Designing a Mixer

DESIGNING A MIXER

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PREPREPREPRELIMINARYLIMINARYLIMINARYLIMINARY

Deciding on and choosing the size of a type of a mixer consists in finding the optimum parameters for the implementation of the desired procedure. Frequently, optimization is limited by constraints such as costs, bulk or physical limits. This approach consists in choosing a certain number of parameters: • Type of agitators and position

- Radial discharge rotors - Axial discharge rotors - Mix discharge rotors - Angled discharge rotors - Dispersion/emulsification rotors

• Geometry of the tank (size, shape) • Rotation of the rotor (speed, rate of discharge) • Length of mixing • Imposed physical conditions (pressure, temperature)

The people who make these choices rely on their knowledge and experience to make them and choices become additionally complex because of a certain number of factors of which the most frequent follow: • The nature and rheology of products can lead to complicated expressions of a certain number of parameters and specifically of their

respective progress during the mixing process. More precisely in the case of non Newtonian liquids (when viscosity of liquids is directly related to the speed of shearing) for which is observed non linear progress of the required power and the rate of flow of circulation in respect to the rotation speed of the agitator. This is observed in rheoliquidifying liquids (fruit juice, blood), threshold or Bingham liquids (paint, varnish, mayonnaise, toothpaste), rheothickening liquids (wet grit, starch suspension, pizza dough) or thixotropic liquids (yogurt).

• Constraints regarding some parameters because of experience or technologic and economic reasons, such as the peripheral speed return from one type of mixer to another, shearing rate, speed of flow or pumping limit the margin of action for the calculation of the other mixing parameters. It is a limiting factor but we must consider that these constraints, in the end, lead to a more rapid result by minimizing choices.

In practice, choosing an agitator becomes a compromiseIn practice, choosing an agitator becomes a compromiseIn practice, choosing an agitator becomes a compromiseIn practice, choosing an agitator becomes a compromise: ::: aaaa dominant parameter isdominant parameter isdominant parameter isdominant parameter is establishedestablishedestablishedestablished and calcul and calcul and calcul and calculated and ated and ated and ated and thenthenthenthen the other parameters the other parameters the other parameters the other parameters are checked to insure they are checked to insure they are checked to insure they are checked to insure they are sufficientare sufficientare sufficientare sufficient....

VMI recommends and implements the following method: StepStepStepStep 1 1 11 ............................................................... Identification of the type of mixing to perform

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StepStepStepStep 2 2 22.................................................................................................................................................................................................... Inventory of the characteristics of mixing materials

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StepStepStepStep 3 3 33 ............................................. Identification of the global characteristics of mixing rotors

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StepStepStepStep 4 4 44 .....................................................................Choice of the rotors

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StepStepStepStep 5 5 55 ................................................... Calculation of the various mixing parameters (tank – rotors)

DESIGNING A MIXER




STEPSTEPSTEPSTEP 1:1:1:1: Identification Identification Identification Identification of the type of mixing to performof the type of mixing to performof the type of mixing to performof the type of mixing to perform

• SSSSolid / liquidolid / liquidolid / liquidolid / liquid mixturesmixturesmixturesmixtures- Soluble powders Soluble powders Soluble powders Soluble powders

� Dissolution � Homogenizing

- Non soluble Non soluble Non soluble Non soluble powderpowderpowderpowderssss� Placing in and/or maintaining in suspension � Homogenizing � Dispersion

• LiquidLiquidLiquidLiquid / l / l / l/ liquidiquidiquidiquid mixtures mixtures mixtures mixtures- Miscible liquidMiscible liquidMiscible liquidMiscible liquids sss

� Placing in and/or maintaining in suspension � Homogenizing � Dilution

- Immiscible liquidsImmiscible liquidsImmiscible liquidsImmiscible liquids � Emulsion

• Complex rheComplex rheComplex rheComplex rheololololoooogy of viscous mixturesgy of viscous mixturesgy of viscous mixturesgy of viscous mixtures� Placing in and/or maintaining in suspension � Dissolution � Homogenizing � Dispersion � Heat transfer � Grinding

