Lecture 4 - Motion of Particles in a Fluid and Sedimentation

STREAMLINE or LAMINAR FLOW

slow fluid flow

TURBULENT FLOW.

in fast motion, fluid particles cross

and re-cross the streamline and the motion

non-viscous fluid

the velocity and direction

of flow vary around the cylinder’s circumference,

resulting in pressure variations. However, no net force

is exerted on the cylinder due to the absence of

viscosity.

viscous fluid

the boundary layer forms near

the surface, and its thickness varies with the pressure

gradient.

Stokes' law

describes the drag force on the particle, which is composed

of skin friction and form drag.

Intermediate Region

( 0. 2 < Re < 500 − 1000), the drag coefficient deviates from Stokes' Law

and various empirical equations have been proposed to

approximate the relationship.

Newton's Law

At higher Reynolds numbers (500 − 1000 < Re < 2 × 10⁵ ), the drag force becomes approximately constant,

independent of the velocity.

Turbulent Flow

When Re' exceeds 2 × 10⁵

Dynamics of Single Particles

1. The particle is spherical of diameter DP.

2. The particle is non-porous and incompressible. The

particle is thus insoluble in the fluid and chemically inert

with it.

3. The density and viscosity of the fluid is constant.

4. The effect of surface characteristics of solid on the

dynamics of the particle is negligible.

5. The particle is freely settling under gravity.

6. The fluid forms an infinite medium.

Dynamics of Single Particles

1. The particle is spherical of diameter DP.

2. The particle is non-porous and incompressible. The

particle is thus insoluble in the fluid and chemically inert

with it.

3. The density and viscosity of the fluid is constant.

4. The effect of surface characteristics of solid on the

dynamics of the particle is negligible.

5. The particle is freely settling under gravity.

6. The fluid forms an infinite medium.

buoyancy force

As the particle moves down, it

displaces a volume of liquid equal to its own volume

and this displaced liquid moves up exerting an

upward force on the particle called _______,

which is thus equal to the weight of the displaced

liquid.

Frictional resistance:

It is offered by the liquid on the

particle due to the relative motion between the

particle and the liquid.

free settling

hindered settling

That the settling is not affected by the presence of

other particles in the fluid. This condition is known

as “_____”. When the interference of other

particles is appreciable, the process is known as

“_____”.

Sedimentation

is a unit operation used to separate a

suspension into a clear supernatant fluid and a dense

slurry with a higher concentration of solids.

Density Currents

Caused by the weight of solids, solids

concentration, and water temperature in the tank.

Eddy Currents

Produced by the flow of water entering and leaving

the tank.

Particle Size:

• Larger and denser particles, such as sand and silt, settle easily under

gravity.

• Smaller colloidal particles remain suspended and require

coagulation and flocculation with chemicals (e.g., iron salts,

aluminum sulfate) to settle.

Water Temperature:

• Lower temperatures slow down the settling rate.

• To compensate for slower settling, increase detention time and

adjust coagulant dosage.

Particle Size:

• Larger and denser particles, such as sand and silt, settle easily under

gravity.

• Smaller colloidal particles remain suspended and require

coagulation and flocculation with chemicals (e.g., iron salts,

aluminum sulfate) to settle.

Water Temperature:

• Lower temperatures slow down the settling rate.

• To compensate for slower settling, increase detention time and

adjust coagulant dosage.

Inlet Zone

Purpose:

➢ Distribute water and control velocity as it enters the basin.

➢ Prevent turbulence and short-circuiting, ensuring even flow

distribution.

• Flow Control:

➢ Water velocity over 0.15 m/s can break up floc, reducing

settling efficiency.

• Inlet Design:

➢ Rectangular Basin: Features a stilling wall (perforated baffle)

for even distribution.

Settling Zone

Purpose:

➢ Water enters the settling zone after passing through the inlet zone.

➢ The settling zone allows the bulk of settling to occur.

• Flow Control:

➢ Water velocity is greatly reduced in the settling zone.

➢ Requires a slow, even flow of water for optimal performance.

• Settling Zone Design:

➢ The settling zone occupies the largest

volume of the sedimentation basin.

➢ The settling zone may be a large area of

open water.

Sludge Zone

Purpose:

➢ The sludge zone is located at the bottom of the sedimentation basin, where

sludge is temporarily collected.

• Flow Control:

➢ Velocity in this zone should

be very slow to prevent resuspension

of sludge.

• Sludge Zone Design:

➢ A drain at the bottom of the basin allows for easy sludge removal.

➢ The tank bottom should slope toward the drains to facilitate sludge removal.

➢ Sludge removal can be continuous using automated equipment or manual in

some plants.

Outlet Zone

Purpose:

➢ Controls the amount of water flowing out of the sedimentation basin.

➢ Ensures only well-settled water leaves the basin and enters the filter.

➢ Prevents short-circuiting of water in the basin.

• Flow Control:

➢ Utilizes an overflow weir to control water level.

➢ Skims the best quality water from the very top of the basin.

• Sludge Zone Design:

➢ Begins with a baffle in front of the effluent to prevent floating material from

escaping and clogging filters.

➢ Effluent structure includes a launder, weirs, and effluent piping.

➢ Weirs attached to the launder sides skim water evenly off the tank.

weir

typically has notches, holes, or slits

along its length, allowing water to flow through. The

most common type is the V-shaped notch, which

allows only the top few centimeters of water to exit

the sedimentation basin. Alternatively, vertical slits

can provide more variation in operational water

levels.

Rectangular tanks

are a common choice for large-

scale water treatment plants due to their high tolerance to

shock overload, predictable performance, and cost-

effectiveness.

Their simple design leads to lower construction and

maintenance costs, while also minimizing short circuiting for

efficient treatment.

Circular and Square Basins

are more

susceptible to short circuiting and particle removal

issues. Effective sludge removal equipment is crucial

for square tank corners.

High-Rate Settlers

are essentially an upgrade for

rectangular clarifiers. They work by adding a series of tubes,

typically angled at 60 degrees, within the tank. This increases

the surface

Batch settling involves distinct zone formations:

1. Zone A

2. Zone B

3. Zone C

4. Critical Point

Batch settling involves distinct zone formations:

1. _____: A zone of clarified liquid just below the liquid mass surface.

2. _____: A suspension zone where free settling occurs. The interface between

zones A and B moves downward at the free settling velocity of the particles.

3. _____: A solid-rich zone forms at the bottom.

4. _____: The AB and BC interfaces meet, leaving only two zones.

K Design Criterion

a correlation to help determine

the range in which the motion of the particle lies.

Hindered Settling

It is an equation used for suspensions of uniformly

sized spherical particles to estimate the settling velocity of

the suspensions of fine particles.

Flocculation

is a crucial process in

sedimentation, significantly affecting the behavior of

fine particle suspensions. It involves the aggregation

of colloidal particles into larger clumps called flocs.

This aggregation is driven by attractive forces

between the particles, primarily van der Waals

forces.

DLVO (Derjaguin-Landau-Verwey-Overbeek)

describes the interaction forces between particles in

lyophobic colloids (sols), considering both repulsive (VR)

and attractive (VA) forces.

repulsive forces

attractive forces

_____ originate

from the interaction of the electrical double layers

surrounding the particles, while the a_____ are

due to van der Waals interactions.

coagulation,

Particle aggregation within this primary

minimum

perikinetic coagulation.

When these collisions are driven by

Brownian motion

orthokinetic coagulation.

collisions result from velocity gradients

in the fluid