effect of structural parameters on drop size distribution in pulsed packed columns

Effect of Structural Parameters on Drop SizeDistribution in Pulsed Packed Columns

The effect of packing type on drop size distribution in pulsed packed columns wasinvestigated by means of different columns and three packing types with threeliquid systems including n-butyl acetate, toluene, and kerosene with water. Theseliquid systems cover a wide range of interfacial tensions. Also the influence ofoperating variables in terms of pulse intensity and volumetric flow rates of dis-persed and continuous phases was examined. Pulse intensity, interfacial tension,and packing shape were found as the main important factors for drop size distri-bution while volumetric flow rates had no significant effect. Correlations are pre-sented to predict drop distribution and mean drop size in pulsed packed columns.

Keywords: Drop size distribution, Packing type, Pulsed packed column, Pulse intensity,Sauter drop size

Received: December 13, 2013; revised: February 06, 2014; accepted: March 31, 2014

DOI: 10.1002/ceat.201300837

1 Introduction

Liquid-liquid extraction in pulsed columns is a frequentlyapplied technique in chemical engineering, hydrometallurgy,nuclear technology, and other areas due to its high separationefficiency by reducing axial mixing and increasing drop break-up and coalescence rate [1–3], and by controlling the pulseintensity which improves the rate of mass transfer by sizereduction of the drops [4]. Mass transfer is a function of theinterfacial area which can be calculated from drop size andholdup [5, 6]. The larger the drops, the smaller are holdup andinterfacial area. For too small drops, however, the mass transfercoefficient decreases [7] owing to reduced internal circulationsin the drops and a move toward stagnant regime [8]. Upondecreasing the drop size, moreover, the axial dispersion coeffi-cient reduces to reach an optimum and then increases again[9]. The overall efficiency of the column also increases until anoptimum drop size is attained; thereafter, it decreases untilflooding [4]. Hence, there should be an optimum drop size toensure the highest mass transfer rate and column efficiency.Knowing the Sauter drop diameter in the system is notadequate because different drop size distributions might havethe same mean drop size while, of course, leading to differentinterfacial areas.On the other hand, knowledge of the drop size distribution

is important for the hydrodynamics of the column and it is asignificant factor in scale-up of the system [10]. The velocity ofthe rising drop along the column is dependent upon the drop

size. The residence time of the drops is then varied with changeof the drop size and, consequently, the holdup is influenced bythe drop size [5, 11, 12].Different parameters influence the drop size distribution and

Sauter drop diameter. Buoyancy and interfacial tension areresponsible for the drop breakup in the absence of pulsation[5, 13]. In the presence of pulsation, however, the drop size dis-tribution is less diffused, and a smaller drop size is formed withincreasing the pulse intensity [14–16] because of an intensifiedcollision between the drops and the internal wall, which in turnleads to a higher breakage rate [17]. Prabhakar et al. stated thatthe continuous-phase flow rate has a trivial effect on the dropsize distribution [18]. They also found that the Sauter drop sizeincreases with higher dispersed phase flow rate. On the con-trary, other works imply that both phases have a little effect onmean drop size and drop size distribution [14, 15, 19, 20]. Theeffect of bed porosity and specific area of Raschig rings havealso been examined by Spaay et al. [19] but only with respectto the Sauter drop diameter. These authors found that themean drop size is smaller with reduction of porosity. Asimplied from their correlation, the specific area had a littleeffect on the drop size. Nevertheless, the influence of packingproperties on the drop size distribution in pulsed packed col-umns has not been investigated.The Sauter mean drop size and behavior of drop size distri-

bution in pulsed packed columns for three different packings isinvestigated. The effect of operating variables, i.e., pulse inten-sity and flow rates of the continuous and dispersed phases, andthe packing properties on the drop size distribution are ana-lyzed. In addition, empirical correlations are presented to pre-dict the Sauter mean drop diameter and drop size distributionas a function of operating variables, physical properties of theliquid systems, void fraction of the column, and equivalentpacking diameter.

