mean drops size in the presence of cetyl trimethyl ammonium bromide in horizontal mixer settler

Research article

Mean drops size in the presence of cetyl trimethylammonium bromide in horizontal mixer settler

Payman Davoodi-Nasab,1 Hossein Abolghasemi,1,2* Jaber Safdari3 and Maliheh Raji-Asadabadi1

1School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran2Oil and Gas Center of Excellence, University of Tehran, Tehran, Iran3Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, Tehran, Iran

Received 18 December 2012; Revised 1 May 2013; Accepted 6 May 2013

ABSTRACT: The mean drop size of toluene/water dispersion in the presence of cetyl trimethyl ammonium bromide(CTAB) as a cationic surfactant has been studied in a horizontal mixer settler. Two 45�-pitched blade turbine impellerswith four blades on a shaft were used to have completed mixing. Additionally, the influences of hydrodynamic parameterssuch as impeller agitation speed and dispersed phase volume fraction on the drops size were investigated. The resultsindicate that the presence of CTAB leads to a decrease in D32 by about 46%, averagely. Furthermore, increase in theimpeller speed from 450 up to 650 rpm causes D32 to reduce by about 30%, and the decreasing rate of D32 diminisheswith increasing impeller speeds. Increase in the dispersed phase volume fraction gives rise to increase in the drops size.Finally, in order to predict the mean drop size, new modified correlations were provided, wherein the influence ofCTAB concentration was introduced as a new parameter. © 2013 Curtin University of Technology and John Wiley& Sons, Ltd.

KEYWORDS: mixer settler; mean drop size; CTAB; impeller speed; dispersed phase volume fraction

INTRODUCTION

Nowadays, liquid–liquid extraction is one of the mostselective and complex separation technologies amongall of the mixing operations, which are typically usedin chemical, mining, and petroleum industry.[1–4] Inaddition, it is more cost-effective to achieve high purityof products in comparison with other separationprocesses such as distillation.[5]

Liquid–liquid extraction is based on contact betweentwo immiscible liquids, which one of them is calledsolvent and the other one is extractant.[6] The commontypes of commercially available extraction equipmentsare categorize into three groups: column extractors,centrifugal extractors, and mixer-settler equipment.The choice of the type of extractor depends on theapplication. Mixer settlers are of the oldest extractionunit operations that have some advantages such asquick and easy start-up, high efficiency, and facileoperating and repairing over the other kinds of

extractors.[5] In mixer settlers, one phase is dispersedin form of drops in the other phase by agitation of animpeller in mixing chamber in order to enhance theinterfacial area.[2,4,7]

Drops size in liquid–liquid dispersions determinesthe interfacial area between immiscible phases andaffects mass transfer rate. As a result, mass transfercoefficients and dimensionless numbers such asSherwood number can be obtained by studying the dropsize distribution. In this way, accurate knowledge of thedrop size is required to optimum design of extractionequipments.[8,9] Drop size distribution results from theinteraction of two opposite processes: drops breakage andcoalescence.[10–13] When the agitation begins, breakupand coalescence processes occur at the same time, andcompetition between them continues until the systemreaches to the steady state. At steady state, the dropsbreakage and coalescence rate is equal, and drops sizeremains constant.[10,14]

To study drop size in various applications, there aredifferent definitions for mean diameter. Among all ofthem, Sauter mean diameter (D32) is extensively usedin characterization of liquid–liquid dispersions becauseit links the dispersed phase area to its volume andconsequently determines mass transfer and chemical

*Correspondence to: Hossein Abolghasemi, School of ChemicalEngineering, College of Engineering, University of Tehran, Tehran,Iran. E-mail: [email protected]

© 2013 Curtin University of Technology and John Wiley & Sons, Ltd.Curtin University is a trademark of Curtin University of Technology

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERINGAsia-Pac. J. Chem. Eng. 2014; 9: 93–104Published online 1 July 2013 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/apj.1749

reaction rates. D32 is generally defined in the form ofthe following equation:

D32 ¼

Xki¼0

nid3i

Xki¼0

nid2i

(1)

where di is the drop diameter and ni is the number ofdrops with the diameter of di.

