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Agitation and mixing

Agitation vs. Mixing

Agitation – induced motion of a material in a specified way

– Usually a circulatory pattern inside a container

Mixing – random distribution, into and through one another, of two or more initially separate phases

– Various degrees of homogeneity

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IntroductionApplications(1) dispersion of solvable solid(2) homogenization of miscible liquids(3) mixing and dispersion of immiscible liquids(4) mixing between gas and liquid(5) suspension of solid particles in liquid(6) acceleration of chemical reaction and physical transport

Agitation methodsmechanical agitatorsgas agitationjet mixing static mixertubular mixing

Agitation EquipmentT-JunctionsStatic MixersTank or vessel

– Cylindrical in form with a vertical axis– Rounded or flatten tank bottom– Depth diameter

Impellers– Axial-flow – generate currents parallel with the axis of the

impeller shaft– Radial-flow – generate currents in a tangential or radial

direction– Propellers, paddles, and turbines

Motionless mixers

Injector mixer with a helical baffle

Flanged perforated plates

Hellical mixing elements with alternating directions (Kenics)

T-junction (similar flow rates)

Perforated plates (orifices) supported on a rod

Pitot tube (different flow rates)

Kenics Static mixers

Komax static mixer

Pump recirculated tank(homogenizer)

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A set of mixing equipment consists of: a mixing tanka driving motor withspeed reduceran agitatorsome attached parts.

Mechanically agitated mixing equipment

Agitator is the main part, like an impeller in a pump to give mechanical energy to liquid.

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standard type：S/d=1，Z=3blade end speed:

5~15 m/s, maximum 25 m/s

Types of agitators – axial typepropeller

Standard type：S/d=1, B/d=0.1Z=1-2 (2 for twin ribbon type)low speed, the outer edge is very close to the tank wall (close clearance impeller).

helical ribbon

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standard typed/B=4-10，Z=2blade end speed 1.5~3 m/s

Types of agitators – radial typeblades

standard type： B/d=1/12d’/d=0.05-0.08, d’=25-50 mmd’- distance between the tank wall and the outer edge of the anchorblade end speed 0.5-1.5 m/s

anchor and frame

Propellers

Propellers – axial-flow, high speed impeller for liquids of low viscosity

– Small – 1150-1750 r/min– Large – 400-800 r/min– Pitch – ratio of movement of liquid over fixed

distance to propeller diameter– Standard – 3-blade marine propeller with square

pitch (1.0)– Rarely exceed 18” in diameter

Paddles

Two or four blades turning on a vertical shaft– Simple mixing problems– 20-150 r/min– Length usually 50-80% of inside diameter– Width is 1/6th to 1/10th of length– Use with baffles at high speed to achieve good

mixing

Turbines

Multi-bladed paddle agitators with short blades– Turn at high speed on centrally-mounted shaft– Smaller diameter; 30-50% of diameter of vessel– Effective over wide range of viscosities

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straight blades on disk (Rushton)

curve blades on disk

open straight blades (paddle)

open curve blades

Types of agitators – radial type turbines

3-blade marine propeller

Simple straight-blade turbine

(paddle)Disk turbine

Concave-blade CD-6 impeller Pitched-blade turbine

Agitator types

Agitator types

three-bladed mixing propeller

turbine with flat vertical blades

Turbine with inclined blades (usually45°)

Flat blades disk turbine (more blades)

Curved blade turbine Shrouded turbine (consisting of a rotor and a stator)

Agitator types

Sawtooth edges flat plate turbine

Cage beater impeller (usuallymounted on the same shaft with a standard propeller)

Anchor paddle

Gate paddle

Hollow shaft and hollow impeller assembly

shrouded screw impeller and heat

exchange coil

Special mixers for powders and pastes

Ribbon blender for powders

double cone blender

Twin shell (Vee type) Twin rotor

Special mixers for powders and pastes

Batch muller Twin mullers

Double-armmixer and kneader

Some types of blades for the

double-arm kneader

Flow Patterns

Depends on type of impeller, characteristics of fluid, size and proportions of tank, baffles, and agitator

Swirling – stratification at various levels with no longitudinal flow between levels

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Types of agitators

axial-flowThe main flow in tank is a circulation onaxial direction (& tangential) with littleturbulent.Suitable for mixing of low viscoseliquids, particle suspension and heattransfer enhance.

Propeller small diameter, high speed, large flow rate and low head.Helical ribbon large diameter and mixing range, low speed, low head. Special design for high viscosity liquid.

