Mixing and Mixing and FlocculationFlocculation

CE 547CE 547

1. Mixing1. MixingIs a unit operation that distributes the Is a unit operation that distributes the components of two or more materials among components of two or more materials among the materials producing in the end a single the materials producing in the end a single blend of the components. Mixing is blend of the components. Mixing is accomplished through agitation.accomplished through agitation.

Type of mixers:Type of mixers: rotational (rotational elements)rotational (rotational elements) pneumatic (gas or air bubbles)pneumatic (gas or air bubbles) hydraulic (flowing of water)hydraulic (flowing of water)

2. Flocculation2. FlocculationIs a unit operation aimed at enlarging small Is a unit operation aimed at enlarging small particles through a very slow agitation. particles through a very slow agitation. Flocculation is accomplished through the use Flocculation is accomplished through the use of large paddles.of large paddles.

MixingMixing

A. Rotational MixersA. Rotational MixersImpellers are used in rotation mixing. Types of Impellers are used in rotation mixing. Types of impellers are (impellers are (Fig 6.2Fig 6.2):):a. propellersa. propellers

standard three-bladestandard three-blade guardedguarded weedlessweedless

b. Paddlesb. Paddles flat paddleflat paddle

c. Turbinesc. Turbines straight bladestraight blade curved bladecurved blade vaned-diskvaned-disk shrouded bladeshrouded blade

Flow Pattern in Rotational Mixers Flow Pattern in Rotational Mixers (Fig 6.3)(Fig 6.3)

fluid is thrown towards the wallfluid is thrown towards the wall fluid is deflected up and downfluid is deflected up and down flow returns back to the blades flow returns back to the blades

(circulation rate)(circulation rate)

Prevention of Swirling Flow (Fig 6.4)Prevention of Swirling Flow (Fig 6.4) putting the agitator eccentric to the putting the agitator eccentric to the

vesselvessel using a side entrance to the vesselusing a side entrance to the vessel putting baffles along the vessel wallputting baffles along the vessel wall

Power Dissipation in Power Dissipation in Rotational MixersRotational Mixers

P = function of (N, DP = function of (N, Daa, g, , g, , , ))

P = power dissipatedP = power dissipated

N = rotational speedN = rotational speed

DDaa = diameter of impeller = diameter of impeller

g = acceleration due to gravityg = acceleration due to gravity

= absolute viscosity= absolute viscosity

= mass density= mass density

If Re If Re 10 10

At high ReAt high Re

KKLL and K and KTT are constants (Power are constants (Power coefficients)coefficients)

a

aL

ND

DNKP

Re

32

53aT DNKP

Dt = Diameter of Vessel; W = Width of Paddle; J= Width of baffle

Example 6.1Example 6.1

B. Criteria for Effective B. Criteria for Effective MixingMixing

G = average velocity gradient in the tankG = average velocity gradient in the tank

V = volume of tankV = volume of tank

P = power dissipatedP = power dissipated

= absolute viscosity= absolute viscosity

V

PG

G Criteria Values for Effective Mixing

t0 (seconds) G (s-1)

< 10 4000 – 1500

10 – 20 1500 – 950

20 – 30 950 – 850

30 – 40 850 – 750

40 – 130 750 – 700

t0 = detention time of the tank

C. Pneumatic MixersC. Pneumatic Mixers

This is accomplished using diffused This is accomplished using diffused aerators (aerators (Fig 6.7Fig 6.7))

porous ceramic tubeporous ceramic tube coarse bubblecoarse bubble open pipeopen pipe perforated pipeperforated pipe fine bubblefine bubble saran wrapped tubesaran wrapped tube diffused aeration schematicdiffused aeration schematic

Pneumatic mixing power = function Pneumatic mixing power = function (number of bubbles formed)(number of bubbles formed)

n = number of bubblesn = number of bubblesPPii = input pressure to the unit = input pressure to the unitQQii = input flow to the unit = input flow to the unitPPaa = atmospheric pressure = atmospheric pressurebb = average rise velocity of bubbles = average rise velocity of bubblesh = depth of submergence of air diffuserh = depth of submergence of air diffuserVVb0b0 = average volume of bubble at surface = average volume of bubble at surface

bba

ii

VP

hQPn

0

b is described in terms b is described in terms of three dimensionless of three dimensionless quantities, Gquantities, G11, G, G22 and Re and Re