[15]

Numerous investigators studied the drops size ofliquid–liquid dispersions and derived variouscorrelations to predict Sauter mean drop diameter inagitated vessels. Some of these correlations aresummarized in Table 1. In most of the works, Hinze–Kolmogorov’s theory was used for correlating theexperimental data. According to this theory, theenergetic eddies with smaller diameters than dropsdiameter may lead to drop breakage, and the maximumstable drop size in the emulsions is related to the rate ofaverage turbulent energy dissipation and impellerspeed with the exponent of �0.4 and �1.2,respectively.[16] According to Eqn (1), the Sauter meandrop size depends on drop size distribution. On theother hand, Sprow[17] showed that D32 is directlyproportional to the maximum stable drop diameter indispersion stems from balance between the deformingand restoring forces acting on the surface of drops. Thisdirect proportionality has been reported by othersubsequent investigators, and various correlations havebeen proposed for D32 on the basis of thisassumption.[15,18–20] Hence, D32 is related to the Webernumber with exponent equal to �0.6 as follows:

D32

DI/ We�0:6 (2)

where We is the Weber number, rc is the density ofcontinuous phase, N is the impeller speed, DI is theimpeller diameter, and s is the interfacial tension.In the majority of correlations for prediction of

Sauter mean drop size, the relation between drop sizeand dispersed phase content in the dispersion waspresented in the form of an increasing linear or a powerfunction, which reflects that with increasing dispersedphase volume fraction or holdup, the rate ofcoalescence increases and drops become larger.[26,29]

Thus, the predicted equations for Sauter mean diameteroften have been proposed in the following form:

D32

DI¼ C1 1þ C2’ð ÞWe�0:6 (3)

where C1 and C2 are constants and ’ is the holdup ordispersed phase volume fraction in the case of batchor continuous systems.

The mean drop size mainly depends on twoimportant parameters: (1) mixing process conditions,which include impeller type, geometry of impellerand mixing chamber, impeller location, agitationspeed, and dispersed phase volume fraction; and (2)physical properties of the system such as interfacialtension, viscosity ratio, and density.[6,24,30,31]

At constant hydrodynamic conditions, drops sizegenerally is affected by interfacial tension of thesystem. Interfacial tension usually alters in the presenceof surface active agents (surfactant) and solutes. Mostof the time, these materials unintentionally appear insystems in the form of pollutions, lubrications, anddetergents. In addition, some of the surfactants aredeliberately applied to industrial processes forstabilizing the emulsions and suspensions, owing totheir applications in lubrication and detergentindustries.[4,22,32] Surfactants can locate at the surfaceof drops and consequently change the interfacialtension and equilibrium drops size. There is a largeamount of work in the literature concerning the dropssize distribution of liquid–liquid dispersions containingsurfactant. The effects of nine types of surfactants infive different systems on mean drop size wereinvestigated by Lee and Soong.[21] They claimed thatadding a trace amount of surfactants into a pure systemleads to considerable reduction in interfacial tension,which results in smaller drops size compared with thepure system. Skelland and Kanel[33] examined thesimultaneous influence of surfactant and mass transferdirection on the mean drop size. Ban et al.[34]

investigated the relation between surfactant masstransfer and drop breakage and coalescence in fiveliquid–liquid systems. Tcholakova et al.[11]

investigated the effect of ionic strength of the aqueoussolution and five types of surfactant on the mean dropsize in the bean oil in water dispersion. The effects ofconcentrations and HLB values of eight non-ionicsurfactant types on drops size of octane in wateremulsion have been studied by Golemanov et al.[35]

Maaß et al.[32] investigated the influence of thedispersed phase fraction on the evolving drop sizedistribution using polyvinyl alcohol (PVA). Theyapplied PVA concentrations around three timeshigher than the critical micelle concentration(CMC) in order to hinder the coalescencecompletely. They found that drop size enhancementis a result of turbulence hindering.Cetyl trimethyl ammonium bromide is an eco-

friendly and nontoxic cationic surfactant, which issoluble in water and readily soluble in alcohol. Itis of great importance in many industrial andmedical applications, especially in detergent anddisinfector manufacturing. Furthermore, this typeof surfactant has the potential for being used inprotein electrophoresis because of its positivecharge.[36]

P. DAVOODI-NASAB ET AL. Asia-Pacific Journal of Chemical Engineering94

© 2013 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2014; 9: 93–104DOI: 10.1002/apj

Table

1.Su

mmaryofso

meco

rrelationsformea

ndropsize

inliq

uid–liq

uid

dispersions.

Investigators

Chemical

system

and

impellertype

Correlatio

ns

Phy

sicalprop

ertiesand

operatingcond

ition

s

r d(g/cm

3)

m d(m

Pas)

s(m

N/m

)N(rpm

)’

Khakp

ayet

al.[4

]Toluene

ineater

dispersion

andaniline

asasurfactant/spiral

impeller

D32 DI¼

0:45

31þ0:61

2’ð

Þ�1þ22

15:137

VI

D32 DI

�� 0:8

28

! We�

0:603

0.87

0.57

5–36

900–

1200

0.4–

0.5

D32 DI¼

0:46

71þ0:22

4’ð

Þ�1þ27

176:9V

ID

32 DI

�� 1:9

26

! We�

0:509

El-Ham

ouz

etal.[2

1]

Silicone

oilin

water

dispersion

andSLESas

asurfactant/six

flat

bladed

turbine

D32 DI¼

0:05

31þ4:42V0:79

I

�� 0:6 W

e�0:6

0.97

10.49

–350

0.21

–47

85–2

80<0.00

2

Lee

and

Soo

ng[22]

