Unit Operations I: Introduction to Materials

Unit Operations I - Introduction and Basic Concepts

• Materials can be classified into three categories:
  • Solids (particles, powders, blocks, etc.)
  • Fluids (liquids or gases)
  • Mixtures of Solids and Fluids (slurries, suspensions, etc.)

Properties of Particulate Solids

• Solid particles can be described by their:
  • Composition (which affects density and conductivity)
  • Size (which affects surface area and settling rate)
  • Shape (which affects behavior in a fluid and sphericity)
• The three most important characteristics of an individual particle are:
  • Particle Composition
  • Particle Size
  • Particle Shape

Industrial Applications of Particulate Solids

• Examples of industries that use particulate solids:
  • Cement
  • Catalysts

Separation Processes

• Separation processes that will be covered in this course:
  • Screening or Classification
  • Size Reduction
  • Filtration
  • Settling or Sedimentation
  • Centrifuging
  • Evaporation-Crystallization-Flotation

Screening or Classification

• Calculations involved in screening:
  • Sieve analysis
  • Average diameter
  • Number of particles
  • Surface area

Size Reduction

• Design considerations for size reduction:
  • Efficiency
  • Processing time
  • Power requirement

Filtration

• Design considerations for filtration:
  • Filter resistance
  • Processing time
  • Efficiency

Settling and Sedimentation

• Design considerations for settling and sedimentation:
  • Processing time
  • Vessel size

Centrifuging

• Design considerations for centrifuging:
  • Processing time
  • Efficiency

Measurement of Particle Size

• A wide range of measuring techniques is available, including:
  • Screen analysis
  • Electrical sensing
  • Laser diffraction
  • Spectrometry
  • Sedimentation
  • Optical microscopy
  • Electron microscopy
• Each technique has an approximate useful range of particle sizes

Sieve Analysis

• Sieve analysis is a common method of particle size analysis
• The sieves are arranged in a series, with each lower sieve having a smaller aperture size
• The ratio of aperture sizes on consecutive sieves is typically 2, 2.5, or 2.25

Particle Size Distribution

• A particulate system consists of particles of a wide range of sizes
• A quantitative indication of the mean size and spread of sizes of a particulate system can be represented by:
  • A cumulative mass fraction curve
  • A differential analysis
  • A cumulative analysis
• The analysis can be tabulated to show the mass fraction in each size range as a function of the average particle size

Mixed Particle Size and Size Analysis

• Mixed particle size and size analysis involves:
  • Screening and sorting into fractions of constant density and size
  • Calculating the volume and surface area of each fraction
  • Calculating the average particle size of the mixture
  • Calculating the number of particles in the mixture
  • Calculating the specific surface area of the mixture

Average Particle Size

• The average particle size of a mixture can be expressed by:
  • Volume-surface mean diameter
  • Mass mean diameter
  • Arithmetic mean diameter
  • Volume mean diameter

Number of Particles in the Mixture

• The number of particles in the mixture can be calculated by:
  • Using the volume of one particle and the total volume of the sample
  • Using the number of particles in each fraction and the mass fraction of each fraction

Voidage and Density

• Voidage (ε) is the fraction of the total volume that is made up of free space between particles
• Bulk density (ρb) is the mass of the material divided by its total volume (particles and voids)### Particle Density
• Particle density (ρp) is the density of a particle including voids within the individual solid
• ρp = msolids / Vsolids, where msolids is the mass of the solids and Vsolids is the volume of the solids
• The more rapidly material is poured onto a surface or into a vessel, the more densely it packs

Solid Particle Hardness

• Measured using the Mohr Scale of Hardness
• Ranges from 1 (talc) to 10 (diamond)
• Examples:
  • Talc: very soft, can be powdered with the finger
  • Gypsum: moderately soft, can scratch lead
  • Calcite: can scratch fingernail
  • Fluorite: can scratch a copper coin
  • Apatite: can scratch a knife blade with difficulty
  • Feldspar: can scratch a knife blade
  • Quartz: harder than 6
  • Topaz: all products harder than 6
  • Corundum: will scratch window glass
  • Diamond: hardest

