New protocol of the Villermaux–Dushman reaction systemto characterize micromixing effect in viscous media

J. Pinot a,b, J.-M. Commenge a,b, J.-F. Portha a,b, L. Falk a,b,n

a CNRS, Laboratoire Réactions et Génie des Procédés (LRGP), UMR 7274, Nancy, Franceb Université de Lorraine, Laboratoire Réactions et Génie des Procédés (LRGP), UMR 7274, Nancy, France

H I G H L I G H T S

� Method for quantification of micromixing in viscous medium in stirred tank.� New protocol based on a phosphate buffer and the use of HydroxyEthylCellulose.� Preliminary micromixing results of viscous solution (60 mPa s) in a stirred tank.

a r t i c l e i n f o

Article history:Received 2 April 2014Accepted 5 July 2014Available online 15 July 2014

Keywords:MicromixingViscous mediumHECMicromixedness ratioVillermaux–DushmanStirred tank

a b s t r a c t

This paper presents the results of the characterization of a new method for quantification of themicromixing efficiency in a viscous medium in stirred tank reactors. The used method is inspired by achemical system based on two competitive reactions, the iodide–iodate reaction system (Villermaux–Dushman method), whose products selectivity is a measure of the mixing efficiency. The approachproposes a new protocol based on a phosphate buffer and the use of HydroxyEthylCellulose (HEC,720, 000 g/mol) as an inert viscosifying agent, exhibiting various interesting properties (no disturbanceof the spectrophotometric measure, low cost, low required amount, eco-friendly product). This agent isalmost Newtonian up to 0.25 wt% in water and becomes non-Newtonian above 0.5 wt%. By means of itsuse, the viscosity of the reactive medium can be raised by around two orders of magnitude while addingless than 1 wt% HEC to the water solution. Preliminary micromixing results of moderate viscoussolutions (50 mP as with HEC 0.5 wt%) in a stirred tank reactor are presented.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In chemical reaction engineering, one of the key steps in manychemical syntheses performance lies in the reactants mixingwhich must be realized before reaction takes place to avoidconcentration gradients which may reduce conversion and selec-tivity. Mixing at molecular scale (micromixing) is especiallyimportant when the characteristic time of the chemical reactionis of the same order of magnitude or smaller than the one of themixing process. Mixing may become a very difficult task in viscousmedium since large energy inputs may be required in the case ofpolymerization reactions. Despite many studies related to mixingefficiency using chemical methods in stirred tanks and variousmixing devices, few of these works have been interested in viscoussystems. On the one hand, the experimental studies focusing onthe influence of viscosity on micromixing (Table 1) have been

carried out by using the diazo-coupling reaction between1-naphthol and diazotized sulphanilic acid (second Bourne reac-tion) and the competitive neutralization of hydrochloric acid andalkaline hydrolysis of ethyl-chloroacetate with sodium hydroxide(third Bourne reaction). The two viscosifying agents used wereCarboxyMethylCellulose (CMC) and HydroxyEthylCellulose (HEC).On the other hand, concerning the Villermaux–Dushman reaction,based on the iodide–iodate reaction system, it has been extendedto study micromixing in viscous medium with the use of glycerinas additive (Guichardon et al., 1997). Later, the iodide–iodate testreaction has also been used with HEC as additive (from 0 wt% to0.375 wt%) to characterize micromixing efficiency in polymeriza-tion reactors (Kunowa et al., 2007).

In order to carry out successfully the test reaction in viscousmedium, the viscosifying agent must respect at best the followingconditions (Bałdyga and Bourne, 1999):

� To be a water-soluble additive,� To preferentially exhibit a Newtonian rheological behavior with

a pH-independent viscosity,

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Chemical Engineering Science

http://dx.doi.org/10.1016/j.ces.2014.07.0100009-2509/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: CNRS, Laboratoire Réactions et Génie des Procédés(LRGP), UMR 7274, Nancy, France. Tel.: þ33 383 175 094.

E-mail address: laurent.falk@univ-lorraine.fr (L. Falk).

Chemical Engineering Science 118 (2014) 94–101

� To produce solutions with a wide range of viscosity,� To be chemically inert towards used reactants,� To not disturb analysis of reactive products.

