Forms of energy requirements in breaking mechanisms
- Elastic & PLastic deformation
- Slip Systems
- Fracture Mechanims
- Brittle Fracture
- Crack initiation
Mechanisms of particle breakage
- Impact (single rigid force)
- Compaction (two rigid forces)
- Shear (fluid or particle-particle interactions)
- Attrition (Particle scraping against eachother or rigid surface)
Key factors to milling
- physicochemical & mechanical properties
- Initial size
- Requirements
- Temp Control
- Cleaning
- Safety
- Energy Requirement
Name the 3 Crushing Laws
dE/dx = -k*x^m
Rittinger: Energy/mass is proportional to new surface area (m = -2)
Kick: Energy is proportional to size reduction ratio (m = -1)
Bond: Intermediate (m = -3/2)
Which crushing law is appropriate when:
Rittinger:
Formation of new surfaces (fine grinding)
Kick: Elastic deformation before fracture occurs (coarse grinding)
Bond: Intermediate
Energy Losses in Milling processes
- Elastic deformation
- Inelastic deformation
- Elastic distortion in equipment
- Friction between particles/wall
- Noise, heat & vibrations
Effects of milling
- Increased rate of reaction
- Greater flow impeding
- Greater leaching
- Increased drying rate
Benefits of agglomeration
- Ease of particle handling
- Fine particles tend to adhere
- reduce environmental/ health issues
- Flowability
- Reduced electrostatic charges
3 stages of wet granulation:
- Wetting & Nucleation (Formation of initail agglomerates)
- Consolidation & Coalescence
- Attrition & Breakage
Critical Stokes Number
St* = (1 + 1/e)*ln(h/h_a)
e = coefficient of restitution h = thickness of liquid surface layer h_a = characteristic height of surface asperities
Stokes number
St = 8mu/(3pimu*d^2)
Measure of the relative kinetic energy absorbed plastically by viscous binder
Three types of granule growth
Non-inertial growth (St < St*)
- Collisions lead to coalescence
Inertial growth (St = St*)
Coating (St > St*)
- Kinetic energy too high to be absorbed by liquid layer (no coalescence)
Iveson Model
Gives Maximum granule pore saturation
S = wro_s(1-eps)/(ro_l*eps)
Physcial properties causing segregation
Particle shape
Size
Density
Size distribution
Size most important and density the least
Consequences of segregation
Variations in:
- size distribution
- Bulk density
- Chemical composition
- Effect functionality of mixing equipment
Mechanisms of segregation
- Trajectory (side to side)
- Sieving/ Vibration (Top to bottom)
- Elutriation (Top to Bottom)
- Agglomeration
Trajectory Segregation
- Horizontal movement of particles
- Drag governed by stokes law
D = Urox^2 /(18*mu)
D = limiting horizontal distance it can travel x = diamter
Percolation of fine particles (Sieving) Segregation
- gaps created allow small particles to fall from above
- occurs whenever mixture is disturbed
(Larger particles move upwards)
Elutriation Segregation
Vessel with air flowing upward and air velocity exceeds terminal freefall velocity
Agglomration Segregation
- one components forms agglomerates easily whilst others do not
Methods of reducing segregation
- Decrease particle size (stronger interparticle forces)
- Reduce particle mobility (addition of liquid)
- Low free fall height
- remove vibrations
- decrease heap size
Mechanisms of mixing
- Convective mixing (transfer of larger particle groups from one location to another)
- Shear mixing (particles of different velocities leads to velocity distribution)
- Diffusive mixing (random motion of particles)
Mixing Index
Ratio of mixing achieved to mixing possible
If zero - completely segregated
If 1 - completely random mixture
Define Bin or Silo
Container for bulk solids