STEPSTEPSTEPSTEP 2: 2: 2: 2: Inventory of the characteristics of mixing materialsInventory of the characteristics of mixing materialsInventory of the characteristics of mixing materialsInventory of the characteristics of mixing materials

• LiquidLiquidLiquidLiquidssss- Density - Viscosity - Percentage - Initial and final temperature - Type of discharge

• SolidSolidSolidSolidssss

- Nature - Percentage - Density - Granulometric dimensions and distribution - Settling speed - Wettability - Solubility

• GaGaGaGassss

- Nature - Flow - Pressure - Solubility

STEPSTEPSTEPSTEP 3:3:3:3: Identifi Identifi Identifi Identification of the gcation of the gcation of the gcation of the globalloballoballobal c c ccharacteristicharacteristicharacteristicharacteristics sss of mixingof mixingof mixingof mixing rotorrotorrotorrotorssss

• Flow mainly generated (axial or radial) • Importance of the pumping effect (high, medium, low) • Importance of the shearing effect (high, medium, low) • Capacity of generating turbulence (high, medium, low)

DESIGNING A MIXER




STEPSTEPSTEPSTEP 4:4:4:4: ChoiceChoiceChoiceChoice of of of of rotorrotorrotorrotorssss

You must then chose between the varieties of rotors offered by VMI the one that is the best adapted to the mixture you want to produce. Your choice should be based on the following: • Intrinsic characteristics of the rotors taking into account the preferred type of flow, knowing that frequently a compromise must be made

between the type of discharge (axial, radial, turbulent…) and mechanical effect generated (circulation, shearing, …), • Laboratory tests, • Financial criteria: example = choice in order to achieve the best Nq/Np performance to minimize installed capacity, • Functional criteria: example = choice of a rotor that is the easiest to clean.

Currently VMI offers the following agitation rotors:

1. Profiled triblade 7. Centripetal 13. Break=up

2. Two way profiled triblade 8. Deflocculator 14. Butterfly

3. PSVB four blade 9. Sevin with inlets 15. Saw teeth

4. PSVH four blade 10. Centrifugal 16. Anchor blade

5. PA four blade 11. Centri=deflocculator 17. Rotor=stator

6. Water propeller 12. Cutting

DESIGNING A MIXER




Table I

Main FlowMain FlowMain FlowMain Flow RotorRotorRotorRotor Type Type Type Type MainMainMainMain FuFuFuFunctionnctionnctionnction Power Power Power Power NNNNPPPP

Pumping Pumping Pumping Pumping NNNNQQQQ

Shearing Shearing Shearing Shearing StrengthStrengthStrengthStrength

Water propeller (6) Circulation 0.21 to 0.28 0.58 to 0.68 Very low

Profiled triblade (1) Homogenizing liquid/liquid 0.34 to 0.60 0.84 to 0.87 Very low

Two way profiled triblade (2)

Dissolution, incorporation charges

0.76 to 1.22 1.15 to 1.2 Very low

PSVB four blade (3) Dilution/Dissolution 1 to 1.95 1 to 1.73 Very low

PA four blade (5) Dilution/Dissolution 1.8 to 2.2 1 to 1.73 Very low

AXIALAXIALAXIALAXIAL

SEVIN with inlets (9) Dissolution/Dispersion 0.4 to 0.55 0.75 to 0.85 Medium Centripetal (7) Dilution/Dissolution 1.6 to 2 1.1 to 1.3 Low Centrifugal (10) Dissolution 2.5 to 4.5 3 to 3.8 Medium Saw teeth (15) Dispersion 0.23 to 0.42 0.19 to 0.31 High

Deflocculator (8) Dispersion 0.34 to 0.8 0.37 to 0.44 High Centri=deflocculator (11) Dispersion 1.1 to 2 0.67 to 0.79 High Rotor/Stator wide slots

(17a) Dispersion/Emulsion 2.1 to 5.9 0.82 to 0.9 Very high

RADIALRADIALRADIALRADIAL

Rotor/Stator narrow slots (17b)