Chem. Eng. Technol. 2014, 37, No. 7, 1155–1162 ª 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cet-journal.com

Mahmoud Gholam Samani1

Jaber Safdari2

Ali Haghighi Asl1

Meisam Torab-Mostaedi2

1Semnan University, School ofChemical, Petroleum and GasEngineering, Semnan, Iran.

2Nuclear Science andTechnology Research Institute,Nuclear Fuel Cycle ResearchSchool, Tehran, Iran.

–Correspondence: Prof. Ali Haghighi Asl ([email protected]),Semnan University, School of Chemical, Petroleum and Gas Engineer-ing, P.O. Box 35195-363, Semnan, Iran.

Research Article 1155

2 Experimental

2.1 Equipment

Experimental work was carried out with two pulsed packedcolumns with internal diameters of 5 and 12.5 cm and threedifferent packings including two ceramic Raschig rings of 0.625and 1.25 cm and an Intalox saddle-type packing of 1.25 cm, sothat the smaller Raschig ring was loaded in the smaller columnand the other two packings were applied in the other column.The active column, i.e., the zone filled by packing, consisted ofglass with a height of 1.5m and was connected to settlers onthe top and bottom of the column to decant the heavy and lightphases. The position of the interface of the two phases at thetop of the column was automatically controlled by an opticalsensor. The vertical pulse was introduced into the column liq-uids at the bottom of the column. The frequency of the pulseintensity was adjusted with a digital board, and the amplitudeof the pulse intensity was controlled by air pressure for thelarger column and by a reversible mechanical piston for thesmaller one. The packing properties are listed in Tab. 1.

2.2 Liquid Systems

Three different liquid-liquid systems were selected according tothe recommendations of the European Federation of ChemicalEngineering [21] to cover a wide range of interfacial tensions.The systems included butyl acetate/water, toluene/water, andkerosene/water with a medium interfacial tension for the firstone and a high interfacial tension for the other two systems.The technical-grade solvents employed as the dispersed phasewere of a purity of at least 99.5 wt%. All experiments were car-ried out at room temperature (20 ± 1 �C). The physical proper-ties of these systems are listed in Tab. 2.

2.3 Droplet Measurement

A digital photograph of the column obtained by a NikonD5000 digital camera served to determine the size of the drops.The real size of the droplets was obtained by comparing the rel-atively measured values against a known scale of the column.Here, the packing size was considered as a reference. Positionand conditions of the measured drops and packing in the glasscolumn were the same. As a result, they were in equivalent situ-ations in the taken photograph. Moreover, when the measureddrop size was evaluated with the known size of the packing as abase, the lens and glass effects could be eliminated.By exerting the pulse intensity to the column, the drop

jumps out of the packing to the wall. Here, it was assumed thatthe considered time for the drop which left the packing wassmall enough to consider the drop size the same as before. Assuch, the drops maintain their size when the photo is taken.The drop size was measured at four levels of the active column:h= 15 ± 5, 55 ± 5, 95 ± 5, and 135 ± 5 cm with the zero point setat the bottom.At least 1000 droplet sizes were measured for each experi-

mental test at each of the four points of the column height toguarantee the statistical significance of the determined Sautermean drop diameter. The Sauter mean drop diameter, d32, wascalculated as follows:

d32 ¼Pn

i¼1 nid3iPn

i¼1 nid2i

(1)

where ni is the number of droplets of mean diameter di withina narrow size range i.

3 Predictive Correlation for Drop Size

As long as the kinetic energy due to the turbulent velocity fluc-tuation and the surface energies acting on the surface are inequilibrium, the drop remains in a stable form when climbingalong the column. A drop breaks up into several smaller oneswhen the kinetic energy exceeds the surface energy. It is thenpossible to calculate the maximum stable drop size by creatinga balance equation between the two energies [23]. The fluidvelocity around a drop changes due to the turbulent fluctua-tions indicating dynamic pressure forces. When the fluid passesthrough the packing media, the interaction between the fluidphase and the packing surface leads to an interfacial drag force,and consequently, to an increase in the pressure drop due toadditional stresses imposed on the surface of the drop and wall.On the other hand, the presence of the packing leads to the re-duction of the column cross-sectional area; hence, the pressuredrop is enhanced further. This increased pressure drop bringsabout intensified energy dissipation and consequently an in-creased turbulent fluctuation velocity. As a result, more viscosi-ty stress and kinetic energy due to the velocity fluctuation acton the drop surface. On the other hand, when a drop collideswith a packing, the drop surface starts to elongate and oscillatedue to change of the normal and tangential momentum as wellas velocity direction and magnitude. If the surface energy can-

www.cet-journal.com ª 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2014, 37, No. 7, 1155–1162

Table 1. Physical properties of the packings.

