Particle Technology

Particle in Motion

I. Introduction
(ppt)
• The objectives of determining the motion of single solid particles in fluids to develop an
understanding of the forces resisting the motion of any such particle and provide methods for the
estimation of the steady velocity of the particle relative to the fluid
• This will help understand the succeeding topics such as on the behavior of suspensions of
particles in a fluid, fluidization, gas cyclones and pneumatic transport

II. Mechanisms of Particle in Motion

• A force balance of a settling particle can be mathematically presented as:

gravity – drag – buoyance = acceleration force

𝑑𝑣
𝑚( 𝑑𝑡 )
W - FD – FB =
𝑔𝑑

• For gravitational forces, W

W = ρPgV

o For spherical particles,

3
𝜋𝐷𝑃
W = 𝜌Pg
6

• For buoyant force, FB

FB = ρfgV

o For spherical particles,

3
𝜋𝐷𝑃
FB = 𝜌Pg
6

• For drag force, FD

1
FD = CDAPρfu2
2

where CD = drag coefficient

AP = projected particle area in direction of motion

𝜌 = density of surrounding fluid

𝑢 = relative velocity between particle and fluid

o For spherical particles,

3
𝜋𝐶𝐷 𝜌𝑓 𝑢2 𝐷𝑃
FD =
8

• For acceleration force, force is balanced when the particle’s acceleration reaches 0 while
achieving the maximum relative velocity (terminal velocity).
III. Terminal Velocity
• Since terminal or free settling velocity, ut, can be achieved when the acceleration force

2𝑔𝑚𝑝 (𝜌𝑝 − 𝜌𝑓 )
ut = √
𝜌𝑝 𝜌𝑝 𝐴𝑝 𝐶𝐷

IV. Drag Content

• At higher relative velocities, the inertia of the fluids begins to dominate (the fluid must accelerate
out of the way of the particle.)
• However, experiments give the relationships between the drag coefficient (CD) and the Reynolds
number (ReP) in the form of the so-called standard drag curve.
• Four regions are identified: the Strokes’ law region, the Newton’s law region in which drag
coefficient is independent of Reynolds number, intermediate region between the Strokes and
Newton regions, and the boundary layer separation region

• The Reynolds number ranges and drag coefficient correlations for these regions according ro PCEH
are the following:
Region Stokes Intermediate Newton’s
ReP range ReP < 0.1 0.1 < ReP < 1000 ReP > 1000
24 24
CD CD = CD = ( )(1+0.14𝑅𝑒𝑃0.70 ) CD = 0.445
𝑅𝑒𝑃 𝑅𝑒𝑃

V. Motion of Spherical Particles

• For spherical particles
2𝑉𝑔 (𝜌𝑝− 𝜌𝑓)
ut = √
𝐶𝐷 𝐴𝑝 𝜌𝑓
3
4𝑔𝐷𝑃 (𝜌𝑃 − 𝜌𝑓 )
4
V = 𝜋R3 =
𝜋𝐷𝑃 𝑢𝑡 = √
3 6 3𝜌𝑓 𝐶𝐷
2
𝜋𝐷𝑃
AP = 𝜋R = 2
4
• For Strokes’ Law

4𝑔𝐷𝑃 (𝜌𝑃−𝜌𝑓 ) 𝑔𝐷𝑃2 (𝜌𝑃 − 𝜌𝑓 )

𝑢𝑡 = √ 24 𝑢𝑡 =
3𝜌𝑓 (𝑅𝑒 ) 18𝜇
𝑃

𝐷𝑃 𝜌𝑓 𝑢𝑡
ReP =
𝜇
VI. Criterion for Settling Region
• K criterion:
𝑔𝜌𝑓 (𝜌𝑃−𝜌𝑓) 1⁄
K = DP ( ) 3
𝜇2

3
𝑔𝑑𝑃 (𝜌𝑝−𝜌)𝜌
Ar = (6-246)
𝜇2

Region Strokes Intermediate Newton’s

ReP range ReP < 0.1 0.1 < ReP < 1000 ReP > 1000
24 24
CD CD = CD = ( )(1+0.14𝑅𝑒𝑃0.70 ) CD = 0.445
𝑅𝑒𝑃 𝑅𝑒𝑃
K K < 3.3 3.3 < K < 44 K > 44
𝑔𝐷𝑃2 (𝜌𝑃 − 𝜌𝑓 ) 0.153𝑔0.71 𝐷𝑃1.14 (𝜌𝑃 − 𝜌𝑓 )0.71
𝑢𝑡 = 𝑔𝑑𝑃 (𝜌𝑝 − 𝜌)
ut 18𝜇 𝑢𝑡 = 𝑢𝑡 = 1.73 √
𝜌𝑓0.29 𝜇 0.43 𝜌

