1. Mixing and Flocculation
CE 547
Mixing and Flocculation

2. 1. Mixing
Is a unit operation that distributes the components of two or more materials among the materials producing in the end a single blend of the components. Mixing is accomplished through agitation.
Type of mixers:
rotational (rotational elements)
pneumatic (gas or air bubbles)
hydraulic (flowing of water)
2. Flocculation
Is a unit operation aimed at enlarging small particles through a very slow agitation. Flocculation is accomplished through the use of large paddles.

5. Mixing

6. A. Rotational Mixers
Impellers are used in rotation mixing. Types of impellers are (Fig 6.2):
a. propellers
standard three-blade
guarded
weedless
b. Paddles
flat paddle
c. Turbines
straight blade
curved blade
vaned-disk
shrouded blade

8. Flow Pattern in Rotational Mixers (Fig 6.3)
fluid is thrown towards the wall
fluid is deflected up and down
flow returns back to the blades (circulation rate)
Prevention of Swirling Flow (Fig 6.4)
putting the agitator eccentric to the vessel
using a side entrance to the vessel
putting baffles along the vessel wall

11. Power Dissipation in Rotational Mixers
P = function of (N, Da, g, , )
P = power dissipated
N = rotational speed
Da = diameter of impeller
g = acceleration due to gravity
 = absolute viscosity
 = mass density

12. If Re  10
At high Re
KL and KT are constants (Power coefficients)

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

14. Example 6.1

16. B. Criteria for Effective Mixing
G = average velocity gradient in the tank
V = volume of tank
P = power dissipated
 = absolute viscosity

17. 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

18. C. Pneumatic Mixers
This is accomplished using diffused aerators (Fig 6.7)
porous ceramic tube
coarse bubble
open pipe
perforated pipe
fine bubble
saran wrapped tube
diffused aeration schematic

20. Pneumatic mixing power = function (number of bubbles formed)
Pi = input pressure to the unit
Qi = input flow to the unit
Pa = atmospheric pressure
b = average rise velocity of bubbles
h = depth of submergence of air diffuser
Vb0 = average volume of bubble at surface

21. b is described in terms of three dimensionless quantities, G1, G2 and Re
G1 = Peebles number
G2 = Garber number
 = surface tension of fluid
r = average radius of bubbles

23. Power Dissipation in Pneumatic Mixers
Qi = input flow to the unit (air)
l = specific weight of water

24. Example 6.2

26. D. Hydraulic Mixers
This is accomplished by the use of energy of a flowing fluid to create the power dissipation required for mixing. Types of hydraulic mixers include:
hydraulic jump mixer
weir mixer

29. Power Dissipation in Hydraulic Mixers
hf = fluid friction loss
Q = flow rate
 = specific weight

30. For hydraulic jump (Fig 6.9)
q = flow per unit width of the channel

31. Using the momentum equation
Solving for y1 and y2, then

33. Examples 6.3 and 6.4

36. For weirs (Fig 6.10)
H = head over the weir crest
HD = drop provided from weir crest to surface of the water below
Then

37. Examples 6.5 and 6.6

40. Flocculators

41. Critical size depends on:
Agitation in flocculation involves gentle motion of the fluid to induce agglomeration of smaller particles into larger flocs
Small flocs build into larger sizes until a point reached where the size can not go on increasing (critical size)
Critical size depends on:
Detention time (larger detention time produce larger critical sizes)
Velocity gradient (larger velocity gradients produce smaller critical sizes)
Critical values for effective flocculation are expressed in terms of:
Gt0 and G

42. 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
80,000 – 190,000

44. Compartments vary in size (from smaller to larger)
G decreases instead
As flow gets larger, rotation of paddle must be made slower to avoid breaking up the flocs
The number of blades decrease also as water moves from compartment to another
If FD is drag by water on the blade and FD is also the push of the blade upon the water
Due to that, water will move at a velocity p equal to the velocity of blade
Since paddle is rotating, (p) is a tangential velocity

45. rp = radial distance to rotational axis
 = angular rotation (radians / time)
CD = drag coefficient
Ap = projected area of blade in the direction of its motion
l = mass density of water

46. Total power = sum of powers in each blade
Apt = sum of projected area of blade
pt = blade tip velocity

47. Due to location of blades, there will be several p’s
To use one velocity, pt, is used multiplied by a factor (a), [ a = 0.75 ]
G and Gt0 are to be checked to see if the flocculator performs at conditions of effective flocculation
Paddle tip velocity should be less than 1.0 m/sec
CD is a function (Re)
p = blade velocity
 = kinematic viscosity

48. For one single blade at Re = 105
CD = for multiple blades must be determined

49. Example 6.7