## Questions and Answers

Which of the following assumptions is made in the expressions for drag force and terminal falling velocity?

The settling is not affected by the presence of other particles in the fluid

In fluidization, solid particles are transformed into a fluid-like state through suspension in a ______.

fluid

What is the condition known as when the settling is not affected by the presence of other particles in the fluid?

free settling

What is the velocity at which all bed particles are completely suspended by the air stream in fluidization?

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Smooth fluidization is desirable for optimal performance in the powder coating process.

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## Study Notes

### 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).

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## Description

Introduction to Unit Operations I, covering basic concepts of materials classification, properties of particulate solids, and separation processes. Learn about the different types of materials and their applications.