VII. Hindered Settling

• Hindered settling happens when particles settling at low
falling rate due to the high solid concentration

• Higher effective viscosity, 𝝁𝒎

𝜇 1
𝜇𝑚 = 𝜑𝑃 =
𝜑𝑃 101.82(1−𝜀)
• Bulk Density of the Slurry, 𝝆𝒎
𝜌𝑚 = 𝜀𝜌 + (1 − 𝜀)𝜌𝑃
• Settling Velocity for Laminar Settling

𝑔𝐷𝑃2 (𝜌𝑃 − 𝜌𝑓 )(𝜀 2 𝜑𝑃 )

𝑢𝑡 =
18𝜇

• In calculating the particle Reynolds’ number, use the slurry properties, 𝜇𝑚 , 𝜌𝑚

𝐷𝑝 𝜌𝑓𝑢𝑡
ReP =
𝜇𝑚 𝜀

• (pangayo clear pic)

 • Maude and Whitmore Equation

𝑢𝑡 = 𝑢𝑡0 (1 − 𝑐)𝑛 (6 – 254)

o where ut = terminal settling velocity

ut0 = terminal velocity of a single sphere (infinite dilution)
c = volume fraction solid in the suspension
n = function of Reynolds number ReP = dp ut0 𝜌/𝜇

VIII. Sample Problems

1. Oil droplets having a diameter of 20 𝜇𝑚 (0.020 mm) are to be settled from air at temperature of
37.8oC (311 K) and 101.3 kPa pressure. The density of the oils is 900 kg/m3. Calculate the terminal
settling velocity of the droplets.
2. Calculate the settling velocity of glass spheres having a diameter of 1.554 x 10 -4 m in water at 293.2
K. The slurry contains 60 wt% solids. The density of the glass sphere is 2467 kg/m3.
3. (Seatwork 1)

IX. Computation Lab

A particle of diameter 10 microns and of density 1600 kg/m3 settling in a liquid density 1000 kg/m3 and of
viscosity 0.001 Pa-s. Calculate the following:
a. K-criterion (0.1805)
b. Terminal falling velocity (mm/s) of the particle (0.033 mm/s)
c. If Strokes’ Law applies for particle Reynold’s number up to 0.2, what is the diameter of the largest
particle whose behavior is governed by Stokes’ law for this solid and liquid? (85 microns)
 SEDIMENTATION

Topic/Equation/Figure/Table PCEH 9th ed

Sedimentation Section 18, pg
Gravity Sedimentation pg 18-62
Kynch Method pg 18-64
Thickeners pg 18-66
Clarifers pg 18-67

I. Introduction

(ppt)

• Sedimentation – gravity settling particles of a dilute slurry creating a clear fluid and a slurry of
higher solids concentration
• Clarification – virtually removes all the particles from a liquid under hindered settling condition. It
converts a dilute slurry into a clear liquid and a concentrated suspension.
• Classification – separates the solids into size fractions
• Flocculation – process of adding inexpensive materials to a slurry of fine particles to promote
agglomeration, e.g. lime alumina, sodium silicate.

(PCEH 9th ed, pg 18-62)

Sedimentation

• partial separation and concentration of suspended solid particles from a liquid by gravity settling
• may be divided into the functional operations of thickening and clarification, these two functions
are similar and occur simultaneously
Thickener
o primary purpose of thickening: to increase the concentration of suspended solids in a feed
stream
o thickener mechanisms are design for the heavier-duty requirements imposed by a large
quantity of relatively concentrated pulp
Clarifiers
o primary purpose of clarification: to remove a relatively small quantity of suspended
particles and produce a clear effluent
o include features that ensure essentially complete suspended-solids removal (greater
depth, special provision for coagulation and flocculation of the feed, and the greater
overflow-weir length)

o “Totally discrete” particles include many mineral particles

(usually greater in diameter than 20 µm), salt crystals, and
similar substances that have little tendency to cohere
o “Flocculent” particles generally will include those smaller
than 20 µm (unless present in a dispersed state owing to
surface charges)
o At low solid concentrations, the type of sedimentation
encountered is called particulate settling
o Regardless of their nature, particles are sufficiently far
apart to settle freely
 o Faster-settling particles may collide with slower-settling ones and, if they do not cohere,
continue downward at their own specific rate. Those that do cohere will form floccules of a
larger diameter that will settle at a rate greater than that of the individual particles