It can be divided by flow pattern

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Types of agitators

Radial-flowComplicated radial and tangential flow.For low & middle viscosity liquids indispersion of immiscible liquids,chemical reaction and heat transfer.

turbines: high speed，wide blade，low flow rate and high head.straight blades: long vane, low speed and low head, for high viscosity liquids.

anchor and frame ：very large diameter and mixing range, very low speed and head. Suitable for high viscosity liquids and capable of preventing the deposit on tank wall.

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Baffle and draft tubetangential vortex- by centrifugal force. Theliquid level on tank center will fall to form aforced vortex. The high the speed , thedeep the vortex.result effective volume reduced and mixingeffect worsen. Sometimes gas is absorbedfrom lower liquid level to disturb operation.

Solution 1 install baffles on tankwall.Maximum 8 baffles (usually 4),called “fully baffled”

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Baffles and draft tube

draft tube mixing throughcontrolling the flow velocity anddirection, reducing the short cut.Especially for particlesuspension.

Solution 2 off-central installedagitator will improve theoperation with increased powerconsumption.

Side entering impellers

Large tanks agitation: side

entering impellers

Vortex inhibition: off-centering & baffles

Axial or radial impellers without baffles produce

vortexes

Off-center located impellers reduces

the vortex

Lateral baffles reduces the

vortex

Flow patterns: radial vs axial impellers

Radial impeller Axial impeller

Multiple-impeller tank

Standard geometry

a

D

d

b

Standard dimensionsD= T/2;T/3 H= Ta= D/4b= D/5c= T/2;T/3d= 0.75Dw T/10

w

T

c

H

4 baffles

Circulation, Velocities, and Power Consumption

Volume of fluid circulated by impeller must be sufficient to sweep out entire vessel in reasonable time

Velocity of stream leaving impeller must be sufficient to carry current to remotest parts of tank

In mixing, also it needs turbulence– Results from properly directed currents and large velocity

gradients in liquid

Circulation and generation of turbulence both consume energy

Large impeller + medium speed = flowSmall impeller + high speed = turbulence

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Flow pattern in mixing tank

Stirring Re

Flow pattern is related with the geometries of tank, stirrer and baffle, liquid properties and stirrer speed.For agitation operation, the useful flows are axial and radial, not the tangential.

For a fully baffled standard tank with an 6 straight blades turbine, the following flow regimes hold:1＜ Re＜10 near the turbine: laminar flow,

other zones: almost staticRe＞10 laminar axis flow, flow starts from blade’s tips100＜Re<103 transition, around turbine: turbulent flow,

other zones: laminar axis flowRe>103 turbulent in whole tank

2Re /D N DN = urotating speed, rps

Tip speed

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Mixing mechanism(1) molecular diffusion：occurring in molecular scale(2)turbulent diffusion ： caused by vortex dissipation,

existed in vortex size .(3)convective diffusion：caused by convection, occurring in

large scale spaces.Convective flow breaks the liquid into large drops (macromixing); the drops are then broken into smaller ones byvortex deformation (inter-drop mixing) ； those vortexbreakage and deformation will increase or renew thecontacting area between drops with different concentrationand promote the molecular diffusion.A fully homogeneous mixing depends on molecular diffusion.

In comparison, the turbulent diffusion is about 105~107 times of molecular diffusion and dominates the turbulent agitation.

Mixing sensitive processesConsidering that a mixer consumes (depending on its shape,dimension and agitation speed) a determined amount ofmechanical power, it can be dissipated inside the vessel byinducing large flow rates (bulk motion) or high levels ofturbulence due to liquid shear (shear stresses). Typically,axial impellers promote bulk motion while radial ones promoteinstead shear stresses.Processes promoted by mixing may be classified on the basisof their sensitivity to bulk motion or shear stress promotion:Bulk motion controlled processes – those which do not needto create new interface (blending, heat transfer promotion)or which must allow the availability of the actual interfacefor exchange processes (solid suspension).Shear rate controlled processes – those which efficiencyrely on the generation of inter-phase exchange surface (gas-liquid and liquid-liquid dispersions).

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Mixing mechanism of homogeneous systems

Large vortex is broken into small ones by shearing effect.The viscose resistance converts part of the mixing energy into heat.Strong mixing effect occurs at the zone near the agitator. Total circulation flow rate is the most important for this type of mixing.