Physical property Porosity[%]

Equivalent packingdiameter [cm]

Ceramic Intalox saddle (1.25 cm) 65 1.273

Ceramic Raschig ring (1.25 cm) 53 1.49

Ceramic Raschig ring (0.625 cm) 60 0.711

Table 2. Physical properties of the systems studied [21, 22].

Physical property Toluene/water

n-Butyl acetate/water

Kerosene/water

qc [kgm–3] 998.2 997.6 998

qd [kgm–3] 865.2 880.9 804

lc [mPa s–1] 0.963 1.0274 1.00

ld [mPa s–1] 0.584 0.734 1.66

r [mNm–1] 36 14.1 46.5

1156 Research Article

not balance this imposed energy, the drop breaks into smallerones.When external stresses such as dynamic pressure and viscos-

ity stress are imposed on the drop surface, the drop shape isdeformed and a breakup of the drop takes place provided thatthere is a sufficient degree of deformation. Hinze proposed acritical Weber number [24] to calculate the maximum stabledrop diameter; then, the drop breaks up if the Weber numberis higher than this critical value. The Sauter drop diameter isproportional to the maximum stable drop size:

d32 ¼ C1rqc

� �0:6

w�0:4 (2)

where C1 is a constant, r is the interfacial tension, qc is the den-sity of the continuous phase, and w is the energy dissipationper unit mass which is written as [19]:

w ¼ DPH

pafeqc

(3)

where DP/H is the pressure drop along the column height, af isthe pulse intensity, e is the bed porosity, and qc is the density ofthe continuous phase. The pressure drop can be defined as afunction of Ergun’s equation with a correction factor. Ergun’spressure drop is estimated as [25]:

DPErgunH

¼ 150ð1� eÞ2

Ue3lc UD2p

þ 1:751� e

e3qcU

2

UDp(4)

where U is particle sphericity, lc is the viscosity of the continu-ous phase, Dp is the packing diameter, and U is the superficialvelocity which is replaced for af as the variable that is moreinfluencing the drop size than the superficial velocity. Theequation of interest for the pressure drop in this research is,therefore, written as follows:

DPH

¼ fDPErgun

H

� �¼ f 150

ð1� eÞ2

Ue3lc afD2p

þ 1:751� e

e3qcaf

2

UDp

!

(5)

A spherical packing type is almost never used in packed col-umns because of low efficiency and early appearance of theflooding point by increasing the volumetric flow rates. There-fore, it is necessary to apply an equivalent packing diameter(De) which is defined in terms of the sphericity rather than thereal packing diameter:

De ¼6Vp

UAp¼

6Vp

Asp(6)

where Vp is the volume of a single non-spherical packing, Ap isits surface area, and Asp is the surface area of the equivalent-volume sphere. A new correlation for the mean drop size isachieved by substitution of Eqs. (3), (4), and (6) into Eq. (2) asfollows:

d32 ¼ C2rqc

� �0:6

150ð1� eÞ2

e4lcaf

2

qcD2eþ 1:75

ð1� eÞe4

af 3

De

" #�0:4

(7)

where C2 is a constant around 0.153p from the experiments.This constant and the powers in Eq. (7) were optimized toachieve an equation with higher accuracy:

d32 ¼ 75:6 · 10�3 rqc

� �0:3945

150ð1� eÞ2

e4laf 2

qcD2eþ 1:75

ð1� eÞe4

af 3

De

" #�0:263 (8)

in which d32 denotes the Sauter mean diameter. Eq. (8) predictsthe mean drop size in the column but it cannot explain howthe drop size varies along the column. It is well known, how-ever, that the drop size becomes smaller while climbing in thecolumn due to collisions with the packing wall. Therefore, it isrequired to apply a correction factor to Eq. (8) to estimate thechanges of the drop size at any point of the column. On thisbasis, Eq. (8) was modified with the aid of a correction factor as(h/H0)