TESTING COMMON TO CLARIFIERS AND THICKENERS

Feed Characterization

Characterization requires the following measurements as minimum:

• General chemical makeup of the solids and liquor phases

• Feed solids concentration
• Particle size distribution—include course (+100 µm) and fine (-20 µm)
• Solids specific gravity
• Liquid specific gravity
• Liquid-phase dissolved materials concentration
• Temperature
• pH

Coagulant and/or Flocculant Selection

• refers to the process of choosing the appropriate coagulant and flocculant for a particular
application.
• widely used to enhance the settling rate of suspended particles
• Effective settling rate reduction allows for smaller equipment sizes in thickeners and clarifiers.
• The aim is to enhance the clarity of overflow or increase the density of underflow in separation
processes.

Coagulation

o A preliminary step to destabilize suspended solids, preparing them for flocculation.

o Types of Coagulants: Can be organic (e.g., polyelectrolytes) or inorganic (e.g., alum).
▪ They can be used alone or in combination to enhance performance or reduce the
quantity of flocculant needed.

Flocculation

o Involves bridging and binding destabilized solids into larger particles.

o Types of Flocculants: Natural (historically used but replaced by synthetic polymers) and
Synthetic polymeric flocculants.
▪ Screening Program for Synthetic Polymers includes testing different types of
flocculant charge (anionic, nonionic, and cationic), molecular weight, and charge
density.
• Purpose of Screening Test: To select a coagulant or flocculant that will likely be effective and
establish the required dosage.
• Both coagulation and flocculation are considered in clarifier design, while flocculation alone is
typically used in thickener design.

TESTING SPECIFIC TO CLARIFICATION

Detention Test

• The test uses a 1- to 4-L beaker or similar vessel. The sample is placed in the container, coagulated
and/or flocculated by suitable means, if required, and allowed to settle.
 • Small samples for suspended-solids analysis are withdrawn from a point approximately midway
between the liquid surface and settled solids interface, taken with sufficient care that settled
solids are not resuspended.

Bulk Settling Test

• After the detention test is completed, a bulk settling test determines the maximum overflow rate.
• This is done by carrying out a settling test in which the solids are first concentrated to a level at
which zone settling just begins

Solid Contact Clarification

• In many instances, the rate of clarification is enhanced by increasing the solids concentration in
the flocculation zone of the clarifier.
• This is done in a full-scale operation by internally or externally recycling previously settled solids
into the flocculation zone where they are mixed with fresh, coagulated feed. The higher population
of solids improves the flocculation efficiency and clarification rate
• In some suspensions, very fine colloidal solids are present and are very difficult to coagulate, and it
is typically necessary to adjust for coagulation mixing intensity and time to obtain coagulated
solids that are more amenable to flocculation

Detention Efficiency

• Conversion from the ideal basin sized by detentiontime procedures to an actual clarifier requires
the inclusion of an efficiency factor to account for the effects of turbulence and nonuniform flow .
• Efficiencies vary greatly being dependent not only on the relative dimensions of the clarifier and the
means of feeding but also on the characteristics of the particles

THICKENERS

• The primary function is to concentrate suspended solids by gravity settling to achieve a steady-
state material balance.
• An inventory of pulp is maintained in order to achieve the desired underflow concentration
• Thickener Components: Tank, feed piping, feed well, rake mechanism, underflow solids-
withdrawal system, and overflow launder.
• Thickener Types: Conventional, high-rate,
ultrahigh-rate, high-density/paste.
o High-Rate Thickeners: Greater
capacity due to effective use of
flocculant, with a noticeable increase
in capacity up to a limit.
▪ Flocculant Addition: Usually
added to the feed line or feed
well, with proprietary feed
well designs optimizing
flocculation.
 o Ultrahigh-Rate Thickeners: Use tall, deep tanks with
steep bottom cones, combining thickener and clarifier
functions, but with smaller diameter.

o High-Density/Paste Thickeners: Designed for high

underflow viscosity and yield stress, useful for disposal
of waste slurries without segregation or free-liquid pond
formation.

