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Mixing and Flocculation CE 547

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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) rotational (rotational elements) pneumatic (gas or air bubbles) pneumatic (gas or air bubbles) hydraulic (flowing of water) 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.

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Mixing

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

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

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

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If Re 10 At high Re K L and K T are constants (Power coefficients)

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D t = Diameter of Vessel; W = Width of Paddle; J= Width of baffle

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Example 6.1

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

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G Criteria Values for Effective Mixing t 0 (seconds) G (s -1 ) < – – – – – – – – – 700 t 0 = detention time of the tank

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

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Pneumatic mixing power = function (number of bubbles formed) n = number of bubbles P i = input pressure to the unit Q i = input flow to the unit P a = atmospheric pressure b = average rise velocity of bubbles h = depth of submergence of air diffuser V b0 = average volume of bubble at surface

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b is described in terms of three dimensionless quantities, G 1, G 2 and Re G 1 = Peebles number G 2 = Garber number = surface tension of fluid r = average radius of bubbles

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Power Dissipation in Pneumatic Mixers Q i = input flow to the unit (air) l = specific weight of water

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Example 6.2

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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 hydraulic jump mixer weir mixer weir mixer

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Power Dissipation in Hydraulic Mixers h f = fluid friction loss Q = flow rate = specific weight

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

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Using the momentum equation Solving for y 1 and y 2, then

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Examples 6.3 and 6.4

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

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Examples 6.5 and 6.6

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Flocculators

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Agitation in flocculation involves gentle motion of the fluid to induce agglomeration of smaller particles into larger flocs 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) Small flocs build into larger sizes until a point reached where the size can not go on increasing (critical size) Critical size depends on: Critical size depends on: Detention time (larger detention time produce larger critical sizes) Detention time (larger detention time produce larger critical sizes) Velocity gradient (larger velocity gradients produce smaller critical sizes) Velocity gradient (larger velocity gradients produce smaller critical sizes) Critical values for effective flocculation are expressed in terms of: Critical values for effective flocculation are expressed in terms of: Gt 0 and Gt 0 and G G

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Critical Values for Effective Flocculation Type of Raw Water G (s -1 ) Gt 0 (dimensionless) Low turbidity and colored 20 – 7050,000 – 250,000 High turbidity ,000 – 190,000

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

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r p = radial distance to rotational axis = angular rotation (radians / time) C D = drag coefficient A p = projected area of blade in the direction of its motion l = mass density of water

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Total power = sum of powers in each blade A pt = sum of projected area of blade pt = blade tip velocity pt = blade tip velocity

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Due to location of blades, there will be several p ’s 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 ] To use one velocity, pt, is used multiplied by a factor (a), [ a = 0.75 ] G and Gt 0 are to be checked to see if the flocculator performs at conditions of effective flocculation G and Gt 0 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 Paddle tip velocity should be less than 1.0 m/sec C D is a function (Re) C D is a function (Re) p = blade velocity p = blade velocity = kinematic viscosity = kinematic viscosity

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For one single blade at Re = 10 5 C D = for multiple blades must be determined

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Example 6.7

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