n to the following correlation:

d32 ¼ 72:4 · 10�3 rqc

� �0:404

150ð1� eÞ2

e4laf 2

qcD2eþ 1:75

ð1� eÞe4

af 3

De

" #�0:269hH0

� ��0:0913ð9Þ

where h is the column height at each point and H0 is the overallheight of the active column. This equation estimates the distri-bution of the mean drop size along the column. The last termon the right-hand side of Eq. (9) is significant to the mean dropsize if only the magnitude of h/H0 is 0.4 or lower, so that themagnitude of the changes amounts to about 12% of the dropsize at the magnitude of h/H0 of 0.1–0.4. At higher values ofh/H0, the last term tends to 1 and is essentially unimportant.This declining trend in the drop size is almost vanished in thelast half of the column height.The average absolute relative error (AARE) was used as an

objective function to calculate the fitted parameters:

AARE ¼ 1n

Xni¼1

PiðdÞðexpÞ � PiðdÞðtheoÞj jPiðdÞðexpÞ

(10)

where n is the number of data points, and Pi(d)(exp) andPi(d)(theo) represent the experimental and theoretical data,respectively. Eqs. (7)–(9) enable the prediction of the meandrop diameter with an AARE of about 15.1, 9.8, and 11.2%,respectively.The drop size distribution can be regenerated by an appro-

priate function such as normal [14, 26], log-normal [26, 27],Weibull [28], and gamma [27] probability density functions. Inthis work, the normal probability function has been adaptedmost precisely than the other functions with the experimentaldata.



PnðdiÞ ¼1

2:62paexp �ðdi � bÞ2

2a2

!(11)

where Pn(di) is the probability of number density defined asthe ratio of number of drops of a specific diameter (di± di/2) tothe total number of drops, di is the drop diameter, and a and bare the parameters to be fitted. The drop size varies betweenthe minimum and maximum stable drop sizes. Hence, for esti-mation of a and b, two numeral groups should be chosenwhich represent the minimum and maximum values of thedrop diameter in Eqs. (13) and (14). Here, the Kolmogorofflength (lc

3/(wqc3))0.25 and the term (r/qc)

0.6w–0.4 were selectedas the numeral groups being representative of the minimumand maximum drop sizes, respectively. The energy dissipationper unit mass appeared in these numeral groups was redefinedas follows:

wc ¼ C3af 3

D2e

ð1� eÞ2

e3(12)

The adjusted parameters are calculated via the followingequations:

a ¼ 7:288m3cD

2e

af 3e3

ð1� eÞ2

!�0:0217rqc

� �0:4147

D0:8e

af 1:2e1:2

ð1� eÞ0:8

!0:6913(13)

b ¼ 11:244m3cD

2e

af 3e3

ð1� eÞ2

!�0:0592rqc

� �0:524

D0:8e

af 1:2e1:2

ð1� eÞ0:8

!0:8734(14)

The AARE values for a and b were obtained as ~ 10.5% and11.6%, respectively. In all of the above equations, the flow ratesof the continuous and dispersed phases originally were incor-porated into the dimensionless term of (1+Qc/Qd)

n, which waspractically omitted in the optimization process, as the magni-tude of the optimized term was very close to unity. As a result,the continuous- and dispersed-phase flow rates are absent inthe above equations. According to Eqs. (13) and (14), a and bare inversely proportional to pulse intensity and directly pro-portional to interfacial tension, equivalent packing diameter,and bed porosity. Hence, the curve of the drop size distributionbecomes sharper with increasing of the pulse intensity. Further-more, the shape of the curve would be extended on enhancingthe interfacial tension, equivalent packing diameter, and bedporosity.