Dispersion/Emulsion 2.3 to 6.2 0.55 to 0.6 Very high

Note: NP, NQ and shearing strength are expressed for equivalent diameters

• Power: 53dN

PN p ρ= (P: agitation power; ρ: density; N: rotation speed; d: rotor diameter) is the coefficient

of drag from the agitator when in the liquid and represents power usage. • Pumping:

3dNQN P

Q = (QP: pumping flow rate; N: rotation speed; d: rotor diameter) is the dimensionless

expression of the pumping flow rate for the agitator. • Shearing strength indicates the capacity of the rotor in breaking the friction effect exerted by two infinitesimal

layers of liquid sliding against one another. Shearing is usually stated as speed of shearingeV=γ& , expressed as

s=1, a value that is very difficult to measure. PERFORMANCE MOBILES

MARINE

TRIPALE BI-DIRECTTIONNELLE

QUADRIPALE

SEVIN

DEFLOCULEUSE

CENTRIFUGE

TRIPALEPROFILEE

ROTOR/STATOR FL

ROTORSTATOR FE

CENTRIPETE

0

0,5

1

1,5

2

2,5

3

3,5

Pouvoir de cisaillement

Rendementd

edébitN

q/Np

MAINTIEN EN SUSPENSION

HOMOGENEISATION

DILUTIONDISSOLUTION

DISSOLUTIONDISPERSION DISPERSION

EMULSION

Très Faible Faible Moyen Fort Très Fort

ROTOR PERFORMANCE

Shearing Strength Very Low Low Medium High Very High

DESIGNING A MIXER




Table II Solid / Liquid Mixtures Liquid / Liquid Mixtures

Soluble Powders

Non Soluble Powders Miscible Liquids Immiscible Liquids

Complex Rheology for

Viscous Mixtures

Heat Transfer

Suspension Homogenizing 1 3 6 7

(*) 1 3 6 7(*)

High

circulation capacity Dissolution

Homogenizing

1 2 3

.

7 10

11 .

1 2.

Dilution 1 3 7 10

.

Dispersion 8 9 10 11 12 .13 15 17

(**)

High shearing strength

Emulsion 8 16 .

2 8 9 14

15 17 .

1 3 6

16 .

(*) Triblade � efficient for high volumes at low rotation speeds Four blade � efficient for low and medium volume at medium rotation speeds Water propeller � efficient for high volumes requiring strong circulation Centripetal � very efficient for dissolution because of the right compromise between circulation and shearing (**) Deflocculator / Sevin � a Sevin insures better circulation at equivalent power input, specifically for high volumes Centrifuge

� very efficient for complex dissolutions Break=up � very efficient for placing compact materials in suspension Centri=deflocculator � very good compromise between the centrifuge and deflocculator

STEPSTEPSTEPSTEP 5555: ::: CalculCalculCalculCalculation of the various mixing parametersation of the various mixing parametersation of the various mixing parametersation of the various mixing parameters

1.1.1.1. Diameter, number and speed of one or more mixing rotorDiameter, number and speed of one or more mixing rotorDiameter, number and speed of one or more mixing rotorDiameter, number and speed of one or more mixing rotor(s)(s)(s)(s)

These calculations are performed taking into account as main parameters one or several criteria for a precise mixture: • Criteria for mixing efficiency

= peripheral speed, = recirculation rate therefore capacity of the turbine, = length of the mixing process.

• Criteria linked to the rheology of the product (the higher the viscosity of the product, the higher the diameter of the rotor at low speed)

• Economic criteria

GuideGuideGuideGuide for selectingfor selectingfor selectingfor selecting the the the the D D DDtool tool tool tool ////DDDDtanktanktanktank ratioratioratioratio in the tank Table III

DDDDtooltooltooltool / D/ D/ D/ Dtanktanktanktank TypeTypeTypeType of of ofof RotorRotorRotorRotor SpeedSpeedSpeedSpeed ((((rpmrpmrpmrpm)))) Low viscosity productLow viscosity productLow viscosity productLow viscosity product Viscous productViscous productViscous productViscous product****