Fiveliq

uid–

liquid

system

sandnine

surfactants/sixflat

bladed

turbine

D32 DI¼

0:05

Cs1þ2:31

6’ð

Þ�We�

0:6Fr�

0:13

DI

DT�� 0

:75

0.78

7–1.21

33.3–

4613

.6–4

2.5

0–95

00.02

–0.2

Chatzi

etal.[2

3,24]

Styrene

inwater

dispersion

andPVA

asa

surfactant/six

bladed

turbine

D32 DI¼

0:0561þ10

:97’

ðÞW

e�0:6

0.87

9,0.90

10.45

9,0.73

7.4,

11.5

150–

300

0.01

–0.03

D32 DI¼

0:04

5�0

:003

ðÞW

e�0:6

3.8–

24.1

200–

300

0.01

Singh

etal.[1

8]

Dilu

teph

osph

oricacid

inamixture

ofn-paraffin,

TBPandD2E

HPA,and

sorbitanmon

ooleateas

asurfactant/fou

rbladed

topshroud

edturbine

with

trapezoidalblades

D32 DI¼

2:94

6�10

�6We�

0:85125

�1þ0:39

2’þ3:24

35’2

��

exp0:43

02t

ðÞ

0.85

94.01

Organic

phase

surface

tension:

26.7

100–

150

0.2–

0.5

Aqu

eous

phase

surface

tension:

19.4

Khakp

ayet

al.[2

5]

Toluene

inwater

dispersion

andSDSas

asurfactant/spiralim

peller

D32 DI¼

0:56

1þ1:55

’ð

ÞWe�

0:52

0.87

0.57

4–36

900–

1200

0.34

–0.44

(Con

tinues)

Asia-Pacific Journal of Chemical Engineering MEAN DROP SIZE: EFFECT OF CETYL TRIMETHYL AMMONIUM BROMIDE 95


Table

1.(Continued

)

Investigators

Chemical

system

and

impellertype

Correlatio

ns

Phy

sicalprop

ertiesand

operatingcond

ition

s

r d(g/cm

3)

m d(m

Pas)

s(m

N/m

)N(rpm

)’

Desno

yer

etal.[2

6]

NiCl 2in

(mixture

oftributyl

phosph

ateand

Solvesso15

0)

D32 DI¼

0:28

1þ0:29’

ðÞ W

e�0:6

1.02

0.94

713

.461

0–90

00.1–

0.4

HClin

(mixture

oftributyl

phosph

ateand

Solvesso15

0)/fou

rpitchedblade

D32 DI¼

0:14

1þ0:48’

ðÞW

e�0:6

1.05

1.06

810

0.1–

0.6

Cou

laloglou

and

Tavlarides[27]

Mixture

ofkerosene

and

dichlorobenzenein

water

dispersion

/six

bladed

RT

D32 DI¼

0:08

11þ4:7’

ðÞW

e�0:6

0.97

11.3

4319

0–31

00.02

5–0.15

Pacek

etal.[1

5]

Chlorob

enzene

inwater

dispersion

D32 DI¼

0:05

21þ22:8’

ðÞW

e�0:6

1.10

6~1

33.4

180–

480

0.00

5–0.1

NaC

lin

water

dispersion

/six

bladedisc

turbine

D32 DI¼

0:02

21þ23:3’

ðÞ W

e�0:43

1.10

233

.8

Wangand

Calabrese

[28]

Silicone

oilsin

water,

methano

landtheir

solutio

ns/six

bladed

RT

D32 DI¼

0:05

31þ0:97VI0:79

ðÞ0:

6We�

0:6

0.83

4–0.98

60.81

–459

0.21

–47

85–280

<0.00

2

Sprow

[17]

Iso-octane

in1%

NaC

lin

water

solutio

ndispersion

/six

bladed

RT

D32 DI¼

0:05

24We�

0:43

0.69

20.51

41.8

250–

2000

0–0.01

5

Note:In

theequatio

nof

Singh

etal.[1

8] ,tisthemeanresidencetim

eandVIistheviscosity

number.RT,R

ushton

turbine;SLES,sodiumLaurethsulfate;PVA,polyvinylalchohol;T

BP:tributyl

phosphate;

D2E

HPA,d

i-2-ethylhexylphosphoric

acid;SDS,sodium

dodecylsulfate.



Despite the importance of CTAB in industrialapplications as a nontoxic and eco-friendly surfactant,there is lack of work on drop size measurement in thepresence of CTAB. Hence, mean drop size in thepresence of CTAB is investigated in the current study.In addition, a new modified correlation is proposedto predict the drop size, and for the first time theconcentration of surfactant is introduced to thepresented correlation as an independent parameter. Itshould be noted that in this work we applied two seriesof four-pitched blade turbine impellers with 45�inclined blades on a shaft that have not been used inthe mixer settler by other investigators for this purposein the identical chemical system to ours.

