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What is a Particle?
 A useful working unit
 individual particle
 aggregate of many small individual particles (pellet, floc, etc.)

Typical Particle Size Ranges
RunofMine < ____
Primary Crusher Product < _____
Secondary Crusher Product < _____
Rod Mill Product < ______
Ball Mill Product < ____
Flotation Feed < ____
 1500 mm
 150 mm
 20 mm
 6 mm
 1 mm
 0.5 m

Particle Sizing Methods (8)
 Sieve Analysis
 Sedimentation Methods
 Elutriation Methods
 Surface Area Methods
 Optical Microscopy
 Electrical Resistance Methods
 Laser Diffraction Methods
 Ultrasonic Methods

Factors Affecting Particle Sizing (3)
 Size
 Shape
 Specific Gravity


Sieve Analysis  Sieve Sizes
Mesh ______
Opening (aperture) Size  _______
 Mesh  number of openings per linear inch (100 mesh screen has 100 openings per inch)
 Opening (aperture) Size  function of mesh number and wire diameter.

Sieve Analysis  Standard Sieve Series
U.S. (ASTM) Standard  ____
Tyler Standard ____
 U.S. (ASTM) Standard  based on a 1 mm opening for an 18 mesh screen
 Tyler Standard  based on a 74 μm opening for a 200 mesh screen.
 Note: The screen aperture sizes in a complete sieve series are related by (2)¼. In practice, it is common to use every other screen in a complete series (i.e., √2). The smallest sieve available in either series is 400 mesh (37 μm).
 Example:
 14 mesh = 1•(2)½= 1.41mm
 16 mesh = 1•(2)¼= 1.19 mm
 18 mesh = 1 mm
 20 mesh = 1/(2)¼= 0.84 mm
 25 mesh = 1/(2)½= 0.71 m

Sieve Analysis  Operating Concerns
Major Operating Concerns:
Screening Time (Probability of particle____)
Sample Weight (Probability of particle _____)
Typical Operating Values (Ball Mill Product):
Screening Time  ___minutes
Sample Weight  ____ grams
Other Operating Concerns:
____ ______.
___ of ___
This problem is usually solved by ___ screening.
Dry screening is generally not appropriate below approximately 200 mesh
 Major Operating Concerns:
 Screening Time (Probability of particle passing through opening)
 Sample Weight (Probability of particle hitting another particle)
 Typical Operating Values (Ball Mill Product):
 Screening Time  20 minutes
 Sample Weight  500 grams
 Other Operating Concerns:
 Blinding  near mesh particles plug holes
 Adherence of Fines  fine particles stick on coarse particles. This problem is usually solved by wet screening.
 Dry screening is generally not appropriate below approximately 200 mesh

Sedimentation  Stokes’ Law

Stokes’ Law Example
A quartz sphere (ρ _{s}= 2.65 g/cm ^{3}) falls in a column of distilled water at 25°C (µ = 0.01 g/cm•s (poise), ρ = 1.0 g/cm3). What is the diameter of the sphere if it falls 20 cm in 30 minutes?

Sedimentation Methods:
TwoLayer Methods introduce sample on top of liquidand monitor particle concentrationat some other level
Homogeneous Suspension disperse particles in liquid andmonitor concentration change
Incremental Method density change monitored:(1) at a fixed depth as f(time)(2) at a fixed time as f(depth
 examples:
 Andreasen Pipette
 Photosedimentometer
 XRay Sedimentometer
Cumulative Method the rate at which material settlesout of suspension is monitored
 examples:
 Sedimentation Balance
 Sedimentation Colum

Elutriation  Size Separation
 a process of sizing particles by means of an upward current of fluid, usually air or water.
 Infrasizer  air
 Cyclosizer  water

Surface Area Methods
 infer particle size from specific surface area
 Gas Adsorption
 Gas Permeability
 Gas Diffusion

Microscopy
 Optical Microscopy (> 1 µm)
 Scanning Electron Microscopy (> 0.001 µm)
 may require the use of 2D to 3D conversion methods
 linked with automatic image analysis

Electrical Resistance
 based on change in resistivity as particle passes between two electrodes (counts and sizes)
 accurate, good resolution, requires skilled operator, applicable from 1 to 400 µm
 Coulter Counter

Laser Diffraction
 particle size distribution is related to the diffraction of laser light as the beam passes through a suspension of the sample
 Honeywell Microtrac

Ultrasonics
 measurement depends on the varying absorption of ultrasonic waves in suspensions of different particle sizes
 Autometrics PSM System (online)

Potential Problems in Size Analysis
 improper screening of fines
 lower detection limits
(Note: Both problems can be detected in the size distribution plot, and both problems can be corrected by adjustments to the size distribution plot or material balancing of the size data.)