In the laminar zone, mixing depends on the total flow. But the agitator efficiency is low at turbulent zone. Large diameter (often “close-clearance”) and low speed agitators should be used. Impeller must sweep the whole vessel volume to assure good mixing.

low viscosity liquids

high viscosity liquids

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Mixing mechanism of heterogeneous system

Immiscible liquid-liquid systems

One phase is continuous and another is dispersed.For zone near the agitator, the shearing effect is strong

under high turbulent and small liquid drops will be achieved.In the zone far away from the agitator, the drops willagglomerate into larger ones.The breakage and agglomeration processes increase and

renew the interface of the liquids, so strengthen theinter-phase mass transfer.

If a surface activation agent is added in this system,the agglomeration will be weaken and the size of liquiddrops tends to be uniform.

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Mixing mechanism of heterogeneous systems

gas-liquid systems

The mechanism is similar to the liquid-liquid systems.Gas is dispersed as bubbles in the liquid .Gas-liquid interface tension is stronger than that of liquid-liquid and the dispersion of gas is more difficult. As aresult, the sizes of bubbles are larger than those of liquiddrops.The large density difference between gas and liquid makesthe gas bubbles rise to the top of the liquid.High shearing agitators are often used to generate relativesmall gas bubbles (radial types are preferable).

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Mixing mechanism of heterogeneous system

solid-liquid systemsThe purpose of the agitation are• to suspend the particles homogeneously in the liquid• to reduce the thickness of liquid film on particle surface

in order to accelerate the reaction or transport processes.

Critical speed for suspension (Njs)It is minimum rotating speed needed to suspend all particles.It depends on the agitator size and type as well as on the physical properties of suspension.

Why Dimensionless Numbers?

Empirical correlations to estimate the powerrequired to rotate a given impeller at a givenspeed, with respect to other variables insystem:

– Measurements of tank and impeller– Distance of impeller from tank floor– Liquid depth– Dimensions of baffles– Viscosity, density, speed

Dimensional analysis for fluid agitation systems

Characteristic length: Impeller diameter D (m)Characteristic time: Inverse impeller speed: 1/N (s)Characteristic mass: Liquid density

Basic quan

and cube

tities

3 of impeller diameter: D (kg)

Characteristic velocity: Impeller diameter and speed: DN (m/s)Characteristic pressure: De

Derived q

nsity and

u

velocity

antities

2 2

3 3

square: D N (Pa)

Characteristic flow rate: Velocity and area ND m /s

Dimensionless numbers

2brake

Re Po 3 5

2i

Q Fr3

2 3

We

WN D Reynolds N = ; Power N = N D

Q N DPumping (Flow) N = ; Froude N = ND g

N DWeber N =

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Dimensionless Mixing Numbers

pumping flow rate Q：flow rate pumped through a “reference” surface of the agitator

Flow rates pumped by the impeller

For turbulent flow, NQ is a constant, not a function of Re

Pumping Number NQ=Q/ND3

3Q ND

Where Q is the volumetric flow rate, measured over a fixed controlsurface (depending on the agitator type), N is the rotational speed (rps), Dis the impeller diameter.

Typical NQ values:Standard flat-blade turbine, NQ = 1.3Marine propellers, NQ = 0.5-0.9 (dep. on pitch)4-blade 45 turbine, NQ = 0.5

Pumping number

q

q

Radial impellers

Axial impellers

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Dimensionless Mixing parameters

For turbulent flow (Re>103) & standard geometry:

Flow rates pumped by impeller

11601

2

dD.NN Q'Q

Circulating flow rate number NQ’ = Q’/ND3

Total circulating flow rate Q’ : all circulating flow rate in the tank by the entrainment from the agitator，Q’ > Q.

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Dimensionless Mixing parameters

The power P dissipated divided by N3D5 corresponds to animportant dimensionless parameter of mixers, the Power Number NP:

Mechanical power required by impeller P

Power Number NP=P/N3D5

NP is ratio of drag force to momentum flow, NP is analogous to the friction factor f for CD .

Typical values:Standard flat-blade turbine, baffled vessels NP = 5Standard flat-blade turbine, unbaffled vessels NP = 1Marine propellers, NP = 1

Where P is the mechanical power dissipated (watts), measured atthe tip of the blades, N is the rotational speed (rps), D is theimpeller diameter and is the fluid density.

Calculation of Power Consumption

At low Re (<10), density is no longer a factor:

3 5PP N N D

2 3 LP L

KN P K N DRe

At Re >10 000 in baffled tanks, P is independent of Reynolds Number and viscosity is not a factor:

3 5 P T TN K P K N D

KL and KT are constants for various types of impellers and tanks

Please note the dependency of P on or depending on the flow regime (laminar or turbulent).