EXPERIMENTAL

Equipments

All the experiments were performed in a single stagehorizontal mixer settler (product of Fisher Co.,Germany), which is schematically shown in Fig. 1.The dispersed and continuous phases were pumped tothe mixer from feed tanks by means of two similardosing pumps. The accuracy of the pumps was �0.01cm3 s�1. In order to adjust the flow rates of the phases,both pumps were equipped with digital flow ratecontrollers. Before the experiments, flow ratecontrollers were calibrated, and calibration was verifiedregularly before and after each run using a chronometerand graduated cylinder. To produce dispersion, twoseries of four-pitched blade turbine impellers with 45�inclined blades on a shaft were employed in allexperiments. The used pitched blade impellers weredown-pumping, which are more conventional than

up-pumping ones. The geometry characteristics ofexperimental apparatus are given in Table 2. Impelleragitation speeds were determined by digital variablerotation motor.

Chemical materials

The studied system was oil in water emulsion whereinthe dispersed phase was toluene (Merck Co.) and thecontinuous phase was distillated water. The physicalproperties of the used material are presented in Table 3.To avoid any interaction between two phases duringthe experiments, both phases were initially saturatedwith each other. CTAB (C19H42BrN) was used assurfactant, which was purchased from Aldrich Co.

Figure 1. Schematic diagram of the used mixer settler.

Table 2. The specifications of mixer settler.

Material Glass

Mixer volume (cm3) 200Mixer inside diameter (cm) 4Mixer height (cm) 18Impeller type 4-pitched blade turbineImpeller diameter (cm) 2.8Settler volume (cm3) 250Settler diameter (cm) 5

Table 3. The physical properties of the used system.

MaterialDensity (kg/

m3)Viscosity(mPa s)

Purity(%)

Distillatedwater

996 0.96 >99

Toluene 870 0.57 >99



The interfacial tension of the system was measured bythe Wilhelmy plate method using digital Krüsstensiometer K10T (Hamburg, Germany) with theaccuracy of �0.0001Nm�1. Figure 2 demonstratesthe interfacial tension of toluene in water dispersionin the presence of different concentrations of CTAB.

Experimental procedure

In order to study the mean drops size in the presence ofcationic surfactant, two series of experiments wereperformed. In the first series, the mean drops size wasmeasured at five different impeller speeds and fourdifferent dispersed phase volume fractions. At thesecond series, the mean drops size was measured atthe same conditions of the first series, albeit with thepresence of four different surfactant concentrations.The operational ranges of experimental parameters aresummarized in Table 4.At the beginning of the experiments, the mixer and

settler were filled out by the continuous phase in orderto prevent adhesion of the dispersed phase to the mixerand settler walls. Then, the oil phase was pumped to thesystem, and the agitator was activated to disperse it.For determining the minimum agitation speed forcomplete liquid–liquid dispersion, we first applied thecorrelation reported by Skelland and Ramsay[37] as aninitial estimation, and then it was obtained using thevisual approach. At this agitation speed (about350 rpm), the dispersed phase was no longer presentedas a distinct layer, such as a light oil phase collectedabove an aqueous solution, but became completelydispersed in the form of drops throughout thecontinuous phase. In order to ensure forming a

homogenous dispersion, the lowest impeller speedwas selected, which was higher than the minimumdispersion speed. In the mixing chambers, the impellerReynolds number determines the flow regime. On thebasis of the work of Rao and Brodkey,[38] the localisotropic turbulence can be assumed for the shear flowsnear the impeller region when the Reynolds number ismore than 300. According to the impeller speeds(450 up to 650 rpm), the impeller Reynolds numberwas in the range of 1.9� 104 up to 2.8� 104. Inaddition, Coulaloglou and Tavlarides[27] reported thatwhen tank Reynolds exceeds 104, the flow can beconsidered isotropic turbulent. In this work, tankReynolds varies in the range of 2.7� 104 up 4� 104.Furthermore, the used impeller in this study was a highshear impeller, which produced combined radial andaxial flow patterns in the mixer and increased theintensity of turbulence. Consequently, it can be assertedthat the flow regime was always turbulent. After formingthe dispersion in the mixer, it was separated into both oiland aqueous phases in the settler. At steady state, thedrop size was measured at the output of the mixer. Itshould be noted that the drops were more influencedby the breakage phenomena in mixer rather thancoalescence in settler because the presence of settlerled to an increase in resident time of drops in mixerand affected both their breakup and coalescence. Inaddition, the steady state has been attained bycontrolling the interfacial surface between phases inthe settler by using a level controller. In this way, theequilibrium drop size with uniform distribution has beenmeasured in the mixer outlet. For this purpose, weemployed a video recording technique by using a digitalcamera (FUJIFILM, FINEPIX HS10 model). Theshutter speed of the camera was 1/4000 s, and it waslocated outside the vessel near the wall. It is worthnoting that the best position of camera was determinedby test trials before the experiments. In this method,several photos of drops in the outlet tube of themixer were taken. After that, the high quality imageswere selected in each experiment and analyzed byAutodesk-AutoCAD 2012 software. Because thediameter of the mixer outlet tube was defined(13.7mm), the real sizes of the drops in these imageswere determined by comparing the size of drops withthe diameter of the mixer outlet tube as a reference withhigh accuracy. In addition, the maximum error of dropmeasurement was �0.0001mm, and more than 300drops were measured for each run to assure the statisticalsignificance of the calculated mean drop size. Also,parallax errors were reduced by determining severalpoints in the photos. A sample of the taken photographsis shown in Fig. 3.In turbulent agitated liquid–liquid dispersions, inertia