3000 0,1 0,2 Rotor/Stator 1500 0,15 0,25

1500 to 750 0,2 0,3 500 to 250 0,25 0,5 170 to 90 0,3 0,6 Propeller or Turbine

60 to 30 0,5 0,8 Anchor or butterfly blade 10 to 200 0,9 à 1

*according to the number of movements

DESIGNING A MIXER




Guide for selecting the peripheral sGuide for selecting the peripheral sGuide for selecting the peripheral sGuide for selecting the peripheral speed and the recirculation ratepeed and the recirculation ratepeed and the recirculation ratepeed and the recirculation rate Table IV

TYPE TYPE TYPE TYPE OF MIXTUREOF MIXTUREOF MIXTUREOF MIXTURE

Speed inSpeed inSpeed inSpeed in m/s m/s m/s m/s Recirculation Recirculation Recirculation Recirculation volume bac/hvolume bac/hvolume bac/hvolume bac/h

Maintaining in suspension, circulation: slow sedimentation product 0,5 to 1,5 50 to 200 Maintaining in suspension, circulation: fast sedimentation product 1,5 to 2,5 200 to 300 Liquid/liquid homogenizing 2,5 to 4 300 to 400 Liquid/solid homogenizing Relatively equal apparent densities Low concentration dissolution: 10 to 20 % max

4 to 5

400 to 700

Solid /liquid homogenizing Very different apparent densities High concentration dissolution: up to 50 %

5 to 8

700 to 1000

Dispersion facile 8 to 10 800 to 1200

Difficult dispersion • Products that swell • Extremely fine products • Mashing

15 to 20

1000 to 1500

Guide for selecting the number ofGuide for selecting the number ofGuide for selecting the number ofGuide for selecting the number of rorororotortortortors in thes in thes in thes in the tanktanktanktank Table V

ViscosityViscosityViscosityViscosity Pa.s Pa.s Pa.s Pa.s No.No.No.No. of of of of

momomomovementsvementsvementsvements Height of workHeight of workHeight of workHeight of work (Nb of (Nb of (Nb of (Nb of

timestimestimestimes ØØØØ))))Flow rate factorFlow rate factorFlow rate factorFlow rate factor K K KK0000

0.001 (eau) 8 to 3 1.3 <0.1 3 to 2 1.2

0.1 to 10 1 movement

2 to 1.5 1 10 to 30 1.5 to 1 0.8 30 to 60

1 or 2 movements 1 0.6

60 to 100 0.8 0.5 100 to 1000 0.65 0.35

> 1000 2 movements minimum

0.5 0.2

2.2.2.2. CalculCalculCalculCalculation of the ation of the ation of the ation of the characteristiccharacteristiccharacteristiccharacteristic parameters of the mixer parameters of the mixer parameters of the mixer parameters of the mixer.

• Sizes used: - D: diameter of the mixing tool (m) - N: rotation speed of the tool (t/s) - ρ: apparent density of the liquid (kg/m3)- µ: viscosity of the liquid (Pa.s) - NP0: Number for nominal capacity - NP: Number for corrected capacity - NQ: Number of pumping actions - KS: Metzner=Otto constant to calculate shearing - K: Consistency index (Pa.sn=1 ) = n: exponent of rheoliquidifying; K and n are determined by a measure of

viscosity where µ = Kγn=1

• Calculation of Reynolds number (Re) Newtonian liquids: Re =ρ x N x D2/µNon Newtonian liquids: Reequivalent = (ρ x N2=n x D2)/K

DESIGNING A MIXER




• Calculation of the nominal capacity number NP0 = f(Re) Experimental values ofExperimental values ofExperimental values ofExperimental values of N N NNP0P0P0P0 = f(Re) = f(Re) = f(Re) = f(Re) (N(N(N(NP0P0P0P0 = 1 for = 1 for = 1 for = 1 for Re = 10 Re = 10 Re = 10 Re = 104444))))