Design Features

• Mechanical Classes of Thickeners: Four classes differentiated

by drive mechanism: (1) bridge-supported, (2) center-column
supported, (3) peripheral-traction drives, and (4) without drives.
• Tank Diameter: Ranges from 2 to 150 meters (6.5 to 492 feet),
with the drive support structure determined by required
diameter.
• Thickener Operation: Requires minimum attention when
operated correctly, maintaining design performance
consistently.
• Monitoring Parameters: Feed and underflow rates, solids
concentrations, flocculant dosage rate, and pulp interface
level, monitored with dependable instrumentation systems.
• Handling Process Variations: Easily managed by changing principal operating controls, such as
underflow rate and flocculant dose, to maintain stability.

CLARIFIERS

• Continuous Clarifiers: Primarily aimed at producing a relatively clear overflow, typically used with
dilute suspensions like industrial process streams and municipal wastes.
• Design Similarities with Thickeners: Clarifiers share design and layout similarities with thickeners,
but with lighter construction and a drive head with lower torque capability. These differences are
allowed because clarified pulp is smaller in volume and has lower suspended solids
concentration, partly due to a large percentage of fine solids.

Rectangular Clarifiers

• Primarily used in municipal water and waste treatment plants, as well as certain industrial waste
plants.
• Raking Mechanism: Often employs a chain-type drag, with suction systems for light-duty
applications. The drag moves deposited pulp to a sludge hopper using scrapers fixed to endless
chains.
• Skimming Function: Flights of the drag mechanism may act as skimming devices for removing
surface scum during their return to the sludge raking position.
• Applications: Used for preliminary oil-water separations in refineries and clarification of waste
streams in steel mills.
• Advantages of Multiple Units: When multiple units are employed, common walls are possible,
reducing construction costs and saving floor space.
• Overflow Clarities: Generally, not as good as with circular clarifiers due to reduced overflow weir
length for equivalent areas.
Circular Clarifiers

• Circular Clarifiers: Available in the same basic types as thickeners: bridge, center-column, and
peripheral-traction.
• Surface-Skimming Device: Includes a rotating skimmer, scum baffle, and scum-box assembly. In
sewage and organic-waste applications, squeegees are provided for rake-arm blades to ensure the
bottom is scraped clean, preventing the accumulation of organic solids and floating decomposing
material.
• Center-Drive Mechanisms in Square Tanks: Installed in square tanks, this mechanism differs
from the standard circular mechanism by providing a hinged corner blade to sweep corners outside
the main mechanism's path.

Clarifier-Thickener

• Clarifier-Thickener: Clarifiers can also function as thickeners, achieving additional densification.

• Center, Deep Sludge Sump: Provides adequate retention time and pulp depth to compact solids
to a higher density.
• Drive Mechanisms: Higher torque capability compared to standard clarifiers is necessary for this
type of clarifier-thickener.

Industrial Waste Secondary Clarifiers

• Industrial Waste Secondary Clarifiers: Facilities previously discharging organic wastes to the
sewer have installed treatment facilities to reduce municipal treatment plant charges.
• Waste-Activated Sludge Process: Preferred approach for organic wastes, involving an aeration
basin for bio-oxidation and a secondary clarifier to produce clear effluent and concentrate biomass
for recycling.
• Design Criteria: Necessary to produce acceptable effluent and achieve sufficient concentration of
low-density solids in the biomass.
• Typical Design Parameters:
o Feed pipe velocity: ≤ 1.2 m/s
o Energy-dissipating feed entry velocity (tangential): ≤ 0.5 m/s
o Downward velocity from feed well: ≤ 0.5−0.75 (peak) m/min
o Feed well depth: entry port depth +1−3 m
o Tank depth: typically 3−5 m
o Radial velocity below feed well: ≤ 90 percent of downward velocity
• Overflow Rate: Can range between 0.68 and 2.0 m/h, depending on the application.
Recommendations can be found in equipment supplier manuals and manuals of practices for
specific applications.