Power constants at low (KL) and high (KT) Reynolds number

Type of Impeller KL KT

Propeller, 3 bladesPitch 1.0Pitch 1.5

4155

0.320.87

Turbine6-blade disk (S3=0.25 S4=0.2)6 curved blades (S4=0.2)6 pitched blades (45, S4=0.2)4 pitched blades (45, S4=0.2)

6570-

44.5

5.754.801.631.27

Flat paddle, 2 blades (45, S4=0.2)

36.5 1.70

Anchor 300 0.35

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Correlations and power curves

For a complicated mixing process, dimensional analysis isoften used to correlate the experimental data and findthe empirical Eqs.

With a standard mixing unit, following results can befound from the dimensional analysis

, , , ,Pw f N D g 2 2

3 5 ,PPw ND N DN fN D g

Re, FrPN f

NP —— power numberRe —— stirring Reynolds number for flow patternFr —— Froude number for circulating flow with free surface

NP vs Re for different turbines

Power number NP vs. Re: baffled & unbaffled tanks (marine propellers and helical ribbons)

Helical ribbonunbaffled

unbaffled

baffled

propellers

helical ribbons

NP vs Re for propellers

NP vs Re for different impellers

Effects of D/T for two axial flow impellers

Decreasing D/T ratio

NQ vs Re (Pitched-blade turbine)

Mixing processes: blendingBlending is the mixing operation aimed to homogenisetwo or more miscible liquids by agitation.The blending efficiency depends on the global flow ratemoved by the impeller (bulk motion controlled process).The residence time required to achieve completehomogenization of inlet flow rate is called “mixing time”(tT). For non viscous liquids it is commonly assumed thatthe mixing time correspond to the time required by theimpeller to recirculate 5 times the whole tank content.

NQ’ = circulating flow rate numberN = rotational speed, rpsT = tank diameter, mH = liquid height, m

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3' '

5 5' 4 T

Q Q

V T H const TtQ N ND N N D

2

'T

Q

const TNtN D

Blending time vs Re

Mixing time correlationsFor standard Rushton turbine (fully turbulent regime) the total flow rate circulated by the impeller is Q’=0.92ND2T , it follows:

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2

5 5 4.3' 4 0.92T

V T TtQ ND T N D

2

4.3TTNtD

Mixing time factortT = mixing time, sN = rotational speed, rpsT = tank diameter, mH = liquid height, m

For HE-3 high-efficiency impeller (fully turbulent regime) the mixing time factor is:

1.67 0.5

16.9TT HNtD T

Mixing time correlationsFor standard Rushton turbine (fully turbulent regime) the total flow rate circulated by the impeller is Q’=0.92ND2T , it follows:

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2

5 5 4.3' 4 0.92T

V T TtQ ND T N D

2

4.3TTNtD

Mixing time factortT = mixing time, sV = liquid volume, m3

N = rotational speed, rpsD = impeller diameter, mT = tank diameter, mH = liquid height, m

Mixing Time factor correlations

When Re>105, ft 52 1/2 1/62 2/3 1/6 1/2

1/2 3/2 2

( )Tt T

t ND g D D T gf NtH T T H N D

For HE-3 high-efficiency impeller (fully turbulent regime) the mixing time factor is:

1.67 0.5

16.9TT HNtD T

For Rushton turbine (fully turbulent regime) the mixing time factor is:the

1/Fr

Mixing time factors in agitated vessels

Dashed lines: unbaffled tanks

Solid lines: baffled tanks

Dimensionless parameter dependency on Resummary

Solid particle suspensionProcesses involving solid particle suspension in liquids(leaching, solid catalysed reactions, crystallization, ...) areoften carried out in agitated systems.The role of agitation is to made available to mass andheat exchange all the solid surface, therefore all particleshould move freely inside the tank. This is a bulk motioncontrolled process.

Aim of agitation:• Produce a homogeneous mixture• Dissolve solids• Catalyze a chemical reaction• Promote growth of a crystalline product from a

supersaturated solution

Solid particle suspension regimesFour different regimes apply for solid suspension:1) Incomplete suspension: all or part of particle rest at the

bottom tank, forming “fillets”. This regime may be acceptable only if the amount of unsuspended particles is small;

2) On-bottom suspension: particles are suspended or, at least, move on bottom.