Table 2 presents a rapid overview of various viscosifying agentsthat have already been tested in order to be used as part of theiodide–iodate test reaction. Some of these works have proved thatseveral agents are incompatible with the test reaction such assaccharose, PEG and Emkaroxs because they react, directly orindirectly, with the iodine formed. Others agents such as CMC orHEC (Natrosols Grade 250 GR) are Newtonian up to 1 wt% inwater without significant effect of pH on viscosity in the range ofpH 7–10. However, in the case of CMC, the reactive systemprovided poor reproducible results: a modification of the rheolo-gical behavior at the level of the impeller could explain thisphenomenon (Fournier, 1994).

Glycerin has already been employed successfully to extend theuse of the iodide–iodate test reaction in viscous medium(Guichardon et al., 1997). Indeed, glycerin has proved to becompatible with the test reaction. It presents the advantage ofbeing chemically inert towards used reactants, to not disturbanalysis of reactive products by spectrophotometry and to exhibita Newtonian behavior. Nevertheless, a modification of normalredox potentials has been observed which leads to a broadening ofthe stability range of iodine towards basic pH. Therefore, theexperiments with glycerin must be carried out in a bufferedmedium at pH 11. Unfortunately, in such basic pH, a possible

disproportionation reaction of iodine may be favored and thiseffect should be checked carefully. However, glycerin presents aweak viscosifying ability, i.e. it must be added in a large amount upto 90 wt% to reach a viscosity up to about 170 mPa.s. To sum up,the reactants are difficult to dissolve in very concentrated solu-tions of glycerin and the presence of large amounts of glycerinnotably modifies physical and chemical properties of the reactivemedium. For instance, the dielectric constant εr is modified,implying that the equilibrium and intrinsic kinetic constants mustbe determined again. Nevertheless, the experiments realized withglycerin have shown the importance of viscosity on micromixing.As viscosity increases, bigger amount of iodine is formed, which issynonymous of an increase in the segregation and a reduction ofthe micromixing quality.

The aim of this work is to propose another viscosifying agentwhich is a fortiori compatible with the test reaction and whichpresents a stronger viscosifying ability than glycerin or HECNatrosols 250 GR (300 000 g/mol) in order to reach higherviscosity without requiring mass fractions larger than 1 wt% or2 wt% in the reactive medium. The selected viscosifying agent isHEC (Sigma-Aldrichs, average viscosimetric molecular weight of720 ,000 g/mol) which corresponds to HEC Natrosols 250 MR. It ismore viscous than HEC Natrosols 250 GR (Table 2) at the samemass fraction in water.

A new protocol based on the Villermaux–Dushman method(original protocol fully described in Appendix A) is proposed tostudy micromixing efficiency in viscous HEC-water solutions.

Table 1Experimental methods for mixing characterization in viscous medium.

Test reaction Viscosifying agent References

Selective iodination of l-tyrosine Polymeric additive (Bourne and Rohani, 1983)(1.08-3.7–6.4 m2/s at 298 K)

Imidization reaction Molten polyethylene (Frey and Denson,1988)(105 mPa s at 423 K)

Second reaction of Bourne CMC (Blanose 7 MF Herculess

) (Bourne et al., 1989) (Bourne and Maire, 1991)(0.9–7.9 mPa s at 298 K)HEC (Natrosols Grade GR) (0.89–3.6- (Gholap et al., 1994) (Baldyga et al., 1995)

(Bałdyga et al., 1997)6.2–8.9 mPa s at 298 K)Third reaction of Bourne HEC (Natrosols Grade 250 GR) (Bourne et al., 1995) (Kunowa et al., 2007)

(1–6.2 mPa s at 293 K)PEPPG (Breox 75 W 18000) (Baldyga et al., 1998) (Bałdyga et al., 2000)

(Rożeń et al., 2001)(from 1 to 270–300 mPa s at 298 K)Iodide-iodate test reaction Glycerin (from 1 to 170 mPa s at 293 K) HEC (0 wt%–0.125 wt%–0.375 wt%) (Guichardon et al., 1997) (Kunowa et al., 2007)

Table 2Viscosifying agents for mixing characterization by the Villermaux–Dushman reaction in viscous medium.