Purpose of Size Distribution Equation
 A convenient way to represent large quantities of data
 A means of characterizing the size of a material
 A basis for comparing sample

Size Distribution Equations
 GaudinSchuhmann Equationz commonly used in mineral processing
 generally fits fine particle distributions, such as ball mill product
 tends to fit best below the 7580% passing size
 RosinRammler Equation
 commonly used in coal preparation
 generally fits coarse particle distributions, such as those used for dense media separation in coal preparation plants
 relatively linear over the entire range of particle sizes

The GaudinSchuhmann Equation
Y = (x/k)^m
 Y = cumulative fraction finer than x
 x = particle size
 k = size modulus (theo max particle size)
 m = distribution modulus (spread of dist)
logY = m * log(X)  mlog(K)

The RosinRammler Equation
Y = 1exp((x/x') ^{n}))
 Y = cumulative fraction finer than x
 x = particle size
 x' = size modulus
 n = distribution modulus

Importance of Crushed Stone Quality
 Over 1 billion tons of crushed stone produced per year.
 Commonly used in concrete, asphalt, road base, construction filler, etc.
 Quality parameters most important for end use.
 Quality specifications often set by federal and state regulations (DOT)

Types of Quality Parameters (8)
 Size and Size Distribution
 Shape
 Specific Gravity
 Permeability
 Abrasion and Degradation Resistance
 Impact Strength
 Weathering Resistance
 Presence of Fines

Size and Size Distribution
 Size Gradations
 Aggregate sizes designated by weight percent ranges in specific size classes
 Coefficient of Uniformity
 Cu> 6: dense or well graded; wide size range; desirable for maximum strength and stability.
 Cu< 4: uniformly or open graded; narrow size range; high permeability

Shape  a major parameter affecting quality of end products:
flat and elongated particles ______
angular particles ____
roughtextured particles provide _____
can reduce strength of asphalt and concrete when load is applied to the thin side
increase shear strength of mixtures and skid resistance of pavements over rounded particles
better bonding with cement or road materials.

Shape  Flatness and Elongation
 Flatness  width/height from an end view
 Elongation  length/width from a top view

Shape percent voids
used as indirect measure of fine particle shape (related to packing

Specific Gravity
Apparent Specific Gravity
Bulk Specific Gravity
Bulk Specific Gravity (saturated, surface dried)
 Apparent Specific Gravity
 ratio of the dry aggregate weight to the volume of the aggregate excluding any permeable pores.
 Bulk Specific Gravity
 ratio of the dry aggregate weight to the volume of the aggregate including all permeable and impermeable pores.
 Bulk Specific Gravity (saturated, surface dried)
 ratio of the saturated aggregate weight to the volume of the aggregate including all permeable and impermeable pores.

Permeability
 Let
 A = dry weight of sample
 B = weight of surface dried, water saturated sample
 C = weight of water saturated sample
 Water Absorption (%) = (BA)/(CA) x 10

Abrasion and Degredation
The slow degradation of a material resulting in the creation of a few large pieces of rock (as opposed to “wear”, which results in the creation of many small particles).
In concrete production, degradation during mixing alters the original gradation of the material.
In pavements, degradation can lead to unstable bedding layers causing pavement cracking
Los Angeles Degradation Test (LA Abrasion)

Impact Strength
Page Impact Test

Weathering Resistance
Sulfate Soundness Test

Presence of Fines
Atterberg Limits:
Liquid Limit
Atterberg Limits
Liquid Limit (LL)  the water content at which a sample of 40 mesh material passes from the plastic to liquid state.
Plastic Limit (PL)  the lowest water content at which a sample of 40 mesh material remains cohesive enough to hold together when rolled with the fingers on a glass plate into a “thread” of 1/8”diameter.
 Plasticity Index (PI) = LL  PL
 Low PI is desirable

What is Comminution?
 Particle Size Reduction
 Purpose:
 liberate minerals (most common)
 reduce particle size (crushing)
 produce material of a controlled particle size (crushedstone production)
 increase surface area (chemical processing)