GG11 = Peebles number = Peebles number

GG22 = Garber number = Garber number

= surface tension of = surface tension of fluidfluid

r = average radius of r = average radius of bubblesbubbles

rP

PrgG

P

gG

bi

ib

i

2Re

3

344

2

3

4

1

225.0

1

25.0

25.01

214.21

50.0

214.21

28.152.0

75.0

Re10.353.1

10.3Re02.435.1

02.4Re233.0

2Re9

2

GGP

g

GGrP

GrP

g

Pr

ib

ib

ib

ib

Power Dissipation in Power Dissipation in Pneumatic MixersPneumatic Mixers

QQii = input flow to the unit (air) = input flow to the unit (air)

l l = specific weight of water= specific weight of water

a

laii P

hPQPP

ln

Example 6.2Example 6.2

D. Hydraulic MixersD. Hydraulic Mixers

This is accomplished by the use of This is accomplished by the use of energy of a flowing fluid to create the energy of a flowing fluid to create the power dissipation required for mixing. power dissipation required for mixing. Types of hydraulic mixers include: Types of hydraulic mixers include:

hydraulic jump mixerhydraulic jump mixer weir mixerweir mixer

Power Dissipation in Hydraulic Power Dissipation in Hydraulic MixersMixers

hhff = fluid friction loss = fluid friction loss

Q = flow rateQ = flow rate

= specific weight= specific weight

fhQP

For hydraulic jump (Fig 6.9)For hydraulic jump (Fig 6.9)

q = flow per unit width of the channelq = flow per unit width of the channel

22

21

22

2112

212

2

22

1

21

2

2

22

ygy

ygyyyqyyh

yg

Vhy

g

V

f

f

Using the momentum equationUsing the momentum equation

Solving for ySolving for y1 1 and yand y22, then, then

dAndvt

FAcv

.

212

0

212

2

210

21

22

21

22

2112

2

12

1

211

2

3

3

6

2

12

1

2

2

1812

yyQ

Wyt

yyWyV

yL

LWyyQQ

Vt

LWyyV

ygy

ygyyyW

QyyQ

P

gy

yy

jump

jump

jump

jumphydraulic

Examples 6.3 and Examples 6.3 and 6.46.4

For weirs (For weirs (Fig 6.10Fig 6.10))

H = head over the weir crestH = head over the weir crest

HHDD = drop provided from weir crest to = drop provided from weir crest to surface of the water belowsurface of the water below

ThenThen

Df HHh

Df HHQhQP

Examples 6.5 and Examples 6.5 and 6.66.6

FlocculatorsFlocculators

Agitation in flocculation involves gentle Agitation in flocculation involves gentle motion of the fluid to induce agglomeration motion of the fluid to induce agglomeration of smaller particles into larger flocsof smaller particles into larger flocs

Small flocs build into larger sizes until a Small flocs build into larger sizes until a point reached where the size can not go on point reached where the size can not go on increasing (critical size)increasing (critical size)

Critical size depends on:Critical size depends on: Detention time (larger detention time produce Detention time (larger detention time produce

larger critical sizes)larger critical sizes) Velocity gradient (larger velocity gradients Velocity gradient (larger velocity gradients

produce smaller critical sizes)produce smaller critical sizes) Critical values for effective flocculation are Critical values for effective flocculation are

expressed in terms of:expressed in terms of: GtGt00 and and GG

Critical Values for Effective Flocculation

Type of Raw Water G (s-1) Gt0 (dimensionless)

Low turbidity and colored

20 – 70 50,000 – 250,000

High turbidity 70 - 150 80,000 – 190,000

Compartments vary in size Compartments vary in size (from smaller to larger)(from smaller to larger)

G decreases insteadG decreases instead As flow gets larger, rotation As flow gets larger, rotation

of paddle must be made of paddle must be made slower to avoid breaking up slower to avoid breaking up the flocsthe flocs

The number of blades The number of blades decrease also as water decrease also as water moves from compartment to moves from compartment to anotheranother

If FIf FDD is drag by water on the is drag by water on the blade and Fblade and FDD is also the push is also the push of the blade upon the waterof the blade upon the water

Due to that, water will move Due to that, water will move at a velocity at a velocity pp equal to the equal to the velocity of bladevelocity of blade

Since paddle is rotating, (Since paddle is rotating, (pp) ) is a tangential velocityis a tangential velocity

rrpp = radial distance to rotational axis = radial distance to rotational axis = angular rotation (radians / time)= angular rotation (radians / time)

CCDD = drag coefficient = drag coefficient

AApp = projected area of blade in the direction of = projected area of blade in the direction of its motionits motion

ll = mass density of water = mass density of water

pp r

2

2plpD

D

ACF

Total power = sum of powers in each bladeTotal power = sum of powers in each blade

AAptpt = sum of projected area of blade = sum of projected area of blade

ptpt = blade tip velocity = blade tip velocity

22

32pi

pDppi

pDblade ACACP

22

33pti

ptDpi

pDblade

aACACPP

Due to location of blades, there will be several Due to location of blades, there will be several pp’s’s

To use one velocity, To use one velocity, ptpt, is used multiplied by a , is used multiplied by a factor (a), [ a = 0.75 ]factor (a), [ a = 0.75 ]

G and G and GtGt00 are to be checked to see if the are to be checked to see if the flocculator performs at conditions of effective flocculator performs at conditions of effective flocculationflocculation

Paddle tip velocity should be less than 1.0 m/secPaddle tip velocity should be less than 1.0 m/sec CCDD is a function (Re) is a function (Re)

pp = blade velocity = blade velocity = kinematic viscosity= kinematic viscosity

pD

Re

For one single blade at Re = 10For one single blade at Re = 1055

CCDD = for multiple blades must be = for multiple blades must be determineddetermined

13.1008.0 D

bCD

Example 6.7Example 6.7