Viscosifying agents Advantages Drawbacks References

CMC (Blanose 7MF Herculess) -Newtonian until 1 wt% -Non-Newtonian above 1 wt% (Bourne et al., 1989) (Gholap et al., 1994)(Fournier, 1994)-Iodine spectrum weakly modified by the

CMC presence-Poor reproducibility-pH dependent viscosity

Saccharose -Enables to reach viscosity around10�3 m2/s

-Parasite reaction: hydrolysis in acidmedium, glucose formed can react withiodine

(Fournier, 1994)

-Iodine spectrum not modified in a newlysolution prepared

PEG (PolyEthylenGlycol) -Discoloration of iodine solution afteradding PEG

(Fournier, 1994)

HEC (Natrosols Grade 250 GR) -Newtonian until 0.5 wt% -Non-Newtonian above 0.5 wt% (Bourne et al., 1995) (Baldyga et al., 1995)-Less pH-dependent viscosity than CMC - For 0.5 wt%, viscosity about 6.2 mPa s:

weak viscosity reachedGlycerin -Newtonian

-Chemically inert towards reactants-Weak viscosifying ability: addition in largeamount about 90 wt% to reach 170 mPa s

(Guichardon et al., 1997)

-Difficulty to dissolve reactants inconcentrated glycerin solutions

Emkarox s -Newtonian with viscosity superiorto 200 mPa s

-Reaction with iodine in the presence ofiodide ions

(Cochard, 2000)

J. Pinot et al. / Chemical Engineering Science 118 (2014) 94–101 95

In the following section, the viscosity of HEC-water solutions isdescribed; the choice of a new buffer and the concentration set arealso reported. Then, in the last section, results of the method arepresented to determine the micromixing efficiency in a stirredtank of moderate viscous medium of 50 mPas (HEC 0.5 wt%).

2. Material and methods

2.1. Experimental set-up

Experiments were carried out in a 730 mL glass stirred-tankreactor of internal diameter T¼0.098 m equal to the liquid height,equipped with a tailor-designed impeller of diameter D¼0.087 m.This impeller (Fig. 1) is very similar to the paravisc impellerEkatos, used as reference model, which is well adapted to viscousfluid mixing. However, the shape of the paravisc impeller couldnot really be respected because a spectrophotometer dip probeand an injection tube had to be placed inside the tank, in the fluidflow. Therefore, an adapted impeller has been realized to respectthese constraints.

The temperature was kept constant at 20 1C for all experimentsby a flow of water through the jacket of the tank. The injectiontube of 2 mm internal diameter was set vertically and the injectionpoint was located at the same height than the optic fibertransmission dip probe Avantess (optical path length l¼1 cm)connected to a spectrophotometer AvaSpec-3648 used to con-tinuously measure the optical density at 353 nm as shown in Fig. 1.The injection point was the same for all experiments. The stirringmotor used is a RM 200 Rheomat Lamyrheology Instrumentss

which also enables to measure the torque and so to estimate themean energy dissipation rate ε.

2.2. Experimental procedure

A specific experimental procedure has been adapted from theoriginal procedure (see Appendix A) of the Villermaux–Dushmanreaction system, required to consider the presence of the viscosi-fying agent in the system.

2.2.1. Viscosity of HEC - water solutionsThe rheological behavior of HEC-water solutions is reported in

Fig. 2 with the representation of viscosity as a function of shearrate. For HEC mass fractions lower than 0.5%, the solution almostexhibits a Newtonian behavior and a shear-thinning behavior isobserved for HEC mass fraction over 0.5%. Indeed, the viscositydecreases with the shear rate. The viscosity η has been measuredat 20 1C as a function of shear rate using a rheometer ARES-G2 TAInstrumentss. It has also been checked that the viscosity of thesolution is independent of pH in the range of 7–10 by adding abuffer to the solution.

2.2.2. Choice of a new bufferThe classical protocol (cf. Appendix A) based on borate/boric

acid buffer (Guichardon, 1996) led to the disappearance of iodineas a function of time after its addition in the tank due to asecondary reaction with HEC in basic medium. Fig. 4 shows thedecrease of the optical density as a function of time after acidinjection. The optical density signal decreases during the first200 s due to macromixing in the stirred tank. It can be noticed thatafter macromixing completion, the signal is not stable and con-tinues to decrease. Therefore in the present study, the neutraliza-tion reaction (see reaction (i) in Appendix A) has been changed in

Impeller

Dip probe

Injection tube

12 3

1

2

3

Injection tube

H T

D

UV-Vis probe

Fig. 1. Experimental set-up: 0.730 l tank – T¼0.098 m – D¼0.087 m – H¼0.094 m.