Inclined-Plate Clarifiers

• Inclined-Plate Clarifiers: Also known as Lamella or inclined-plate

separators.
• Plate Geometry: Plates inclined at 45° to 60° from the horizontal,
with various feed designs allowing influent to pass into each inclined
channel.
• Solids Settling: Solids settle only a short distance in each channel
before sliding down to the collection zone beneath the plates.
• Liquid Clarification: Clarified liquid passes beneath the ceiling of
each channel in the opposite direction to the overflow connection.
 • Theoretical Separation Area: Equal to the sum of projected areas of all channels on the horizontal
plane.
• Advantages: Increased solids capacity per unit of plane area.
• Disadvantages: Lower underflow solids concentration compared to other gravity clarifiers,
difficulty in cleaning when scaling or fouling occur, inability to perform feed flocculation within the
unit, requiring external mixers and tankage.
•

Ultrahigh-Rate (Rakeless)

• Ultrahigh-Rate (Rakeless) Thickeners: Thickeners that utilize internal cones to achieve the
inclined-plate effect, allowing for internal flocculation.
• Design Features: Tall tank with a 60° bottom cone, providing sludge compression height and
volume.
• Resulting Effect: Higher-density underflow compared to conventional thickeners.

Solid-Contact Clarifiers

• Ultrahigh-Rate (Rakeless) Thickeners: Thickeners that utilize

internal cones to achieve the inclined-plate effect, allowing for
internal flocculation.
• Design Features: Tall tank with a 60° bottom cone, providing
sludge compression height and volume.
• Resulting Effect: Higher-density underflow compared to
conventional thickeners.

COMPONENTS AND ACCESSORIES FOR SEDIMENTATION UNITS

Refers to the various parts and features necessary for sedimentation systems, which can be supplied in
different variations based on application, sedimentation characteristics, and desired performance.

Basic Components:

Consist of the same elements for both thickeners and clarifiers

Tank

• Tanks or Basins: Constructed from various materials including steel, concrete, wood, compacted
earth, plastic sheeting, and soil cement.
• Selection Criteria: Based on factors such as cost, availability, topography, water table, ground
conditions, climate, operating temperature, and chemical-corrosion resistance.
• Typical Construction Materials: Industrial tanks up to 45 meters (150 feet) in diameter are
typically made of steel. Concrete is commonly used in municipal and large industrial applications.
Extremely large units may use earthen basins with impermeable liners for cost-effectiveness.
• Rakeless Ultrahigh-Rate Thickeners: Utilize elevated tanks up to 12 meters in diameter.
• Advantages: No drive required, high throughput rate, and small footprint.
• Disadvantages: Height of the elevated tank.
Drive-support structure

• Drive-Support Structures: Three basic types: (1) bridge-supported mechanism, (2) center-
column-supported mechanism, and (3) traction-drive thickener with a center-column-supported
mechanism and motorized carriage at the tank periphery.
• Bridge-Supported Thickeners: Common in diameters up to 30 meters, offering advantages such
as load transfer to tank periphery, denser underflow concentration with single draw-off point,
simpler lifting device, fewer structural members prone to mud accumulation, maintenance access
from both ends of the bridge, and lower cost for units smaller than 30 meters in diameter.
• Center-Column-Supported Thickeners: Typically 50 meters or more in diameter, with the
mechanism supported by a stationary center column and raking arms attached to a rotating cage
around the center column.
• Traction Thickeners: Most adaptable to tanks larger than 60 meters in diameter, with
maintenance generally less difficult. Drive may be supported on the concrete wall or outside the
wall on the ground. Disadvantages include difficulty in using practical lifting devices, operational
challenges in snowy climates due to potential friction loss on the traction drive rail, and the need to
transmit driving torque from the tank periphery to the center where the heaviest raking conditions
occur.