forces, which tend to deform the drops, influence theoutward stretching and shape of drops in the bulkliquid. Drops in the mixing chamber are usually in

Figure 2. Interfacial tension vs CTAB concentration.

Table 4. The operational ranges of the experimentalparameters.

Parameter Values

Impeller speed (rpm) 450, 500, 550, 600, and 650Dispersed phase volumefraction

0.202, 0.253, 0.299, and0.315

CTAB concentration (wt%) 0.001, 0.003, 0.005, and0.007



spherical or elliptical shapes. In order to determine theequilibrium diameter of elliptical drops, the horizontaldiameter (DH) and vertical diameter (DV) must bemeasured.[4,39] In this way, for calculating the area ofan elliptical drop, we used the following equation:

A

Ae¼ 1

2E2=3 þ 1

E1=3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiE2 � 1

p ln E þffiffiffiffiffiffiffiffiffiffiffiffiffiffiE2 � 1

p� � (4)

E ¼ DH

DV(5)

where A is the area of an elliptical drop, Ae is the equaldrop area, and E is the drop inertia. The drop inertia is adimensionless parameter, which is the ratio of DH toDV. In fact, this parameter presents a proportion of dropstretching in vertical direction to that in horizontaldirection. Then, the equal drop diameter (De) wasobtained from Eqn (6):

De ¼ffiffiffiffiffiffiffi4Ae

p

r(6)

Finally, the Sauter mean diameter was calculated byEqn (1).[4] Dispersed phase volume fractions werecalculated by the following formula:

D32

DI¼ 0:053 1þ 4:42V0:79

I

� �0:6We�0:6 (7)

where ’d is the dispersed phase volume fraction, Qd isdispersed phase flow rate, and Qc is the continuousphase flow rate. To verify the integrity and repeatabilityof the results, each run of the experiments was repeatedthree times. In all experiments, it was attempted to keepthe temperature of the laboratory constant at 25� 1 �C.

For this purpose, the environment temperature wascontrolled by an air conditioner. The liquid systemwas in thermal balance with the environment becauseno reaction occurred to change the temperatureand the only source of energy input in the system wasthe impeller agitation, which could not appreciablychange the temperature. Hence, the temperature wasconsidered constant during the experiments.

Surfactant solution preparation

To prepare the surfactant solution with the desiredconcentration, a given amount of CTAB powder wasweighted by a digital balance with a �0.0001-gaccuracy. Then, the powder was added to the aqueousphase and agitated for about 15min. To preventthe aqueous phase foaming, the agitation speed wascontrolled. Finally, the prepared solution was pumpedto the system in the way mentioned earlier.

RESULTS AND DISCUSSION

Effect of surfactant concentration

Figure 2 demonstrates the influence of CTAB con-centration on the interfacial tension of toluene/waterdispersion. As shown in this figure, introduction ofCTAB into the system leads to significant decrease ininterfacial tension, especially at low concentrations.The addition of 0.007wt% of CTAB to the systemreduces the interfacial tension by about 70%. Accor-ding to Fig. 2, the CMC is about 0.002wt% of CTABbecause for higher concentrations, interfacial tensionreduces gently and shows an independent tendency.Figure 4 presents the influence of CTAB concen-

tration on D32 at five various impeller agitation speeds.As the drop size variation with CTAB concentrationwas similar in different dispersed phase volumefractions, only the figures correspond to the maximumand minimum dispersed phase volume fractions arepresented. According to this figure, increases in CTABconcentration up to 0.007wt% gives rise to a 45.8%decrease in the Sauter mean drop size. The reason isthat the presence of surfactant in the system causedto eliminate insignificant effect of coalescence in themixing chamber. Chen and Lee[40] showed that insolutions containing surfactant, the interfacial tensionbetween two drops would be higher because of thestretching of the interface. The surface convectionmoves adsorbed surfactant molecules on the dropsurface to the outside surface of the two drops, wherethey accumulate, further reducing the interfacialtension there. Consequently, coalescence diminishes,and decrease in interfacial tension leads to more dropbreakage. Based On the basis of turbulent breakuptheory of Hinze–Kolmogorov, Weber number is the