4 Results and Discussion

The effects of different parameters on the drop size distributionwere investigated. These parameters included operational pa-

rameters, i.e., pulse intensity and flow rates of the continuousand dispersed phases, as well as interfacial tension and packingproperties such as equivalent packing diameter and bed porosi-ty. The main reasons of the drop breakage phenomena in thecolumn are turbulent fluctuations, drop-eddy collisions, andviscous shear stress [29]. The examined parameters are differ-ently important in terms of their effects on the mentioned rea-sons of the drop breakup.The drop size distribution varies between minimum and

maximum stable drop sizes. If a drop diameter is larger thanthe maximum drop size, it will be broken up in a short time asa consequence of the external stress imposed on its surface. Onthe contrary, if a drop is smaller than the minimum stable size,the drop will coalesce into another drop by an eddy force thatpresses the drops together [30]. The eddy length is responsiblefor the drop breakup as smaller eddies break up the drop, andthe drop is carried out with the larger eddies.The pulse intensity is one of the important parameters that

affect the drop size distribution and mean drop size because itinfluences principally the turbulence, and the turbulent fluctua-tions will be intensified with increasing the pulse intensity.According to Eqs. (3) and (4), the energy dissipation dependsdirectly on the pulse intensity where the Kolmogoroff scale ofthe turbulence is decreased with higher pulse intensity. There-fore, the number of eddy-drop collisions and the breakup fre-quency are enhanced and the probability of drop breakage isincreased. All collisions between a drop and an eddy cannotcause breakup and only those collisions of enough energy canbreak the drop. Turbulent pressure exerted on the drop surfacedeforms the drop shape, and the drop surface starts to oscillate.The oscillation leads to breakup when the kinetic energyexerted on the surface exceeds the surface energy [31]. Increas-ing the af raises the probability of collisions with a kinetic ener-gy higher than the surface energy.Another factor which is of importance in drop breakup in a

packed column is the energy of the collision between a dropand a packing surface wall. The collision force is controlled bythe drop velocity. As a result, the drop collides more severelywith the packing wall with increasing the pulse intensity, andthis gained collision force leads to breakup of the drop into sev-eral smaller ones if the collision force overcomes the surfacetension force. The drop breakage term is dominant at low hold-ups and for dilute dispersions because the drop-drop collisionwhich is responsible for the coalescence is negligible comparedto eddy-drop and drop-packing wall collision which are themain cause of drop breakage.A higher af increases the holdup and the drop-drop colli-

sions which, in turn, raise the drop coalescence by increasingthe coalescence frequency. From another point of view, a highervalue for the pulse intensity brings about a more turbulentpressure and a stronger collision force exerted on the drop sur-face. Therefore, breakage frequency and efficiency will increasewith higher af and the coalescence term can be enhanced whileincreasing the af. At very high values of af, the coalescenceterm approaches the breakage term in magnitude and, hence,the slope of the drop size versus af decreases because the pulseintensity is higher as illustrated in Figs. 1 and 2. As expected,with increasing the pulse intensity, the drop size distributioncurve has a tendency to form a narrower range of the drop size



and the shape of the curve also becomes more uni-form as illustrated in Fig. 1. Moreover, the meandrop size decreases with higher pulse intensity asindicated in Fig. 2.The properties and shape of the packing play an

important role in determining the drop size distri-bution and mean drop diameter. These features arerepresented by the bed porosity and the equivalentpacking diameter, which influence the turbulenceand the pressure drop, and consequently the dropsize distribution. As observed in Eqs. (3) and (4),the energy dissipation depends on the pressuredrop which, in turn, is a function of the equivalentpacking diameter and porosity. The right-hand sideof Eq. (4) consists of two terms: the first term is re-lated to the laminar flow and the second term tothe turbulent flow. At low af values, the first termhas a considerable magnitude in comparison withthe turbulent term and is proportional to (1–e)2/e3

and De–2. The order of magnitude of (1–e) and e is

the same if e is lower than 0.9; hence, the value of (1–e)2/e3 willbe ~ 10–1 whereas De

–2 is about 10–6 to 10–4. As a result, the ef-fect of equivalent packing diameter is stronger than that of po-rosity. In the second term, the pressure drop is proportional to(1–e)/e3 and De

–1, which are of a magnitude of 10–2 and 10–3 to10–2, respectively. Hence, e and De have the same effect on thepressure drop for De greater than 1 cm. But if the packing di-ameter is lower than 1 cm, the corresponding effect is higherthan that of e. The effects of packing properties on the dropsize distribution and the mean drop size are depicted in Figs. 3and 4, respectively. As observed, the smaller packing (Raschigring 0.625 cm) gives a lower drop size in spite of its larger po-rosity when compared to the Raschig ring 1.25 cm due to thepreviously described reason.