Table VI Four bladeFour bladeFour bladeFour blade

ReReReRe TribladeTribladeTribladeTriblade ProfiléeProfiléeProfiléeProfilée

Water Water Water Water PropellerPropellerPropellerPropeller PAPAPAPA PSVBPSVBPSVBPSVB PSVHPSVHPSVHPSVH CentripetalCentripetalCentripetalCentripetal DeflocculatorDeflocculatorDeflocculatorDeflocculator

SEVIN SEVIN SEVIN SEVIN with with with with inletsinletsinletsinlets

1 / 100 22,4 36,2 31,5 53 94 128 2 59 60 13,5 21 19 31 55 77 3 29,5 44 8,8 14,3 12,4 22 39 57 4 23,5 36 7,6 12,4 11,4 18 34 49 5 19,1 30 6,5 10,5 9,5 16 30 41 6 16,2 26 6,2 10 9 12 24 31 7 14,7 23,2 5,3 8,6 7,6 11 22 28 10 11,2 18 4,1 5,7 5,2 9,5 16 23 20 6,8 10 2,8 3,8 3,2 6 10 14 30 5,3 7,6 2,4 3,1 2,7 4,7 7,9 10,5 40 4,4 6 1,9 2,8 2,2 4 7 9 50 3,8 5,2 1,8 2,6 2 3,4 6 7,7 70 3,2 4,4 1,5 2 1,8 2,8 5 6,2 100 2,7 3,6 1,2 1,7 1,3 2,3 4 5,2 150 2,2 2,8 1,2 1,4 1,2 2 3 3,8 200 1,8 2,6 1,1 1,1 1,05 1,8 2,5 3,1 250 1,6 2,2 1,06 0,95 0,95 1,7 2,4 2,8 300 1,5 1,8 1, 0,95 0,95 1,7 2,2 2,6 500 1,2 1,4 0,95 0,86 0,86 1,5 1,8 2,1 1000 1,1 1,2 0,95 0,86 0,86 1,2 1,4 1,6 5000 0,94 1 1 0,95 0,95 1,05 1 1,05 10000 1 1 1 1 1 1 1 1 50000 1,03 0,88 1,06 1 1 0,96 1 0,97 100000 1,12 0,84 1,1 1,05 1,05 0,95 1 0,9

• Calculation of Froude number (Fr) if required (appearance of a vortex) Fr = N2 x D/g (g=9,81 ms=2)

A vortex will be considered formed if Fr ≥ 3

• Calculation of corrected capacity number NP

- If Fr ≤ 1 (no vortex), then NP = NP0 - if Fr ≥ 3 (vortex), then NP = NP0 x Fry et y = (a – Log Re) / b

radial effect rotors: a = 1 b = 40 axial effect rotors: a = 2,1 b = 18

• Calculation of absorbed pump power Pab (in W) Pabs = NP x ρ x N3 x D5

• Calculation of turbine flow rate Q (in m3/s) Q = NQ x N x D3

• Calculation of drag flow rate Qe (the viscosity of the liquid is taken into account) Qe = Q x K0 (flow rate factor, see Table V)

• Calculation of recirculation rate TRC (in volume / hour) Directly deducted from the drag flow rate Qe and the volume V of the tank

• Calculation of mixing time Tm

Tm = K x V/Qe where K is an experimental coefficient varying from 10 to 10000 (tests from Grenville and Co in 1992 or Nienow in 1997) If K is unknown the value for K0 can be used (Table V), and you will get: Tm = K0/TRC

• Calculation of peripheral speeds (VP), flow speeds (or transversal) (VF), and rising speed (VR)Peripheral Speed (in m/s) (linear speed of the extremity of the turbine)

DESIGNING A MIXER




VP = π.D.N Flow Speed (in m/s) (linear speed of the liquid in the turbine)

VF = (4 x NQ x D x N)/πRising Speed (in m/s) (linear rising speed of liquids on the side of the tank)