3) Off-bottom suspension: all particles do not rest at bottom for more than 1-2 seconds (Just Suspension regime). This a commonly adopted working regime of suspension;

4) Homogeneous suspension: particles are uniformly distributed inside the whole tank (particle concentration is almost constant). It is a high power requiring regime and it is impossible to achieve for heavy particles. It is needed for very special applications.

Solid particle suspensionThe most used correlation to estimate the Just Suspension agitation speed (NJS) is that proposed by Zwietering:

0.450.1 0.2 0.85 0.13

JS pL

N S d g D B

NJS= just suspension speed, rpsS= geometry factor, -= kinematic viscosity, m2/sdp= particle diameter, mg = gravitational acceleration, m/s2

= particle to liquid density difference, kg/m3

L = liquid density , kg/m3

D = impeller diameter, mB = particle mass to liquid mass ratio x 100, %

Dimensional correlation!

Shape Factor, S

Impeller type T/D T/E(E is height of

impeller above vessel floor)

S

6-blade turbineD/W = 5NP = 6.2

234

444

4.17.511.5

2-blade paddleD/W = 4NP = 2.5

234

444

4.88

12.53-blade propellerNP = 0.5

344

44

2.5

6.58.59.5

For the same geometry, critical speed is about the same for standard turbine and paddleHowever, turbine requires twice as much power as paddle, and 15-20 times as much power as propellerSole purpose to suspend solids – use propellerFor good gas dispersion or high shear – use turbine

Power required for complete suspension of solids in agitated tanks using pitched-blade turbines

Gas-Liquid dispersionsGas liquid mechanically agitated systems are used for thoseprocesses where a gas-liquid mass transfer phenomena areinvolved (hydrogenation, chlorination, oxidation, ...).

The role of mixing is to:• generate as much interfacial area as possible (by disrupting

the gas phase)• disperse the bubbles throughout the liquid• keep the bubbles in the liquid (i.e. recirculate) for

sufficient time• homogenize the liquid concentration• enhance mass and heat transfer coefficients.

To this aim, impellers that produce large shear stresses(high velocity turbines) are preferable.

Gas-Liquid dispersionsThe gas phase is fed on the lower part of the tank, below the impeller, through a gas sparger.Gas spargers may consist simply of open end tubes or may be slightly more complicated (perforated rings, porous plates).The importance of gas sparger is not as crucial as in other non agitated systems (e.g. bubble columns) as the gas phase dispersion is mainly performed by the impeller.

sparger

Gas-Liquid dispersions regimesDepending on the agitation speed N and the gas flow rate QG different dispersion regimes hold:

a) & b) Flooding Loading Complete dispersion

Highly gas recirculation

regime

Surface aeration (open systems)

Gas-Liquid dispersions regimes

Correlation to regime transition parameters estimation:

Flooding Loading (NF)3.5 3.52

3 30 30G FF F

F

Q N DD DFl FrN D T g T

Loading Compl. Disp. (NCD)0.50.5 0.52

0.53 0.2 0.2G CD

CD CDCD

Q N DD DFl FrN D T g T

Compl. Disp. High Gas Rec. (NR)25 52

23 13 13G R

R RR

Q N DD DFl FrN D T g T

Gas-Liquid power requirementsThe gas strongly affects the fluid dynamics inside the tank as itinterferes in the impeller momentum transfer. Thereforecorrelations of NP valid for single phase do not hold anymore.The figure shows how the ratio of power in gassed conditions (Pg)over the power consumed in ungassed systems (P) varies with theFlow Number (Fl) at constant gas flow rate QG:

Power curves at constant gas rate for Rushton turbines.

Pg/P always < 1

Gas cavities behind blades

disc

Increasing agitation

speed

Gas-liquid dispersion empirical correlationsMichel & Miller correlation to predict Pg in standard systems:

2 3

0.56

m

gG

P NDPQ

Dimensional correlation (SI units required)P=ungassed power requirement [W], Pg [W]N [rps], D [m], QG [m3/s]= 0.83 (Rushton turbine, standard geometry)m=0.45 normally coalescent liquids

Van’t Riet correlation to calculate the volumetric gas-liquid mass transfer coefficient (kLa) in standard systems:

gL sg

L

Pk a v

V

Dimensional correlation (SI units required):Pg [W], VL [m3] liquid volume kLa [1/s], vsgsuperficial gas velocity (Qg/Stank) [m/s]

Coalescentsystems

Non coalescentsystems

0.026 0.002 0.4 0.7 0.5 0.2

Pg/P vs QG for different impellers

Pg/P always < 1

Typical power curves for gassed agitators (D.T.= disc turbine; V.D.= vaneddisc; P.B.T. = pitched blade turbine. All curves for one N and D.)