Another effective parameter on drop size distribution andmean drop size is the interfacial tension which represents thesurface energy influencing the drop size according to Eq. (2).When an external stress is introduced to the drop surface, it


Figure 1. Effect of pulse intensity on drop size distribution forbutyl acetate/water system on Raschig ring 1.25 cm.

Figure 2. Effect of pulse intensity on mean drop size of butyl ac-etate/water (B–W), toluene/water (T–W), and kerosene/water(K–W) systems on Raschig ring 1.25 cm.

Figure 3. Effect of packing type on drop size distribution for tol-uene/water system at af= 2 cm s–1.

Figure 4. Effect of packing type on Sauter drop size for the binary systems ofbutyl acetate/water (B–W), toluene/water (T–W), and kerosene/water (K–W).


operates to deform the shape of the drop and, at the same time,the surface energy operates to preserve the stability of the dropshape and prevent from rupture of the drop surface. Wherethere is no exerted mechanical energy in the column, the sur-face energy interacts with the buoyancy, and the drop size isdetermined by the interfacial tension and the density differencebetween the two phases [5]. The curve of the drop size distribu-tion becomes narrower and the mean drop size is reduced withdecreasing the value of the interfacial tension.The effect of the volumetric flow rates of the continuous and

dispersed phases was also examined. The effect of dispersed-phase flow rate on the drop size distribution is illustrated inFig. 5 at the same pulse intensity and continuous-phase flowrates. The dispersed phase holdup is a strong function of thedispersed-phase volumetric flow rate so that a higher dis-persed-phase volumetric flow rate enhances the holdup and,consequently, the number of drop-drop collisions and the coa-lescence frequency. On this basis, the drop size distributionbecomes a little wider with a slightly larger mean drop size withincreasing the volumetric flow rate of the dispersed phase. Thisobservation is more pronounced at low and medium values ofinterfacial tension, mainly because the drop-packing wall andeddy-drop collisions are more severe under these conditions,and the effect of the dispersed phase flow rate on the drop coa-lescence can be ignored compared to the drop breakup in thepulsed packed column.

The impact of the continuous-phase volumetric flow ratecan be observed in Fig. 6 for the same values of pulse intensityand dispersed-phase volumetric flow rate. An increase in thecontinuous-phase volumetric flow rate raises the drag force onthe drop surface. In addition, this higher velocity leads tostronger eddy-drop and drop-packing wall collision forces.Consequently, the drop size distribution becomes slightly nar-rower with raising the volumetric flow rate of the continuousphase, and the mean drop size increases slightly with reductionof this variable. However, the flow rates of both phases had atrivial effect on the drop size as compared to the pulse intensity

so that the mean drop size changed by less than 10% in re-sponse to a ± 36% alteration of the flow rates of both phases atthe center point af value (Figs. 5 and 6). Alteration of the valueof af by a range of ± 30% at the same flow rates, however,changed the mean drop size in excess of 60% as indicated inFigs. 1 and 2. Therefore, it is concluded that the effect of thevelocity of the liquid phases is negligible in comparison withthat of the pulse intensity.Spaay et al. presented an equation to estimate d32 in the pres-

ence of the pulse intensity for pulsed packed columns, referredto as the Spaay’s equation hereafter [19]:

1d32

� 1d0

¼ 67001� e

e

� �0:95 qcaflcS

� �l2cS

rqc

� �0:53 rS2

gDq

� �0:23

(15)

where d0 = 1.39[r/(gDq)]0.5, Dq is the density difference be-tween the two phases, S is the specific surface area (m2m–3),and g denotes the acceleration due to gravity (9.8m s–2). TheAARE of Spaay’s equation estimated from our data was foundto be about 37.9%. The large error of the correlation is due tothe fact that the correlation was obtained from a study on Ra-schig rings while we used an Intalox saddle packing. Therefore,the shape of the packing was totally changed. Furthermore, theeffect of the specific surface area is practically ignored inEq. (15) due to the value of S0.99/S1 in the Spaay’s correlation.Gholam Samani et al. recently presented another correlation

to predict the mean drop size in the pulsed packed columnwith Raschig ring as follows [14]:

d32 ¼ 8:26 · 10�5 afð Þ4qcrg

!�0:2304l4cg

Dqr3

� ��0:0514

1þ Qc

Qd

� ��0:0321(16)

A disadvantage of this correlation is that the influence of bedporosity and specific surface area has been neglected in the pre-


Figure 5. Effect of dispersed-phase flow rate on drop size distri-bution at the same pulse intensity for the binary systems of tol-uene/water (T–W) or butyl acetate/water (B–W) at af= 2 cm s–1

and Qc = 19.0 L h–1.

Figure 6. Effect of continuous-phase flow rate on drop size dis-tribution at the same pulse intensity for the binary systems oftoluene/water (T–W) or butyl acetate/water (B–W) at af= 2 cm s–1

andQd = 19.0 L h–1.


diction of the drop size due to a lack of relevant experimentaldata. The correlation has then a poor value of AARE which isabout 27%. In this work, however, the last two parameters werealso considered in Eq. (8). Comparisons between experimentaldata and Eqs. (8), (15), and (16) are illustrated in Figs. 7, 8, and9, respectively.

5 Conclusions

Two pulsed packed columns and three different packings wereemployed to examine the effect of packing properties on dropsize distribution and Sauter drop diameter. The impact of oper-ating variables and properties of the liquid system was alsoinspected, covering a wide range of interfacial tensions. Theresults implied that the packing properties, pulse intensity, andinterfacial tension play important roles in determining the dropsize distribution. The packing properties were represented byvoid fraction and equivalent packing diameter, which affect theenergy dissipation per unit mass in the column. This energy

influences the maximum stable drop size as well as the dropsize distribution. The distribution curve of drop size is taperedwith the reduction of the void fraction or the equivalent pack-ing diameter. Another significant factor is the pulse intensity:higher pulse intensity leads to an increase in the packing wall-drop and eddy-drop collisions. As a result, the drop breakuprate is enhanced. Therefore, the Sauter drop diameter isreduced and the drop size distribution shifts to a narrower one.The interfacial tension represents the surface energy which is

responsible for maintaining the shape and the surface integrityof the droplet, so that larger drops are formed at higher interfa-cial tensions. The volumetric flow rates of the continuous anddispersed phases proved to have no significant effect on dropsize distribution and drop mean diameter as compared to theaforementioned parameters. Indeed, the drop size changes byless than 10% in response to the change of the flow rates.Finally, correlations were presented to predict the drop size dis-tribution and Sauter drop diameter. All correlations were ingood agreement with the experimental data.

The authors have declared no conflict of interest.

Symbols used

af [m s–1] pulse intensityAp [m2] packing surface areaAsp [m2] surface area of the equivalent-volume

sphered32 [m] Sauter mean diameterDp [m] particle diameterDe [m] equivalent particle diameterdi [mm] drop diameterg [m s–2] acceleration due to gravityh [m] height at each point of the active

columnH0 [m] overall height of the active columnni [–] number of droplets of mean diameterdiP [–] probability of number density


Figure 7. Comparison between experimental data and predic-tions of Eq. (8).




Q [m3s–1] volumetric flow rateS [m2m–3] specific surface areaVp [m3] volume of a single non-spherical

particle

Greek symbols

a [–] constant parameter in probability ofdensity function

b [–] constant parameter in probability ofdensity function

e [–] void fractionU [–] sphericity coefficientm [Nsm–2] viscosityt [m2 s–1] kinematic viscosityq [kgm–3] densityDq [kgm–3] density difference between two phasesr [Nm–1] interfacial tension between two phasesw [Wkg–1] energy dissipation per unit mass

Subscripts

c continuous phased dispersed phasen normal probability density function

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effect of structural parameters on drop size distribution in pulsed packed columns

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