Drive Assembles

• Drive Assemblies: Key component of a sedimentation unit, providing force to move rakes through
thickened pulp, support for rotating mechanism, reserve capacity for withstanding upsets, and
reliable control to protect against damage during major overloads.
• Drive Components: Main spur gears, alloy-steel pinions, or planetary gears mounted on bearings.
Direct-drive hydraulic systems also used. Gearing components preferably enclosed for maximum
service life.
• Torque-Measuring System: Typically included with torque indicated on mechanism and often
transmitted to remote indicator. Excessive torque can activate safeguards against structural
damage, such as sounding an alarm, raising the rakes, and stopping the drive.
• Rake-Lifting Mechanisms: Provided for abnormal thickener operation or excessive torque.
Abnormal operation may result from factors like insufficient underflow pumping, surges in solids
feed rate, large particle amounts, or miscellaneous obstructions. Mechanisms may automatically
raise rakes when specific torque levels are encountered until normal torque returns or maximum
lift height is reached. Corrective action typically required to eliminate upset causes.
• Motorized Rake-Lifting Devices: Designed for vertical lift of rake mechanism up to 90 cm (3 ft).
• Cable Arm Design: Uses cables attached to truss above or near liquid surface to move rake arms,
which are hinged to drive structure. Allows rakes to lift when excessive torque encountered.
Advantages include small raking mechanism surface area, reducing solids accumulation and
downtime. Disadvantages include limited lift at center and difficulty returning rakes to lowered
position in settlers with firmly compacted solids.
• Rake Mechanism: Assists in moving settled solids to discharge point and thickening pulp by
disrupting bridged floccules. Designed for specific applications, typically with two long rake arms
and option for two short rake arms for bridge-supported and center-column-supported units.
Traction units usually have one long arm, two short arms, and one intermediate arm.
• Rake-Blade Design: Blades may have attached spikes or serrated bottoms to cut into compacting
solids. Lifting devices often used with these applications.
• Rake-Speed Requirements: Depend on types of solids being thickened, with peripheral speed
ranges ranging from 3 to 30 m/min (10 to 100 ft/min) based on settling characteristics.
Feedwell

• Feedwell: Designed to allow feed entry into the thickener with minimal turbulence and uniform
distribution while dissipating most kinetic energy.
• Entry Mechanisms: Feed slurry enters feedwell through pipe or launder suspended from bridge.
Open launder typically has slope no greater than 1 to 2 percent to prevent excess velocity and
sanding at inlet. Nonsanding pulps may enter upward through center column from pipeline
beneath tank.
• Design Considerations: Standard feedwell designed for maximum vertical outlet velocity of about
1.5 m/min (5 ft/min). High turbidity due to short-circuiting feed to overflow can be reduced by
increasing feedwell depth. Deep feedwells of large diameter used for important overflow clarity or
when solids specific gravity is close to liquid specific gravity. Shallow feedwells used when
overflow clarity not critical, overflow rate low, or solids density significantly greater than water.
• Flocculation Considerations: Optimum feed solids concentration for flocculation may be less
than normal concentration when flocculants used, leading to significant reagent cost savings
through dilution of feed prior to flocculation. Feedwell designs allowing for internal feed dilution to
achieve this. One design utilizes energy from incoming feed stream for dilution through momentum
transfer, requiring no additional energy expenditure and achieving up to three to four times dilution.

Overflow arrangement

• Overflow Arrangements: Clarified effluent removed in peripheral launder inside or outside tank.
Effluent enters launder by overflowing V-notch or level flat weir, or through submerged orifices in
bottom of launder.
• Control of Overflow Rates: Submerged orifices or V-notch weirs used to control uneven overflow
rates caused by wind blowing across liquid surface in large thickeners. Radial launders used for
uniform upward liquid flow to improve clarifier detention efficiency and reduce effect of wind.
• Hydraulic Capacity: Launder capacity must prevent flooding, which can cause short-circuiting of
feed and deterioration of overflow clarity. Industrial clarifiers may have higher overflow rates based
on application and desired clarity.
• Alternative Configurations: Various launder configurations to achieve desired overflow rate,
including annular launder inside tank, radial launders connected to peripheral launder, and
Stamford baffles below launder to direct flow currents back toward center of clarifier.
• Partial Perimeter Launder: In many thickener applications, complete peripheral launders not
required. No difference in overflow clarity or underflow concentration with launders extending over
fraction (e.g., one-fifth) of perimeter. Weir-loading rate in range of 7.5 to 30.0 m³/(h ⋅ m) [10 to 40
gpm/ft] used for design, higher values for well-flocculated, rapidly settling slurries. Overflow
launder may occupy single section of perimeter rather than multiple shorter segments spaced
uniformly around tank.