0.00

0.01

0.10

1 10 100 1000

Dyn

amic

vis

cosi

ty η

(Pa.

s)

Shear rate γ (1/s)

HEC 0.12% HEC 0.25% HEC 0.50%

Fig. 2. Dynamic viscosity as a function of shear rate for HEC-water solutions.

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 2 4 6 8 10 12 14

Pote

ntia

l E (V

)

pH

IO3-I2

I3-

I -

pH*≈7.1

Fig. 3. Potential-pH diagram of water-iodine system. Iodine element total concen-tration equal to 0.014 mol/L.

J. Pinot et al. / Chemical Engineering Science 118 (2014) 94–10196

order to provide a better stability of the formed iodine. The boratebuffer has been replaced by the phosphate and the first reactiontaking place in the reaction system is:

HPO42� þHþ-H2PO4

� ðiÞ

Typical pH values used for the phosphate buffer solution are7.4opHo7.8 compared to the borate buffer solution 8.5opHo9.5. Moreover, the pH of iodine disproportionation, pHn isclose to 7 with the concentration sets used (Fig. 3). As a result, thechoice of the phosphate buffer enables to limit the disproportio-nation of iodine formed without forming it before the addition ofthe acid. Fig. 5 shows the improved stability of formed I3

� ,observed both in water and HEC-water solutions, using the newphosphate buffer.

Moreover, another reason to replace borate/ boric acid buffer byphosphate buffer resides in the fact that the conventionally-usedboric acid in the neutralization reaction has been identified as aCMR (Carcinogenic Mutagen Repro-toxic) substance and classifiedas repro-toxic category 2 in 2008 by the European Commission(European Chemicals Agency (ECHA), 2010). For that reason, itsuse in routine protocols should be avoided definitely.

2.2.3. Choice of the concentration setTo characterize micromixing in a stirred tank with a volume of

730 mL, 1.5 mL of sulfuric acid ([Hþ]¼1N) are injected to a volumeof 730 mL of solution containing iodide, iodate (stoichiometricmixture) and hydrogen phosphate ions with the following con-centrations:

½I� �0 ¼ 1:16 � 10�2mol=L

½IO�3 �0 ¼ 2:33� 10�3mol=L

½H2PO�4 �0 ¼ 0:02mol=L

½HPO2�4 �0 ¼ 0:09mol=L

)Buffer solution : pH 7:8

The sulfuric acid solution is prepared from a commercial concen-trated solution (36N). The buffered iodide/iodate solution isprepared by first dissolving, on the one side the needed amountsof powders KI and KIO3 in water. On the other side, the powdersNaH2PO4 and Na2HPO4 are dissolved in water to obtain the buffersolution to which is finally added the KI/KIO3 solution. Thissequence enables to avoid contact of iodide and iodate in acidmedium. For the preparation of HEC-water solutions, the HECpowder is dissolved (720, 000 g/mol Sigma-Aldrichs) in aqueoussolution and stirred during at least one night. For micromixingexperiments, a solution of HEC 2 wt% or 1 wt% in water isprepared, which is then added in required quantity to the bufferediodide–iodate solution in order to obtain a solution with thedesired HEC mass fraction. Several mass fractions of HEC(0–0.12–0.25 and 0.5 wt%) have been used to increase the viscosityof the solution contained in the tank.

The injected acid solution remains aqueous (without viscosify-ing agent) to avoid the hydrolysis of HEC in the acid mediumbefore injection. Indeed, in a solution of sulfuric acid ([Hþ]¼1N),the viscosity on the Newtonian plateau of HEC 0.5 wt% solutionsdecreases of more than 50% after the recording of the rheogram,which lasts 40 min (Fig. 6). Without this precaution, the injectedsolution would not have the expected acid concentration since asmall amount of acid would have been consumed implyinginsignificant results.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 200 400 600 800 1000

Opt

ical

den

sity

OD

(353

nm

)

Time (seconds)

water and borate bufferHEC 1% and borate buffer

Fig. 4. Optical density OD as a function of time in water and in HEC-water withborate buffer.

0.000.200.400.600.801.001.201.401.601.802.002.202.40

0 200 400 600 800 1000

Opt

ical

den

sity

OD

(353

nm

)

Time (seconds)

water and phosphate buffer

HEC 1% and phosphate buffer

Fig. 5. Optical density OD as a function of time in water and in HEC-water with thenew phosphate buffer.