Figure 3. Sample of taken picture in the mixeroutput.



ratio of deforming force due to turbulence to restoringforce due to interfacial tension. The presence ofsurfactant reduces the interfacial tension, which givesrise to the decrease in restoring force. Hence, the valueof Weber number and consequently breakup of dropsin the system increases, which leads to reduction indrops size. In addition, according to Fig. 4, there is alsoa critical concentration above which the decreasing rateof D32 shows an independent trend against CTABconcentration variation. It is observed that the criticalconcentration of CTAB for drop size is close to thecritical concentration of CTAB for interfacial tension.This fact confirms the direct relation between drop sizeand interfacial tension. For higher concentrations thanCMC, D32 is mainly affected by dispersed phasevolume fraction and impeller agitation speed. Theseresults are in line with the results of Khakpay et al.[4]

Effect of impeller agitation speed

Figure 5 exhibits the influence of impeller agitationspeed on D32 at four different dispersed phase volumefractions and two CTAB concentrations. For differentCTAB concentrations, the curves corresponding tothe variation of D32 vs impeller speed had the sametrends and were close to each other. Hence, the curvesin Fig. 5 were plotted just for 0 and 0.007wt% ofCTAB. The results show that D32 decreases withincreasing impeller agitation speed. Indeed, increasein impeller speed intensifies the drop breakage andleads to reduction in D32. For constant concentrationof CTAB, increase in impeller speed from 450 to650 rpm results in averagely 29.8% decrease in D32.As mentioned before, D32 depends on impeller speedby a power law function. For the system withoutsurfactant, the exponent of the power function betweenD32 and impeller speed is averagely equal to �1.204.As can be seen, when CTAB is added to the system,the exponent increases up to averagely �0.894. Hence,the presence of CTAB in the system reduces thedecreasing rate of D32 with agitation speed.Figure 6 presents the effect of impeller agitation speed

onD32 for different dispersed phase volume fractions for0 and 0.007wt% of CTAB in a logarithmic diagram.When D32 was plotted vs impeller speed in logarithmicform, it resulted in a linear function. The obtained resultsare similar with the reported results of Desnoyer et al.[26]

Figure 6 shows that the slopes of the lines increasewith increasing dispersed phase volume fraction.Increase in dispersed phase volume fraction leads toincrease in the content of the dispersed phase in themixer. Hence, the collision rate of a drop with otherdrops increases, which promotes coalescence and resultsin forming larger drops. In addition, the collision ofdrops with impeller blades and mixer wall increases withincreasing dispersed phase volume fraction. A probablereason is that the number density of drops in the mixer

Figure 4. The influence of CTAB concentrations on D32:(a)ϕd = 0.315 and (b) ϕd=0.202. This figure is available incolour online at www.apjChemEng.com.

Figure 5. The effect of impeller agitation speed on D32: (a) φd = 0.315, (b) φd=0.299, (c) φd=0.253, and (d) φd=0.202. This figure is available in colour online at www.apjChemEng.com.



increases with increasing dispersed phase volumefraction (at a constant impeller agitation speed) and thedistances between drops and mixer wall reduce in thissituation. Therefore, the decreasing rate of D32 withimpeller speed (slopes of the lines in Fig. 6) increaseswith increasing dispersed phase volume fraction. Similarresults have been reported by Zaheri et al.[41]

Effect of dispersed phase volume fraction

Figure 7 displays the influence of dispersed phasevolume fraction on D32 for five different impellerspeeds and two CTAB concentrations. As mentionedbefore, for each CTAB concentration, the curves hadthe same trends, and drops size was close together.Hence, the curves in Fig. 7 were plotted for 0 and0.007wt% of CTAB. The results indicate that anincrease in dispersed phase volume fraction gives riseto an increase in D32. As discussed in the previoussection, this behavior is mainly because of the increasein drops coalescence possibility. By plotting D32 vs ’d

(in constant CTAB concentration) for five differentimpeller speeds, it can be found that D32 depends on’d in the form of a linear function with positive slope.Additionally, the slopes of these curves diminish withincreasing the impeller speed. As a result, increase inagitation speed leads to the decrease in the effect ofdispersed phase volume fraction on drop size.The positive slope of the linear function of D32

against ’d presents the increasing rate of D32 withdispersed phase volume fraction. For the systemwithout CTAB, the enhancement rate of the D32

decreases from 1.413 to 0.727 when the impellerspeed increases from 450 up to 650 rpm. Addition ofCTAB into the system causes the enhancement rateof D32 to reduce 19–32% for different concentrationsof CTAB. The same results have been reported byDesnoyer et al.[26]

Figure 7. The influence of dispersed phase volume fraction on D32: (a) N=450 rpm, (b) N=500 rpm,(c) N=550 rpm, (d) N=600 rpm, and (e) N=650 rpm. This figure is available in colour online atwww.apjChemEng.com.