VR = (4 x Q)/ π(Dc2 = D2) = (VF x D2)/(Dc

2= D2) with Dc = diameter of the tank

DESIGNING A MIXER




MIXING LEXICONMIXING LEXICONMIXING LEXICONMIXING LEXICON

Behaviour indexParameter of Ostwald=Dewaele’s Law, the behaviour index defines the pseudoplastic character of a liquid for n<1 or dilatant for n>1. For n=1, the apparent viscosity is independent from the speed gradient, which defines a Newtonian liquid. BinghamA Bingham liquid is one that flows only if shearing stress is superior to a certain threshold τ0. Beyond this threshold, the product reacts like a Newtonian liquid, pseudoplastic or dilatant. Chocolate, toothpaste and drilling mud are examples of Bingham liquids. Consistency indexParameter of Ostwald=Dewaele’s Law the consistency index defines the consistency of a liquid. The higher the value of the index the higher the apparent viscosity, at a given speed gradient, is important DilatantA dilatant like liquid is one whose apparent viscosity increases with the speed gradient. The rheologic model of Ostwald=Dewaele defines this liquid. The dilatant characteristic will be will be even more apparent as the behaviour index increases. Aqueous clay suspensions and some slush are examples of dilatant liquids. DilutionDilution is the transformation of a concentrated solution to a more diluted solution by adding a continuous phase compatible with the solution. This operation requires an important circulation of the product. DispersionDispersion is the incorporation of a solid phase divided in a continuous liquid phase where the particles of the solid phase are not soluble in the liquid phase. DissolutionDissolution is the incorporation of a soluble solid phase in a continuous liquid phase often called solvent. This operation requires good circulation. EmulsionAn Emulsion is a mixture of two immiscible liquids. One liquid (the dispersed phase) is dispersed in the continuous phase. This operation requires a very high degree of shearing from the agitation rotor. The stability of the emulsion is essentially linked to the size of the droplets of the dispersed phase, their surface tension and distribution in the dispersed phased.

EndothermicA reaction is endothermic when it absorbs heat. Dissolution of citric acid in water is endothermic.

ExothermicA reaction is exothermic when it emits heat. Dissolution of soda in water is exothermic.

DESIGNING A MIXER




ExtractionExtraction is made up of the dispersion or suspension of a solid phase divided in a liquid phase obtaining a very high

concentration that can reach 75% of the end product. FroudeThe Froude number is a dimensionless number (no units) comparing inertial and gravitational forces. It occurs only when gravitational forces are sensitive and it is characterized by the forming of a vortex on the interface of the liquid. GrindingGrinding is an activity that reduces the sizes of solid particles, either in a liquid phase or directly in its dry state. HomogenizingHomogenizing is the action of homogenizing a medium. This means that the value of a characteristic quantity (example = temperature or concentration) is identical in every part of the medium. Significant circulation of the product favours this operation. LaminarA discharge is laminar when the layers or threads of liquids slide one against the other without merging. It is characterized by a Reynolds number lower than a limit value which depends on the geometric conditions of the agitation system. The transversal motion of linear momentum is caused only by molecular momentum. MixtureThe term mixture defines a system made up of several chemical species which can found in various states (solid, liquid, gaseous). To perform a mixture for which at least the dispersion phase is in liquid state, the agitation rotor creates two distinct actions: a pumping action to ensure a wide scale global mixture (macro=mixture) and a turbulent action or shearing to ensure a small scale local mixture (micro=mixture). NewtonNewton’s Law expresses the quantity of motion transferred through a given surface, represented by the formula: d mV

dtS

dVdx

( )= µ .

NewtonianA liquid is Newtonian when its viscosity is constant when in given temperatures and pressures. Viscosity does not depend on operational conditions (speed gradient, shearing rate, time …). All gases, water, light organic products are Newtonian liquids. Non NewtonianA liquid is non=newtonian when its viscosity is dependent of operational conditions. Notably we can distinguish liquids for which the apparent viscosity depends on: = the speed gradient (pseudoplastic, dilatant, of Bingham) = the speed gradient and length of the application of the constraint (thixotropic, rheopectic) = the speed gradient, length of the application of the constraint and modulus of elasticity (viscoelastic). Ostwald>DewaeleOstwald=Dewaele’s Law, also called power law, is the rheologic model used to characterize the behaviour of pseudoplastic and dilatant liquids. It expresses the apparent viscosity as a function of gradient speed using the equation: µ γa

nm= −& 1 where m and n are respectively the consistency and behaviour index of a liquid.