0.01

0.1

1 10 100 1000

Dyn

amic

vis

csoi

ty η

( Pa

.s)

Shear rate γ (1/s)

HEC 0.5% HEC 0.5% in acid 1N

Fig. 6. Evolution of dynamic viscosity as a function of shear rate for HEC 0.5% in asolution of sulfuric acid 1N.

0.35

0.4

100 150 200 250 300 350

Segr

egat

ion

inde

x X

s

Injection time (seconds)

Fig. 7. Evolution of the segregation index as a function of the injection time.Experimental conditions: HEC 0.5 wt% - N¼0.83 rps.

J. Pinot et al. / Chemical Engineering Science 118 (2014) 94–101 97

For this procedure, an injection flow rate of about 0.5 ml/mn isused to inject 1.5 mL of sulfuric acid during 180 s in the tankcontaining 730 mL of reactants solution. This injection time hasbeen chosen so that macromixing does not play a role duringinjection. In order to do this, the injection time for which thesegregation index (defined in Appendix A) reaches a constantvalue, called critical injection time tcrit, has been determined. Theworst micromixing conditions such as the lowest stirring speed(N equal to 0.83 rps corresponding to 50 rpm) and the highestpercentage in HEC (0.5 wt%) have been used. The results areshown in Fig. 7. The segregation index Xs decreases with theinjection time and reaches a plateau for a critical injection time of180 s, corresponding to the sole influence of micromixing effects.This value of the critical injection time has to be determined foreach reactants concentrations set and for the worst micromixingconditions.

2.2.4. Determination of triiodide ion molar extinction coefficientin viscous medium

The extinction coefficient at 353 nm, ε353, of triiodide ions I3�

has been assessed in HEC - water solutions and found to be nearlyindependent of the composition within experimental errors(Table 3). This evaluation has been carried out by measuring theoptical density of a solution initially containing iodide ions andiodine at 353 nm with a spectrophotometer AvaSpec-3648. Theequilibrium triiodide ions concentration has been determined byusing the equilibrium constant Keq(iii) (see Eqs. (4) to (6) inAppendix A) equal to 786 L/mol at 20 1C in pure water (Palmeret al., 1984), which enables to draw the curve representing theoptical density as a function of triiodide ion concentration fordifferent HEC mass fractions (Fig. 8).

The absorption spectrum of the I2/I3� system is therefore notdisturbed by the presence of HEC. The value obtained in purewater is in good agreement with results given in the literature(ε353¼2450072000 L/mol/cm, cf. Table 4). The observed differ-ence between the values is essentially due to the diversity of theapparatuses used.

3. Preliminary results of micromixing characterization

Four solutions of different compositions were used withviscosities ranging between 1 mPa s (HEC 0 wt%) and 50 mPa.s(HEC 0.5 wt%). All the experimental data are reported inFig. 9 where the micromixedness ratio α (Appendix A Eq. (11)) isplotted with respect to the stirring speed N for different HEC masspercentages. For a given HEC wt%, a higher stirring speed inducesan increase in α, i.e. a more efficient micromixing. For a givenvalue of N, a higher HEC mass percentage, i.e. a higher apparentviscosity, induces a decrease of α, i.e. less efficient micromixing.It is also observed that α decreases sharply with an increasing HECmass fraction until 0.25 wt% but remains quasi-constant from0.25 wt% to 0.5 wt%. The experimental error on α is estimated tobe around 15%.

By using the results from Fig. 9 and the measure of torquerealized by means of a RM200 Rheomat Lamyrheology Instru-mentss, the mean energy dissipation rate ε can be evaluated at

each point which enables to plot the micromixedness rationversus the mean energy dissipation rate in Fig. 10.

The logarithmic plot in Fig. 10 shows the linearity between αand εn with a value of n almost constant, and approximately equalto 0.19 for all HEC mass fractions.

To take into account the effect of the solution viscosity,estimated in first approximation by the value on the Newtonianplateau, a correlation of the micromixedness ratio as a function ofthe stirring Reynolds number and the Schmidt number is pro-posed:

α¼ A RebScc

The mass diffusivity D considered in the Schmidt number issupposed to be unchanged by the presence of HEC and is takenequal to 10�9 m2/s, because the low concentration of long chain ofHEC macromolecules does not perturb the inter-diffusion of smallionic reactive molecules in the solution. Fig. 11 shows that theproposed correlation α¼ 1:7� 10�3 Re0:61Sc1=3 represents with afair agreement the experimental results corresponding to differentHEC mass fractions.

