Ch6 Sedimentation

8/13/2019 Ch6 Sedimentation

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Sedimentation


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Outline IntroductionObjective & ApplicationTheory for sedimentation

Gravitation forceBuoyant forceDrag force

Drag coefficientTerminal velocity of particle for sedimentationTerminal velocity of particle for hindered settling


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Introduction

Sedimentation describes the motion ofmolecules in solutions or particles insuspensions in response to an externalforce such as gravity, centrifugal force orelectric force.The separation of a dilute slurry orsuspension by gravity settling into a clearfluid and s slurry of higher solids content iscalled sedimentation.


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Objective & Application

The pu rpos e is to remove the particles from thefluid stream so that the fluid is free of particlecontaminants.Ap pl icat ions o f sed imentat ion include removalof solids from liquid sewage wastes, settling ofcrystals from the mother liquor, separation ofliquid-liquid mixture from a solvent-extraction

stage in settler, water treatment, separation offlocculated particles, lime-soda softening iron andmanganese removal, wastewater treatment,solids/sludge/residuals.


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Theory for sedimentationWhenever a particle is moving through a fluid, anumber of forces will be acting on the particle.First, a density difference is needed between theparticle and the fluid.

If the densities of the fluid and particle are equal,the buoyant force on the particle willcounterbalance the external force and the particlewill not move relative to the fluid.

There are three forces acting on the body:- Gravity Force- Buoyant Force- Drag Force


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Mechanics of particle motion

in fluids

To describe, two properties need:Drag coefficientTerminal velocity


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Drag Coefficient

For particle movement influids, drag force is aresistance to its motion.Drag coefficient is acoefficient related to dragforce.

Overall resistance offluids act to particle canbe described in term ofdrag force using dragcoefficient.


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Comparing with fluid flow in pipe principle, dragcoefficient is similar to friction coefficient or frictionfactor (f).

f lowof volumeunit energykinetic stress shear f

2

2

21

21

)/(

Av f F

V mv

A F f


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For drag coefficient:

f lowof volumeunit energykinetic

area per forcedrag C D

2

2

21

21

)/(

AvC F

V

mv

A F C

D

D


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Frictional drag coefficient For flat plate with a laminar boundary layer:

For flat plate with a turbulent boundary layer

5.0

328.1

R D N C

58.2log455.0

R D N C

sphereof diameter plateof length D

Dv N R


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Frictional drag coefficient For flat plate with a transition region:

R R D N N C 1700)(log 455.0 58.2

sphereof diameter plateof length D

Dv N R


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If a plate or circular disk is placed normalto the flow, the total drag will contain

negligible frictional drag and does notchange with Reynolds number (N R)


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Sphere object

At very low Reynolds number (


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Terminal or Settling Velocity

Settling velocity (v t ): the terminal velocity at which a particles falls through a fluid.

When a particle is dropped into a column of fluid itimmediately accelerates to some velocity andcontinues falling through the fluid at that velocity

(often termed the terminal settling velocity ).


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The speed of the terminal settling velocity of a particledepends on properties of both the fluid and the particle:

Properties of the particle include:

The size if the particle (d).

The shape of the particle.

The density of the material making up the particle ( p).


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FG, the force of gravity acting to

make the particle settle downwardthrough the fluid.

FB, the buoyant force which opposes

the gravity force, acting upwards.

FD, the drag force or viscousforce, the fluids resistance to the

particles passage through the fluid;also acting upwards.


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Particle Settling Velocity

Put particle in a still fluid what happens?

Speed at which particle settles depends on:

particle properties: D, p, shape

fluid properties: f , , Re

Fg

Fd

FB


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STOKES Settling Velocity

Assumes: spherical particle (diameter = d P)

laminar settling

FG depends on the volume and density ( P) of the particleand is given by:

FB is equal to the weight of fluid that is displaced by the

particle:

Where f is the density of the fluid.