Agglomeration of Particles

• Agglomeration arises from interaction between particles, causing them to adhere to each other and form clusters
• If particles agglomerate, poor flow properties are expected
• Factors affecting flow characteristics:
  • Particle size (particles smaller than 10 μm)
  • Particle shape (deviation from isometric form)
  • Angle of repose (measured by pouring solid from a nozzle onto a plane surface)

Angle of Repose and Friction

• Angle of repose: the angle between the sloping side of a conical heap and the horizontal
• Measured by pouring solid from a nozzle onto a plane surface
• Angles of repose vary from 20° (free-flowing solids) to 60° (solids with poor flow characteristics)
• Powders with low angles of repose tend to pack rapidly to give a high packing density almost immediately
• Classification of particulate solids based on flow properties:
  • Cohesive: wet clay
  • Non-cohesive: dry sand

Angle of Internal Friction

• Angle of internal friction: the angle between flowing particles and bulk or stationary solids in a bin
• Measures frictional forces between particles

Storage of Solid Particles

• Storage options:
  • Silos, bins, or hoppers (for valuable or soluble solids)
  • Large piles (for coarse solids like gravel)
• Flow of solids in hoppers:
  • Solids are stored in hoppers which are usually circular or rectangular in cross-section with conical or tapering sections at the bottom
  • Size distribution of particles can affect flow behavior

Measurement and Control of Solids Flowrate

• Methods:
  • Measuring flowrate as solids leave the hopper
  • Continuous monitoring of solids level in the hopper using load cells or transducers
• Problems associated with measurement and control:
  • Dependence on particle size, shape, and packing
  • Influence of surface and electrical properties and moisture content on flow behavior

Conveying of Solids

• Methods:
  • Gravity chutes
  • Air slides
  • Belt conveyors
  • Screw conveyors
  • Bucket elevators
  • Vibrating conveyors
  • Pneumatic/hydraulic conveying installations

Pressure in Bulk of Particles

• Solid particles behave like a fluid in terms of:
  • Exerting pressure on the side walls of a container and on the floor
  • Ability to flow through openings and be pumped
• Differences from fluids:
  • Friction between the wall and solid particles reduces pressure on the floor
  • Pressure is not the same in all directions
  • Bulk density of solid particles may vary depending on packing

Force Balance

• Equations for force balance:
  • Fv = Pvπr^2
  • dFv = Pvπr^2dz - μ'PL2πrdz
• Coefficient of friction (μ'): 0.35-0.55### Energy for Size Reduction
• It is impossible to estimate accurately the amount of energy required for size reduction of a given material.
• Several empirical laws have been proposed, including:
  • Rittinger's law: E = P/mo, where P is the power required and mo is the feed rate to the crusher.
  • Kick's law: supposes that the energy required is directly related to the reduction ratio L1/L2.

Energy Utilization

• Energy is utilized in crushing in the following ways:
  • Producing elastic deformation of the particles before fracture occurs.
  • Producing inelastic deformation, resulting in size reduction.
  • Causing elastic distortion of the equipment.
  • Friction between particles and between particles and the machine.
  • Noise, heat, and vibration in the plant, and friction losses in the plant itself.
• Only about 10% of the total power is usefully employed.

