Dx)1n(D n11

n10

is wear What is n?

0.01

0.1

1

10

100

0.1 1 10 100 1000

0.01

0.1

1

10

100

0.1 1 10 100 1000

Inform Geomorphic Laws of Comminution

x0eDD

1

0D

1xD

Sklar: shows very good comparisonWith lab simulations of fining1n2,

D

dDCdE

n

What about two parameter laws