Underflow arrangement

• Underflow Arrangements: Concentrated solids removed from thickener by centrifugal or positive

displacement pumps, or by gravity discharge through flow control valve or orifice suitable for slurry
applications.
• Risk Mitigation: Duplicate underflow pipes and pumps recommended in all thickening
applications to mitigate risk of plugged underflow pipe. Provision for recycling underflow slurry
back to feedwell or near tank wall and floor intersection (tank knuckle) useful for temporary storage
if capacity and torque allow. Pumps used under thickener to recirculate high-yield-stress
thickened underflow back into discharge cone, cylinder, or external mixing vessel to reduce yield
stress before pumping to next stage.
 • Basic Underflow Arrangements:
o Underflow pump adjacent to thickener sidewall with buried piping from discharge cone.
o Underflow pump under thickener at discharge cone or adjacent to sidewall with piping in
tunnel.
o Underflow pump located in center of thickener on bridge or using piping through center
column.
• Pump Adjacent to Thickener: Least expensive but most susceptible to plugging. Used when solids
don't compact to unpumpable slurry and can be easily backflushed if plugging occurs. Typically,
two or more underflow pipes installed for continued solids removal if one line plugs. Valves
installed for flushing with water and compressed air.
• Tunnel Construction: Provides access to discharge cone when underflow slurries are difficult to
pump and prone to plugging. Underflow pump may be installed under thickener or at perimeter.
More expensive but offers operational and maintenance advantages. Safety hazards and
regulations related to working in tunnel must be considered.
• Center-Column Pumping Arrangement: Bridge-mounted pump with suction line through wet or
dry center column. Another design has pump located in room under thickener mechanism and
connected to openings in column. Access through drive gear at top of column. Requires attention
to priming, net positive suction head, and maximum density pump can handle.

INSTRUMENTATION

• Torque: Indicates force necessary to rotate rakes. Higher torque indicates higher underflow
density or viscosity, deeper mud bed, higher fraction of coarse material, island formation, or heavy
scale buildup on rake arms.
• Rake Height: Lifting devices minimize torque on arms by lifting them out of heavy bed solids and
enable rake to continue running during upset conditions. Rake drives should not run for extended
periods at torques above 50 to 60 percent to prevent accelerated wear. Ultrasonic and
potentiometer types with reeling cable are common rake height indicators.
• Bed Level Detection:
o Ultrasonic: Sends pulse from just under overflow surface, calculates distance based on
elapsed time. Relatively low cost but may not work on all applications, susceptible to
interference from cloudy overflow or scaling.
o Nuclear: Sensing background radiation level or attenuation between source and detector.
Reliable when properly applied but measures over limited range, relatively expensive.
o Float and Rod Types: Ball with hollow sleeve slides on rod extending into bed. Subject to
fouling and sticking, installed and measured only above rakes, relatively inexpensive.
o Reeling Devices: Drops sensor down on cable, senses bed level by optical, conductivity, or
point ultrasonic sensors. May become entangled with rakes, midrange to high-end price.
o Vibrating or Tuning Fork Sensors: Sense difference in vibrating frequency in different
masses of solids.
o Bubble Tube or Differential Pressure: Measures bed level by detecting pressure
difference.
o External Density Through Sample Ports: Takes slurry samples from nozzles on tank side,
passes through density meter to determine solids presence. Requires external piping and
disposal of sample stream.
• Bed Pressure: Indicates overall specific gravity in tank, converted to rough solids inventory. Useful
for thickener control, relatively low cost and highly reliable.
• Flow Rate: Essential for newer generation thickeners. Usually measured by magnetic flowmeters
or Doppler-type flowmeters. Open launder flow measurement is more difficult but can be done
using ultrasonic devices.
 • Density: Nuclear gauges or low-level sources for density measurement. Require handling permits,
subject to drifting, and should be recalibrated regularly.
• Settling Rate: Indicates degree of flocculation, used to maintain consistent flocculation over
varying feed conditions. Settleometer automatically pulls sample from feedwell and measures
settling rate.
• Overflow Turbidity: Used as feedback to control flocculant or coagulant. Generally used as alarms
or for trim only due to lag time between flocculation process and sensor position at overflow
discharge point.

(ppt)

II. Batch Sedimentation

• There are several stages in the settling of a flocculated suspension and
different zones are formed as sedimentation proceeds
• Usually the concentration of solids is high enough that sedimentation of
individual particles or flocs is hindered by other solids to such an extent that
all solids at a given level at a common velocity

Figure 5.1. Sedimentation of concentrated

suspensions (a) Type 1 settling (b) Type 2 settling

Where:

• Zo = initial bed height

• Zc = critical bed height
• Z = bed height at any settling time
• 𝑍∞ = final bed height