Liquid-liquid dispersionsLiquid-liquid dispersion operations may be performed inagitated tanks provided by high shear rate impellers(e.g. turbines).As in the case of gas dispersion, the interfacial surfacebetween phases is generated by the agitation and varieswith it. Also the droplet size of the dispersed phase willdepend on the degree of the agitation being the resultof the two opposite processes of disruption (due toagitation) and coalescence.Liquid-liquid systems are characterised by majorcomplexity with respect to solid-liquid and, also, gas-liquid dispersions. In particular, in some cases, it is notpossible a priori to establish which one of twoimmiscible phases will perform as dispersed andcontinuous one.

Mean diameter of dropsThe main global parameter describing the characteristic ofdispersion is the mean droplet diameter dp. Considering that thedroplets are characterised by a dimension distribution, the averagediameter usually adopted is the surface-based mean diameter(Sauter diameter) dS obtained starting from the ratio of totalvolume to total surface of all dispersed drops in the volume:

3

31

22

1

66 6

ntoti

idisp i tot S S

ntotdisp tot S

i ii

dnV n d da S n dn d

ntot= total number of drops = disp. phase hold-upa = specific surface, m2/m3

6Sd

a

Sauter mean diameter

Liquid-liquid dispersionsLiquid-liquid dispersion operations may be performed inagitated tanks provided by high shear rate impellers(e.g. turbines).As the impeller action is produce high liquiddeformations (shear) in order to deform drops ofdisperded phase and break them in smaller ones, thisaction depends on the ratio of fluid kinetic energy atthe impeller tip speed to a surface-tension stress basedon D which define the Weber Number (We):

2 2 3C CND N DWe

D

C= density of continuous phase= surface tension

Correlation for dS

Several empiric correlation have been proposed to estimatemean drop diameter depending on agitation conditions,relevant to different mixing devices.

Rushton turbine: 0.60.058 1 5.4Sd D We

Static Kenics mixers: 0.6 0.40.35Sd D We f

Where:2

2

pipe diameter, maverage fluid velocity, m/s

friction factor, -2

C

C

v DWe

Dv

D Pfv L

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Design of agitation

(1) Decide the type and geometry of the tank and the agitator.(2) Find the performance of the installation first, including the

size, rotating speed and power, then scaling up to commercial scale.

Scaling up criteriageometric similarity all the sizes have same ratio, such as H/D. dynamic similarity there are same velocity ratio and direction on corresponding points.kinetic similarity all have same forces ratio on corresponding points (with same Re, Fr or We).where： Re：the ratio of inertia to viscous forces

Fr： the ratio of inertia to gravitational forcesWe = N3D2 /：the ratio of inertia to surface tension

Relevant parameters

D = impeller diameter (m), N = impeller speed (1/s)Ws = shaft power, Wbrake = brake power (W or HP)T = tank diameter, Z = liquid level m.Viscosity Pa.s, density kg/m3, Surface Tension N/mQi = impeller pumping capacity (m3/s)

Scale-Up

Based on geometrical similarity, if possiblePower consumption predicted by curves of NP vs NReROT for power

– ½-1 hP per 1000 gal of thin liquid gives “mild” agitation– 2-3 hP per 1000 gal gives “vigorous” agitation– 4-10 hP per 1000 gal gives “intense” agitation– Actual power delivered to the liquid

Ratio of Dimpeller to Dvessel– Dispersing a gas in a liquid – 0.25– Contacting two immiscible liquids – 0.4– Blending – 0.6 or more

Smaller the impeller, higher the impeller speed

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Scaling up criterion(1) power consumption per volume (Pw/V) =Const.

Used for constant liquid properties and relatively smallscaling-up ratio. Good for turbulent mixing dominatedsituation in fully turbulent flow.

3 2 3 21 1 2 2N D N D

1 1 2 2N D N D

(2) Tip speed constantKeep the agitator torque constant in a geometricalanalogue system. Suitable for operation of high head.

(3) Reynolds number, Re= Const.2 2

1 1 2 2N D N D

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(4) Froude number, Fr=Cost.

(5) Webber number, We= Const.

Which scaling up process should be used?depends on the practical situation.

2 21 1 2 2N D N D

2 3 2 31 1 2 2N D N D

Scaling up criterion