33

66 P P P P G gd g d F

33

66 P f f P B gd g d F


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FD is known experimentally to vary with the size of the

particle, the viscosity of the fluid and the speed at which the particle is traveling through the fluid.

Viscosity is a measure of the fluids resistance to

deformation as the particle passes through it.

vd v AC F P P f D D 321 2

Where (the lower case Greek letter mu) is the fluidsdynamic viscosity and v is the velocity of the particle; 3 d is proportional to the area of the particles surface over whichviscous resistance acts.

R D N

C 24


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From basic equation, F = mg = resultant force:

With v = terminal velocity or v t:

D BG F F F dt dv

mma F

0

dt

dvm F F F D BG


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In the case of 0.0001


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In the case of 0.2


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Laminar (Stokes) vs. Turbulent (Gibbs) settling

Comparison of Stokes and Gibbs

0

50

100

150

0 0.05 0.1 0.15

Diameter, cm

S e t

t l i n g

V e l o c

i t y , c

m / s

Stokes

Gibbs


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Stokes Law has several limitations:

i) It applies well only to perfect spheres.

The drag force (3 d vt) is derived experimentally only forspheres.

Non-spherical particles will experience a different distributionof viscous drag.

ii) It applies only to still water.

Settling through turbulent waters will alter the rate at which

a particle settles; upward-directed turbulence will decreasevt whereas downward-directed turbulence will increase vt.


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Coarser particles, with larger settling velocities,experience different forms of drag forces.

iii) It applies to particles 0.1 mm or finer.

Stokes Law overestimatesthe settling velocity ofquartz density particleslarger than 0.1 mm.

When settling velocity is low When settling velocity is high


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When settling velocity is low (d0.1mm) flow separatesfrom the sphere and a wake ofeddies develops in its lee.

Pressure forces acting on thesphere vary.

Negative pressure in thelee retards the passageof the particle, adding anew resisting force.

Stokes Law neglectsresistance due to

pressure.


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iv) Settling velocity istemperature dependant

because fluid viscosity anddensity vary with

temperature.

Temp. vt C Ns/m 2 Kg/m 3 mm/s

0 1.792 10 -3 999.9 5

100 2.84 10 -4 958.4 30


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EXAMPLE

Settling velocity of dust particles

Calculate the settling velocity of dust particles of60 m diameter in air at 21 C and 100 kPapressure. Assume that the particles are sphericaland density = 1280 kg m -3 , and that the viscosityof air = 1.8 x 10 -5 N s m -2 and density of air = 1.2

kg m-3

.


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For 60 m particle:

v = (60 x 10

-6

)2

x 9.81 x (1280 - 1.2)(18 x 1.8 x 10 -5)

= 0.14 m s -1

Checking the Reynolds number for the 60 m particles,

Re = ( v bD / )

= (60 x 10 -6 x 0.14 x 1.2) / (1.8 x 10 -5)

= 0.56

18

)(2 p pt

gD


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HINDERED SETTLINGDefinition:If the settling is carried out with high concentrations of solids to liquidso that the particles are so close together that collision between theparticles is practically continuous and the relative fall of particlesinvolves repeated pushing apart of the lighter by the heavier particles

it is called hindered settling.

particles interferewith each other

Hi d d S ttli


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Hindered Settling particle interactions change settling velocity

discrete particles

flocculating particles

higher solids concentration reducesvelocity

experiments only


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Hindered Settling

)(18

)( 22 p

p pt

gD

= void fraction

p= empirical correlation fraction

=

)1(82.1101


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Zone Settling & Compression

Zone Settling


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Zone Settling

Cu = C o h o h

u

Cu

C o

C oho = C ch c = C u hu

tu t i

h c

h u

C c


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Compression - Compaction

C c

Cu


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Zone Settling

Vs = h o h u = ho h itu - to ti

Settling Velocity

Co


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ZSV = f (C) solid flux theory

- limiting flux of solids through a settling tank


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water treatment

wastewater treatment

solids/sludge/residuals management

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Ch6 Sedimentation

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