DESIGNING A MIXER




dilatant

newtonien

pseudoplastique

Bingham contrainte decisaillement

gradient de vitesse

Phase reversalPhase reversal created by a very significant mechanical or thermal effect characterizes an emulsion where the dispersed phase becomes the dispersion phase and vice versa. PropellerThe word propeller is a generic term used to qualify an agitation rotor that generates a main axial discharge, meaning parallel to the agitation shaft. Shearing constraints are generally low. PseudoplasticA liquid is pseudoplastic when its apparent viscosity decreases as the gradient speed increases. Ostwald=Dewaele’s rheologic model defines this liquid. The pseudoplastic character will be more significant the lesser the behaviour index. Carbomer solutions and cosmetic creams are examples of pseudoplastic liquids. ReynoldsReynolds’ number is a dimensionless number (no units) that represents the relationship between inertial forces and viscous forces. A low value of this number indicates the dominance of viscous friction: it is the laminar regime. A high value indicates the dominance of dynamic friction: it is the turbulent regime. RheogramA rheogram represents the progress curve of shearing constraint in respect to the speed gradient used. Using this diagram you can determine the rheologic behaviour of the liquid (newtonian, pseudoplastic, dilatant, thixotropic or rheopectic) and associate this behaviour to one of the existing rheologic models. RheometerA rheometer is a device which can be used to trace a rheogram. It determines the viscosity of a liquid continuously; at a constant gradient speed or within a range of gradient speed. RheopecticA liquid is rheopectic when its apparent viscosity increases when the length of application of constraint increases. A gypsum suspension presents a rheopectic character. SuspensionA suspension is the setting in motion of a non soluble divided solid phase in an internal liquid phase. Without agitation the particles, which usually have a different density from the liquid phase, depending on the situation, tend to settle or float. ThixotropicA liquid is thixotropic when its apparent viscosity decreases when the length of application of the constraint. Paint,

ink, polymers in a solution are generally thixotropic liquids.

DESIGNING A MIXER




∆y

V

plaque entraînée

plaque immobile

F

F

A

V

y= µ

∆par définition :

TurbineA turbine is a generic term used to designate an agitation rotor that creates a main radial discharge, meaning perpendicular to the agitation axis. Shearing constraints are generally very high because the speed of flow located close to the turbine is significant compared to the speeds of surrounding liquids. TurbulentA discharge is turbulent when the sizes characterizing the motion of the liquid are turbulent. Streams of liquid no longer have any individuality. It is characterized by a Reynold’s number superior to a limit value which depends on the geometric conditions of the agitation system. Molecular motion is insignificant, the transversal motion of the linear momentum is ensured by the vortices. ViscoelasticA viscoelastic liquid includes simultaneously viscous properties (distortion when submitted) and elastic properties (reverts to its initial state when constraints are removed). Several polymers are viscoelastic, like polyacrylamide solutions. ViscosimeterA viscosimeter is a device used to determine the viscosity of a liquid in given operational conditions. Its operation is based more often than not on the measure of working torque from the setting in motion of a solid in contact with a liquid. Apparent viscosityA characteristic of non newtonian liquids. The definition of apparent viscosity is the relationship between shearing tension and the speed gradient. Kinematic viscosityThe definition of kinematic viscosity is the relationship between the dynamic viscosity and the density of the liquid. It is seen as the coefficient of diffusion of linear momentum. Dynamic viscosityA property of a liquid, dynamic viscosity usually called viscosity, characterizes the resistance of transfer of linear momentum. It is the coefficient of proportionality between tangent shearing tension to the transverse speed and the speed gradient. At a given speed, a higher viscosity requires greater power for movement. For a given applied force, an increase in viscosity is characterized by a lower speed of movement.

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Designing a Mixer