Nature of the Material to be Crushed

• The choice of a machine for a given crushing operation is influenced by the nature of the product required and the quantity and size of material to be handled.
• The more important properties of the feed, apart from its size, are:
  • Hardness
  • Structure
  • Moisture content
  • Crushing strength
  • Friability
  • Stickiness
  • Soapiness

Types of Crushing Equipment

• Coarse Crushers:
  • Stag jaw crusher
  • Dodge jaw crusher
  • Gyratory crusher
  • Rotary materials breaker
• Intermediate Crushers:
  • Edge runner mill
  • Hammer mill
  • Pin-type mill
• Fine Crushers:
  • Buhrstone mill
  • Centrifugal attrition mills (e.g. Babcock mill, Lopulco mill)
  • Szego grinding mill
  • Ball mill

Ball Mill: Factors Influencing the Size of the Product

• Rate of feed: high rates of feed result in less size reduction.
• Properties of the feed material: larger feed results in a larger product, and harder materials result in a smaller size reduction.
• Weight of balls: a heavier charge of balls produces a finer product.
• Diameter of balls: smaller balls facilitate the production of fine material.
• Slope of the mill: an increase in the slope of the mill increases the capacity of the plant but results in a coarser product.
• Discharge freedom: increasing the freedom of discharge of the product has the same effect as increasing the slope.
• Speed of rotation of the mill: affects the crushing action, with low speeds resulting in little crushing action and high speeds resulting in considerable wear of the mill lining.

Advantages of the Ball Mill

• Can be used wet or dry.
• Low installation and power costs.
• Can be used with an inert atmosphere for grinding explosive materials.
• Grinding medium is cheap.
• Suitable for materials of all degrees of hardness.
• Can be used for batch or continuous operation.

Specialized Applications

• Electrohydraulic crushing
• Ultrasonic grinding
• Cryogenic grinding
• Explosive shattering

Sedimentation

• Sedimentation describes the motion of molecules in solutions or particles in suspensions in response to an external force such as gravity, centrifugal force, or electric force.
• The separation of a dilute slurry or suspension by gravity settling into a clear fluid and a slurry of higher solids content is called sedimentation.

Sedimentation of Fine Particles

• Particles settle in a fluid under the influence of gravity, and the rate of sedimentation depends on the properties of the fluid and the particles.
• The terminal settling velocity of a particle depends on the size and density of the particle, the shape of the particle, and the fluid properties.

Zone Settling and Compression

• The height of the interface between the clarified zone and the zone settling zone is plotted against time to determine the zone settling velocity.
• The velocity of the interface is steady after some induction period but changes with time as compression begins.
• Initial suspended solids concentration has a significant effect on the zone settling velocity.

Factors Affecting Sedimentation

• Height of suspension: does not generally affect the rate of sedimentation or the consistency of the sediment.
• Diameter of vessel: affects the rate of sedimentation, with a larger diameter resulting in a faster rate.
• Concentration of suspension: affects the rate of sedimentation, with a higher concentration resulting in a slower rate.
• Shape of vessel: an inclined tank can be used to accelerate the rate of settling.

Coagulation and Flocculation

• Coagulation concentrations are the electrolyte concentrations required to coagulate a sol.
• Flocculation creates large conglomerations of elementary particles.
• The behavior of suspensions of fine particles is influenced by whether the particles flocculate.

Kynch Theory of Sedimentation

• The behavior of concentrated suspensions during sedimentation.
• Assumes uniform particle concentration across any horizontal layer, and no differential settling of particles.

Hindered Settling

• Higher solids concentration reduces the settling velocity.
• Collision between particles is practically continuous, and the relative fall of particles involves repeated pushing apart of the lighter by the heavier particles.

Thickener

• A unit in which the concentration of a suspension is increased by sedimentation, with the formation of a clear liquid.
• May operate as batch or continuous units.
• Incorporates a slow stirrer, which causes a reduction in the apparent viscosity of the suspension.

Thickener Function

• Produces a clarified liquid.
• Produces a given degree of thickening of the suspension.
• The clarifying capacity is determined by the diameter of the tank.
• The required degree of thickening is controlled by the time of residence of the particles in the tank.

Thickening Zone

• The concentration at which the total flux is a minimum must be established to calculate the required area.

Continuous Thickener: Overflow

• The liquid flowrate in the overflow is the difference between that in the feed and in the underflow.
• The required area is given by the equation: A = Q´ / (C´ - C).