4. Conclusion

This study presents experimental results of a new protocoldeveloped in order to characterize mixing of viscous fluids in

Table 3Extinction coefficient of I3� at 353 nm in HEC/water solutions (T¼20 1C).

HEC mass fraction (%) 0 0.12 0.25 0.50

Extinction coefficient of I3� ions (L/mol/cm) 262007400 2570071000 252007200 249007400

Table 4Triiodide ion extinction coefficient.

Wavelength λ (nm) Extinction coefficient(L/mol/cm)

References

353 26400 (Awtrey and Connick, 1951)353 22100 (Morrison et al., 1971)353 22240 (Fournier, 1994)

25900353 23959 (Guichardon, 1996)

26060

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.00002 0.00004 0.00006

Opt

ical

den

sity

OD

(353

nm

)

Equilibrium triiodide ions concentration (mol/L)

HEC 0%

HEC 0.12%

HEC 0.25%

HEC 0.5%

Fig. 8. Optical density as a function of equilibrium triiodide ions concentration forHEC-water solutions.

J. Pinot et al. / Chemical Engineering Science 118 (2014) 94–10198

stirred tank reactors. More precisely, the Villermaux–Dushmanmethod has been adapted to the study of micromixing in HEC-water solutions by changing the neutralization reaction. The newphosphate buffer has been demonstrated to provide stable oper-ating conditions without impacting the absorption propertiesof the mixture for in-line monitoring by spectrophotometry.HEC-water solutions constitute an interesting system which maybe thereafter used to characterize non-Newtonian media byincreasing the mass fraction of HEC in water over 0.5 wt%.

However, the difficulty is then to take into account this non-Newtonian behavior of HEC-water solutions in the results analysis.

Nomenclature

Ci concentration of species i (mol/L)D impeller diameter (m)D mass diffusivity (m2/s)E potential (V)K kinetic constant (L4/mol4/s)Keq(iii) reaction (iii) equilibrium constant (L/mol)l optical path length (m)N stirring speed (rps)nj moles number of species j (mol)OD optical density (dimensionless)r reaction rate (mol/L/s)Re stirring Reynolds number (dimensionless)Sc Schmidt number (dimensionless)T internal diameter of the tank (m)Vinjection injection volume ( mL)Vtank volume of the liquid in the tank (L)Xs segregation index (dimensionless)Y selectivity towards iodine (dimensionless)[Z] concentration of species Z (mol/L)[Z]0 initial concentration of species Z (mol/L)zi charge number of ion i (dimensionless)

Greek letters

α micromixedness ratio (dimensionless)_γ Shear rate (1/s)ε Energy dissipation rate (W/kg)ε353 Molar extinction coefficient (L/mol/cm)εr dielectric constant (dimensionless)η dynamic viscosity (Pa.s)λ wavelength (nm)m ionic strength (mol/L)

Subscripts

ST total segregationPM perfectly mixed0 initial concentration before mixing

Abbreviations

HEC HydroxyethylcelluloseCMC CarboxymethylcellulosePEPPG PolyEthylenePolyPropyleneGlycolPEG PolyEthylenGlycolCMR Carcinogenic Mutagen Repro-toxicGR Grade R which means that this type of Natrosol can be

treated to provide a powder that displays fast dispersionwithout lumping when added to water

MR medium viscosity type of grade Rwt relative to weight

Acknowledgments

This work has been supported by French research NationalAgency (ANR) through project PROCIP (n1ANR-2010-CD2I-013-06).Authors want to thank the ANR for their financial support.

y = 0.0017x0.61

R² = 0.9783

0.00

0.20

0.40

0.60

0.80

1.00

50 500 5,000 50,000

α/Sc

(1/3

)

Stirring Reynolds number ReHEC 0% HEC 0.12% HEC 0.25% HEC 0.5%

Fig. 11. Micromixedness ratio α divided by Schmidt number Sc to the power of 1/3as a function of stirring Reynolds number for different HEC mass fractions.

1

10

0.5 5

Mic

rom

ixed

ness

ratio

α

Stirring speed N (rps)

HEC 0% HEC 0.12% HEC 0.25% HEC 0.5%

Fig. 9. Micromixedness ratio α as a function of the stirring speed N for differentHEC mass fractions.