Figure 6. Logarithmic diagram of impeller speed vs D32: (a)without CTAB and (b) with 0.007wt% CTAB. This figure isavailable in colour online at www.apjChemEng.com.



As discussed in the next section, the addition ofCTAB to the system amplifies the drops breakage. Thisintensification decreases the increasing rate of dropscoalescence corresponding to the increase of thedispersed phase volume fraction.

CORRELATION OF SAUTER MEAN DROP SIZE

Sauter mean drop size in clean systemwithout CTAB

In order to present a new correlation for prediction ofD32, we considered the following form of formula forthe clean system:

D32

DI¼ a 1þ b’dð ÞWen (8)

where a, b, and n are constants. This equation is similarto Eqn (3) but includes the Weber exponent as a fittingparameter. In fact, the Weber exponent did not set to�0.6 in this equation.To calculate the constants, we applied the least

square technique method using the ‘DataFit software’version 9.0.59. The best data correlated form for cleansystem was as follows:

D32

DI¼ 0:057 1þ 0:9’dð ÞWe�0:593 (9)

According to the correlation, D32 is related to thedispersed phase volume fraction in the form of a linearfunction (as it was predicted by other investigators). InEqn (9), the exponent of the Weber number is �0.593,which is close to �0.6, which is in conformity withHinze–Kolmogorov’s theory. To test the correlationaccuracy, we calculated the average absolute relativedeviation (AARD) as follows:

%AARD ¼ 1NE

XMi¼1

D32ð Þi; exp � D32ð Þi;calD32ð Þi; exp

��

� 100 (10)

where NE is the number of the experiments, (D32)i,expis the experimental measured D32, and (D32)i,cal is thecalculated D32 from Eqn (9). The %AARD and R2 valuefor this correlation were measured to be about 0.96%and 0.99, respectively. This shows that the correlationis in good agreement with our experimental data andhas sufficient accuracy.

Sauter mean drop size in the presence of CTAB

For the system containing CTAB, we also used thefunctional form of Eqn (8). For each concentration ofCTAB, the experimental data were correlated with high

accuracy, and the results of the calculations werecompared with the correlation of the clean system. Itwas found that the presence of CTAB in the systemled to some deviations from the Hinze–Kolmogorov’stheory. In fact, the addition of CTAB into the systemcaused the reduction in the Weber exponent and theunsteady change in the proportional constant (a) andthe empirical constant of the dispersed phase volumefraction (b) in the correlations. Hence, the aforesaidfunctional form was not appropriate enough to predictthe drop size for the systems containing surfactant.In order to account the effect of CTAB concentration

on the mean drop size, we introduced CTAB concen-tration as a new parameter into our correlation andpresented a new correlation for the system with CTABin the following general form:

D32

DI¼ a 1þ os

pð Þq 1þ b’dð ÞWen (11)

where a, b, n, p, and q are the numerical constants andthe os is the surfactant (CTAB) weight fraction. Theconstants were calculated, and the followingcorrelation was achieved:

D32

DI¼ 0:0514 1þ os

0:586� �

1þ 1:227’dð ÞWe�0:58

(12)

This correlation was acquired by applying 85% ofrandomly selected data between minimum andmaximum values, and the other 15% rested data wereused to test the accuracy of the correlation. In thismethod, 15% rested data were replaced in the proposedcorrelations, and %AARD was measured by comparingthe calculated and experimental D32. A fair comparisonof correlations with each other is not always possiblebecause of the differences in operating conditions andthe studied range of variables. However, in this way,the accuracy of the proposed correlation was evaluatedby using the experimental data obtained in the sameoperating conditions of correlated data. The R2 valueand the %AARD for this correlation were measuredabout 0.96% and 5.46%, respectively. For the 15%rested data, %AARD was about 5.02%. These %AARDvalues demonstrate that the proposed correlation havehigh accuracy. According to Eqn (12), addition ofsurfactant into the system influences both the newindependent proposed parameter (os) and Weberexponent (as a result of the decrease in interfacialtension). Because the Weber value has the prominenteffect on drop size, D32 diminishes with increasing thesurfactant concentration in the correlation, which is inline with the obtained results in the previous sections.In fact, introducing the new independent parameter(os) causes that the general form of the presented



correlation to have sufficient agreement with the Hinzetheory. In this way, the Weber exponent is still closeto �0.6, which was predicted by Hinze. To verify theHinze theory, the exponent of Weber number wassupposed exactly equal to �0.6, and the other constantswere recalculated by using 85% of our experimentaldata. By appointing the exponent of the Weber numberequal to �0.6, the other constants showed smallvariations. Hence, the new correlation was attained inthe following form:

