12.3 Size reduction and classification

Size reduction is a crucial process in many industries, breaking down materials into smaller particles. From crushing rocks to grinding pharmaceuticals, various techniques and equipment are used to achieve specific particle sizes and distributions.

Energy efficiency is key in size reduction, with different laws describing the relationship between energy input and particle size reduction. Particle analysis and classification techniques ensure the final product meets desired specifications, optimizing downstream processes and product quality.

Principles and Equipment of Size Reduction

Principles of size reduction

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• Size reduction principles
  • Particle breakage mechanisms reduce material size through different methods
    • Compression squeezes particles between two surfaces (jaw crushers)
    • Impact fractures particles through high-velocity collisions (hammer mills)
    • Attrition wears down particles by rubbing against surfaces or other particles (ball mills)
    • Cutting slices particles into smaller pieces (knife cutters)
• Objectives of size reduction
  • Increase surface area enhances reaction rates and extraction efficiency (catalyst preparation)
  • Improve material handling facilitates transport and storage (coal processing)
  • Enhance reactivity accelerates chemical reactions (pharmaceutical ingredients)
  • Facilitate separation processes improves efficiency of downstream operations (mineral processing)
• Classification principles
  • Separation based on particle size or density sorts materials into uniform fractions (screening)
  • Improve product uniformity ensures consistent quality (food processing)
  • Remove unwanted size fractions eliminates over- or undersized particles (aggregate production)

Types of reduction equipment

• Crushers break down large particles into smaller pieces
  • Jaw crushers use reciprocating plates to compress and fracture material (rock crushing)
  • Gyratory crushers employ a rotating cone to break material against a fixed shell (mining)
  • Cone crushers utilize a gyrating cone to crush material in a reduced space (aggregate production)
• Grinders further reduce particle size for finer products
  • Ball mills use tumbling balls to grind material in a rotating cylinder (cement production)
  • Rod mills employ long rods instead of balls for more uniform grinding (ore processing)
  • Hammer mills utilize high-speed rotating hammers to impact and shatter material (recycling)
• Ultrafine grinders produce very small particle sizes
  • Fluid energy mills use compressed air to create particle collisions (pigment production)
  • Stirred media mills employ small grinding media in a stirred chamber (nanoparticle synthesis)
• Cutting machines slice or chop materials into specific shapes or sizes
  • Knife cutters use sharp blades to slice soft materials (plastic recycling)
  • Granulators employ rotating knives to cut materials into small, uniform pieces (rubber processing)

Energy in size reduction

• Energy laws for size reduction describe relationships between energy input and particle size reduction
  • Kick's law: $E = C_k \ln(D_f/D_i)$ applies to coarse crushing where $E$ is energy, $C_k$ is a constant, $D_f$ is final size, and $D_i$ is initial size
  • Rittinger's law: $E = C_r(1/D_f - 1/D_i)$ used for fine grinding where $C_r$ is Rittinger's constant
  • Bond's law: $E = C_b(1/\sqrt{D_f} - 1/D_i)$ applicable for intermediate size reduction where $C_b$ is Bond's work index
• Factors affecting energy efficiency
  • Feed material properties influence breakage behavior (hardness, brittleness)
  • Equipment design impacts energy transfer to particles (mill geometry, liner design)
  • Operating conditions affect grinding efficiency (feed rate, rotation speed)
• Energy efficiency metrics
  • Specific energy consumption measures energy used per unit mass of product (kWh/ton)
  • Size reduction ratio quantifies extent of size reduction (feed size / product size)

Particle analysis and classification

• Particle size measurement techniques
  • Sieve analysis uses stacked screens to separate particles by size (soil analysis)
  • Laser diffraction measures particle size through light scattering patterns (pharmaceutical powders)
  • Image analysis employs microscopy and software to analyze particle dimensions (quality control)
• Particle size distribution representation
  • Cumulative distribution curves show percentage of particles below a given size
  • Frequency distribution curves display proportion of particles within size ranges
• Classification techniques
  • Screening separates particles using perforated surfaces
    • Vibrating screens use oscillating motion to improve separation efficiency (mineral processing)
    • Rotary screens employ rotating cylindrical screens for continuous operation (compost screening)
  • Air classification sorts particles based on their aerodynamic behavior
    • Cyclones use centrifugal force to separate particles in a spinning air stream (dust collection)
    • Elutriators employ upward air flow to classify particles by terminal velocity (flour milling)
  • Hydraulic classification separates particles in liquid media
    • Hydrocyclones utilize centrifugal force in a conical chamber (mineral beneficiation)
    • Settling tanks allow particles to settle based on size and density (wastewater treatment)
• Efficiency of classification processes
  • Cut size defines the particle size at which separation occurs (50% probability of separation)
  • Sharpness of separation measures the precision of the classification process (steepness of efficiency curve)