1

10

0.001 0.01 0.1 1

Mic

rom

ixed

ness

ratio

α

Mean energy dissipation rate (W/kg)

HEC 0% HEC 0.12% HEC 0.25% HEC 0.5%

Fig. 10. Micromixedness ratio α as a function of the mean power rate dissipation εfor different HEC mass fractions.

J. Pinot et al. / Chemical Engineering Science 118 (2014) 94–101 99

Appendix A. Presentation of the Villermaux-Dushmanreaction

The chemical method is based on a competitive parallelreactions system named Villermaux–Dushman method (Fournieret al., 1996). The conventional first reaction is a neutralizationreaction and the second a redox reaction.

H2BO�3 þHþ-H3BO3 ðiÞ

5I� þ IO�3 þ6Hþ-3I2þ3H2O ðiiÞ

The redox reaction (ii) is fast, in the same range as themicromixing process, but is much slower than the neutralizationreaction (i).

A kinetic model for the reaction (ii) has been developed byGuichardon (Guichardon et al., 2000) and the expression of therate law can be written as:

r¼ k ½Hþ �2½I� �2½IO�3 � ð1Þ

where k, the kinetic constant, is a function of the ionic strength m:

m o 0:166 mol=L log 10ðkÞ ¼ 9:28105�3:664ffiffiffim

p

m40:166mol=L log 10ðkÞ ¼ 8:383�1:5112ffiffiffim

p þ0:23689m ð2Þwhere m is defined as:

m¼ 12

∑i ¼ all species

Ciz2i ð3Þ

with Ci the molar concentration of ion i and zi its charge number.The principle for the measure of micromixing consists in

adding in stoichiometric defect a small quantity of sulfuric acidto a premix solution containing iodide I� and iodate IO3

� in aH2BO3

�/H3BO3 buffer. In perfect mixing conditions, the injectedacid is only consumed by the first reactionwhich is infinitely fasterthan the redox reaction. Under poor mixing conditions, local over-concentrations of acid can react with iodide and iodate surround-ing ions to yield iodine I2 after complete consumption of borateion. Formation of iodine can then be considered as a measure ofthe segregation state of the fluid.

The formed iodine can further react with iodide ions I� to yieldtriiodide ions I3� according to the quasi-instantaneous equilibrium.

I2þ I�⇌I�3 ðiiiÞ

Keq iiið Þ ¼½I�3 �

½I2�½I� �ð4Þ

with Keq(iii) the equilibrium constant (L/mol), as a function oftemperature T (Palmer et al., 1984):

log 10ðKeqðiiiÞÞ ¼555T

þ 7:355�2:575log 10T ð5Þ

The concentration of the triiodide ions can be easily measured byUV–vis spectrophotometry at 353 nm. By application of the Beer–Lambert law, the triiodide ions concentration is evaluated:

½I�3 � ¼ OD353 nm

ε353 � lð6Þ

where OD denotes the optical density or absorbance, ε353 themolar extinction coefficient of I3� at 353 nm and l the optical pathlength.

Then, as iodide ions I� are introduced in large excess, theirconcentration can be considered as quasi-constant during thereaction. So, by writing the expression of the equilibrium constantof reaction (iii), iodine concentration can finally be deduced as:

½I2� �½I�3 �

KeqðiiiÞ½I� �0ð7Þ

To quantify the micromixing quality, segregation index Xs andmicromixing ratio α concepts are introduced. Xs is defined as theratio between Y and YST:

Xs ¼YYST

ð8Þ

Under perfect micromixing conditions, Xs is equal to 0 whereas intotal segregation, Xs equal to 1.Y is defined as the ratio betweenthe number of acid moles consumed by the reaction (ii) and thetotal injected number of acid moles:

Y¼ 2ðnI2þ n�I3 Þ

nHþ ;0¼ 2Vtankð½I2�þ½I�3 �Þ

Vinjection½Hþ �0ð9Þ

With YST defined as the value of the ratio Y in total segregation.

YST ¼6½IO�

3 �06½IO�

3 �0þ ½H2BO�3 �0

ð10Þ

The micromixedness ratio α is then defined as the ratiobetween the perfectly mixed volume VPM and the totally segre-gated volume VST:

α¼ VPM

VST¼ 1�Xs

Xsð11Þ

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