• Particle Settling – particles are at low concentration or free settling

𝑍𝑐 − 𝑍𝑜
𝑢𝑡 = −
𝑡𝑐
• Zone Settling – particles settles as a mass, settling rate is a function of the solid concentration
𝑑𝑍 𝑍− 𝑍∞
=-K (Z - 𝑍∞ ) −𝐾(𝑡 − 𝑡𝑐 ) = ln( )
𝑑𝑡 𝑍𝑐 −𝑍∞
• Compression Settling – particles are restrained by hydrodynamic forces, settling rate is a function
of both concentrations and solids depth.
• Sedimentation time for a Commercial Tank given Batch Data
𝑡𝐿𝑇 𝑡𝐶𝑇
=
𝑍𝑜 𝐻𝑜
Where:

o tLT = time in the laboratory test to reach height Z

o Z0 = initial bed height in the laboratory test
o tCT = time in the commercial tank to reach height H
o H0 = initial bed height in the commercial tank
 Figure 5.24. Settling behaviour of a mixture consisting of equal volumes of polystyrene and ballotini
at a volumetric concentration exceeding 15 percent

• (a) Solid is uniformly distributed in the liquid.

The total depth of the suspension is Z0.
• (b) Solids have settled to a give a zone of
clear liquid, zone A and a zone D of settled
solids. Above zone D is a transition layer, zone
C, in which the solids content varies from that
in the original pulp to that in zone D. In zone B,
the concentration is uniform and equal to the
original concentration, since the settling rate is
the same throughout the zone. The boundaries
between zones D and C and between C and B
may not be distinct, bu the boundary between zones A and B is usually sharp
• (c) Depths of zones D and A increase. The depth of zone C remains nearly constant, and that of
zone B decreases.
• (d) Zone B disappears and all the solids are in zones C and D.
• Gradual accumulation of solids puts stress on the material at the bottom which compresses solids
in layer D.
• (e) Weight of the solid is balanced by the compressive strength of the flocs. Settling process stops.

III. Types of Sedimentation Equipment

Clarifier

• To produce a relatively clear overflow; they are generally employed with dilute suspensions,
principally industrial process streams and domestic municipal wastes. They are basically identical
to thickeners in design and layout except that they use a mechanism of lighter construction and a
drive head with a lower torque capability.

Thickener

• To concentrate suspended solids by gravity settling so that a steady-state material balance is

achieved: solids being withdrawn continuously in the underflow at the rate they are supplied in the
feed
 IV. Thickener Design
• A. Coe and Clevenger
𝐿0 𝐶0
𝐴=
𝐹𝐿
Where:

o A = minimum area required

o L0 = feed volumetric flow rate
o C0 = feed concentration
o FL = limiting solid flux

• B. Talmadge and Fitch

𝐿0 𝜃𝑢
𝐴=
𝑍0
Can determine the time when the critical concentration is reached (graphical)
Where
o 𝜃 = time to reach the desired underflow concentration

• Steps for Talmadge & Fitch Approach

o 1. Plot height vs time – settling curve.
o 2. Create a line through points where the height varies linearly with time.
o 3. Construct a line through points where the height is constant.
o 4. Draw an angle bisector at the point of intersection. Intersection of the angle bisector and
the settling curve is the critical settling point.
o 5. Draw a tangent line through the settling point.
o 6. Draw the line of Zu >> C0Z0 = CuZu
𝐿0 𝜃𝑢
o 7. Solve for the area >> 𝐴 =
𝑍0

V. Sample Problems
a. (Batch sedimentation) Laboratory testing prior design of a large suspension tank was done through
suspension of a defined solid in a liquid medium. The original height of the sludge prior settling was
found to be 10 inches. The height of the sludge at the end of the free settling period was found to be
6.5 inches, concluding a 0.10 in/min settling rate. After 2 hours, the height of the sludge was found
to be 4 inches and after having left for a couple more hours, the height of the sludge was 1,5 inches.
Calculate the constant, K, in zone settling. (8.15x10-3/min)
b. (HW, Due Mar 19, 2024) Consider a secondary classifier design at peak flow that accepts effluent
from secondary treatment at a rate of 120 m3/day containing 4500 mg/L solids. Target underflow
concentration is 32 g/L. Calculate the required settling area (m2) if the time ti reach the underflow
concentration?
Time, hr 0 1 2 3 4 5 6
Interface height, in 30 14 8 5.1 4.5 4.4 4.4

Quiz #3: Particle in Motion and Sedimentation (March 19, 2024)

CENTRIFUGATION