D32

DI¼ 0:052 1þ os

0:529� �

1þ 1:239’dð ÞWe�0:6 (13)

The R2 value and %AARD of Eqn (13) weremeasured to be 0.96% and 5.56%, respectively. Thesevalues are indicative of good compatibility of thecorrelation with the Hinze theory and its highaccuracy. Figure 8 shows the experimental D32 vscalculated D32 from correlations. It shows that thepoints are close to the bisector line, which confirmsthat the correlations have a satisfactory agreementwith the experimental data.In this work, for the first time, we proposed a

new correlation that is able to indicate the effect ofsurfactant on drop size as a new independentparameter. This correlation can be used to predictdrop size in a system containing differentconcentrations of surfactant and also for a puresystem by assigning the value of (os) equal to zero(os = 0). Also, it can be applied for chemicalsystems with similar physical properties andsurfactants with similar structures to ours. Also, thegeometry of the mixing unit and impeller are soimportant, because the impeller type and presenceof the settler have fundamental effects on the dropsformation and size. In the case of a clean system,the presented correlation was compared with

Sprow[17] and Wang and Calabrese[28] correlations,which were close to our proposed correlation indensity, viscosity, and interfacial tension. Thecalculated %AARD values for each of them wereabout 25% and 26%, respectively. Also, in the caseof a system containing various concentrations ofCTAB, the presented correlation was comparedwith Lee and Soong[22] and El-Hamouz,[21] andthe calculated %AARD values for each of themwere about 24% and 35%, respectively. The othercorrelations in Table 1 show more deviations, whichare related to their physical properties and operatingconditions, impeller type, and surfactant structurecompared with this study.

CONCLUSION

In this paper, Sauter mean drop size of the toluene/water liquid–liquid dispersion in the presence of CTAB(nontoxic cationic surfactant) was investigated, and theobtained results are as follows:

• Addition of CTAB into the system caused intensedecline (about 70%) in interfacial tension of thesystem and averagely 46% decrease in the meandrop size. This is related to the increase in dropbreakage and decease in drop coalescence, whichresulted in smaller drops, especially at lowconcentrations. For the low concentrations ofCTAB (less than 0.002wt%), the mean drops sizedepended on the CTAB, whereas for higherconcentrations of CTAB, the mean drop sizebecame independent of CTAB concentration andwas mainly affected by impeller speed anddispersed phase volume fraction.

• Increase in the impeller speed from 450 up to650 rpm causes D32 to reduce about 30%, andaddition of CTAB led to about 26% reduction inthe decreasing rate of D32 with impeller speed.

• The drops size increased with increasing dispersedphase volume fraction, and addition of CTAB tothe system causes the enhancement rate of D32 toreduce to 19–32%.

• In order to predict the Sauter mean diameter, newmodified correlations were presented. For the cleansystem without CTAB, the measured %AARD valuewas less than 1%, and the correlation was in goodagreement with Hinze–Kolmogorov’s theory. Afterthat, for the first time, CTAB concentration wasintroduced to the correlation as new independentparameter to demonstrate the effect of the presenceand concentration of CTAB on Sauter mean dropsize. The new correlation was also in adequateconformity with Hinze theory, and the measured %AARD was 5.46%. This proposed correlation can beused for systems with and without surfactant.

Figure 8. Comparison between experimental D32and calculated D32 from correlations. This figure isavailable in colour online at www.apjChemEng.com.



Also, it is suggested employing this correlation forthe systems with similar properties and surfactantstructures.

Terminology:a Numerical coefficientA Drop Area (mm2)Ae Equal drop area (mm2)b Numerical coefficientC1 Numerical coefficientC2 Numerical coefficientdi Drop diameter of class i (mm)De Equal drop diameter (mm)DH Horizontal drop diameter (mm)DV Vertical drop diameter (mm)DI Impeller Diameter (mm)D32 Sauter mean diameter (mm)(D32)i,exp Experimental measured D32 (mm)(D32)i,cal Calculated D32 from correlations

(mm)E Inertian Numerical exponent coefficientni Number of drops with di diameterN Impeller agitation speed (rpm)NE Number of experimentsp Numerical exponent coefficientq Numerical exponent coefficientQd Dispersed phase flow rate (cm3/s)Qc Continuous phase flow rate (cm3/s)VI Viscosity number

(V I ¼ mdNDI

srcrd

� �0:5)

We Weber number (We ¼ rcN2D3

Is )

Greek letters:rc Continuous phase density (kg/m3)rd Dispersed phase density (kg/m3)s Interfacial tension (N/m)t Mean residence time (s)md Dispersed phase viscosity (Pa s)’ Holdup’d Dispersed phase volume fractionos Surfactant weight fraction

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mean drops size in the presence of cetyl trimethyl ammonium bromide in horizontal mixer settler

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