Magnitude of Comminution
Energy Consumption:
Steel Consumption (Wear):
Total Energy Consumtion
Over 1.5 billion tons of ores and rocks are comminuted annually in the U.S.
 Energy Consumption
 Total Energy Consumption  1020 kwh/ton
 Primary Crushing  0.25 kwh/ton
 Secondary Crushing  0.55 kwh/ton
 Rod Mill Grinding  5.4 kwh/ton
 Ball Mill Grinding  5.7 kwh/ton
 Steel Consumption (Wear)
 Total Steel Consumption  1.82.5 lb/ton
 Grinding Rods  1.2 lb/ton
 Grinding Balls  0.9 lb/ton
 Crusher Liners  0.03 lb/ton
 Mill Liners  0.2 lb/ton
 Total Energy Consumption
 33 billion kwh (including energy associated with steel consumption)
 1.5% of the total U.S. output of electricity (1978)
 4075% of direct operating costs for mineral processing

Comminution Energy Fundamentals
Possible courses of energy:
 Size Reduction Energy
 Material Being Broken
 Lattice rearragements
 Surface Energy
 Elastic Deformation  Heat
 Plastic Deformation Heat
 Communition Machine and Interparticle effects
 Friction Heat
 Kinetic Energy
 Electrical Effects
 sound

Communition Efficiency
 If surface energy is only form considered useful  0.11%
 If lattice rearrangements are considered part of the breakage process  12%
 If elastic and plastic deformation are considered part of a necessary precursor to breakage  2050%

Modes of Fracture
 Rapid Compression  impactors and tumbling mills
 Slow Compression  crushers and tumbling mills
 Abrasive Shear  crushers and tumbling mills
 Tension  1/10 of compressive strength; no available commercial method (Spin rock  F. Bond)

Novel Methods of Comminution
 Steam or Chemical Expansion (tensile)
 Microwave Heating (heat stressed)
 Ultrasonic

Comminution Laws
A method of relating Energy Consumption to Size Reduction
Useful in design of comminution devices
 Three basic “laws” of comminution:
 Rittinger’s Law (1867)
 Kick’s Law (1885)
 Bond’s Law (1951)



Bond’s Law

Practical Form of Bond’s Law
Let Wi(Bond Work Index) equal the energy (kwh/ton) required to break a material from infinite size to 80% passing 100 µm.

Liberation
 Physical detachment of minerals from one another
 One of the major objectives of comminution
 Maximize liberation at coarsest possible particle size

Modes of Fracture (2)
 Transgranular  fracture across grain boundaries
 Intergranular  fracture along grain boundaries

Particle Composition Types
Free (or liberated)  a particle consisting of only one mineral type
Locked (or middlings)  a particle consisting of more than one mineral type

Degree of Liberation
The percentage of a given mineral occurring as free particles in an ore in relation to the total content of that mineral.
 D.O.L. =
 100 * (weight of free particles in mineral A)/(free particles" + weight of locked particles in min A)

Methods of Determining Optimum Mesh of Grind
Direct  Degree of Liberation (Gaudin)
Equivalent number of locked particles
Consider five particles containing 5%, 50%, 25%, 90% and 30% of mineral A, respectively. The equivalent number of locked A is 0.05 + 0.50 + 0.25 + 0.90 + 0.30 = 2.00

Locking Factor:
Gives additional weight to underestimated locked particles since locked particles can appear as free under a microscope, but free particles can never appear as locked.

Differential Liberation
Separate or discard some material at a coarse size and regrind the remaining material to produce a concentrate (save on grinding costs).

Limitations of Energy/Size Relationships
 Based on only one particle size (e.g., 80% passing size)
 Unable to predict the effect of operating variables on grinding circuit performance
 Complete size distribution needed for simulating subsequent processes

Probability Model of Comminution

Components of K(Selection Function)
Selection Function (S)  the probability that particles in a given size range will be selected for breakage (Diagonal Matrix).

Components of K(Selection Function (cont.))

Breakage Function
Breakage Function  the manner in which particles distribute after breakage

OpenCircuit Ball Mill Model

Kinetic Model of Comminution
 Consider grinding to be analogous to a chemical reaction having a reaction rate constant, k.
 Consider M1to represent the mass of material in the top size class in the mill.
 Assuming this is a batch ball mill and all material that breaks must leave size class 1, the change of mass in size class 1 is given by
dM _{1}/dt = k _{1}M_{1}

Kinetic Model of Comminution
(Breakage Rate Function)

Kinetic Model of Comminution(Breakage Distribution Function)
Breakage Distribution Function (b _{ij})  the fraction of broken particles of size class j which report to size class i


