Chemical Engineering Science 100 (2013) 421–432

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Chemical Engineering Science

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Direct contact heat transfer via injecting volatile liquid in a hot liquidpool: Generation and motion of bubbles

Amol A. Kulkarni n, Vivek V. RanadeChemical Engineering and Process Development Division, CSIR-National Chemical Laboratory, Dr. Homi Bhabha Road, Pashan, Pune 411008, India

H I G H L I G H T S

� Experimental analysis of injection of low boiling liquid into a hot viscous liquid.� Data on drobble size, rise velocity, transient phase fractions and contact angle.� Phenomenological model predicts the transient phase change and drobble motion.� Initial drop size governs the accuracy of predictions significantly.

a r t i c l e i n f o

Article history:Received 12 October 2012Received in revised form25 February 2013Accepted 28 February 2013Available online 15 March 2013

Keywords:Slightly miscible liquidsDirect contact HTDropBubbleDrobbleEvaporation

09/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.ces.2013.02.057

esponding author. Tel.: þ91 20 25902153; faxail address: aa.kulkarni@ncl.res.in (A.A. Kulkar

a b s t r a c t

Direct contact heat transfer via injection of volatile liquid is an effective strategy for removing heat froma viscous liquid pool. The rapid evaporation effectively removes heat and the generated bubbles movequickly to the top surface. In this paper, we present an experimental and phenomenological analysis ofthe evaporation of a drop in a slightly miscible liquid. The phenomenon was visualized using a two-dimensional transparent experimental set-up with a single inlet at the bottom. The videos were used toestimate bubble dimensions, its rise velocity, distance from the detachment point, and fraction of vaporand the liquid phases in the evaporating drop. The initial drop size, temperature difference between thehot fluid and the low boiling solvent and the nucleation rate governed the rate of change of the drobble(combined entity of drop and bubble) diameter and its rise velocity. A phenomenological modeldescribing transient behavior of drobble (motion and heat transfer) is developed. The transient variationin the interfacial areas for heat transfer and the projected area were found to have effect on thepredictions. The model and results will also provide useful basis for extending the work towards betterunderstanding of direct contact heat transfer in viscous systems like polymerization reactors.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Evaporation of low boiling miscible or immiscible liquid in acontinuous liquid at high temperature is an interesting approachfor the direct contact heat transfer. The advantages of thisapproach lies in the fact that for the case of miscible systems ifthe rate of mixing is faster than rate of heat transfer, one canexpect to achieve uniform heat removal through the entire vessel.While a vast body of literature on the direct contact heat transferbetween immiscible phases with phase change exists, a fewvery early reports give excellent description of the complexityin such flows (Prakash and Pinder, 1967a,b; Sideman and Gat,1966; Sideman and Hirsch, 1964; Sideman and Shabtai, 1964;Sideman, 1966; Wanchoo and Raina, 1987; Wanchoo et al., 1997).

ll rights reserved.

: þ91 20 25902621.ni).

As discussed in Sideman and Taitel (1964), upon coming in contactwith the surrounding liquid at higher temperature, the drop ofthe immiscible liquid undergoes a phase change while it rises.If the viscosity of the surrounding liquid is similar to that of theviscosity of the droplet, the droplet undergoes even shape fluctua-tions as it rises due to phase change. However the time requiredfor initialization of nucleation for evaporation and the timerequired for complete phase change strongly depend uponthe composition/purity of the immiscible droplet as well as thetemperature difference between the surrounding liquid and thedroplet fluid. However the overall fluid dynamics achieved withthe help of discrete drops for direct contact heat transfer isrelatively easy to model than the complicated case of jet injection(Gat and Green, 1976). In general, the direct contact heat removalfrom viscous liquids can be done by having a bubble column kindof configuration by injecting the low boiling low density liquid inthe hot viscous liquid or in a stirred tank reactor. While thehydrodynamics of such systems will be complex to model from the

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432422

first principles, here we develop a model for relatively simplecomponent which will later be used for developing a model forheat transfer in such complex systems. A recent work (Cai et al.,2012) on hydrodynamics of conjunct drops the mobility of inter-face has been used for analysis of rise velocity and this approachwill be useful for interfaces with relatively noticeable interfacialmovement and can be extended for complex situations withtransient phase change.

Typically, evaporation of a drop gets initialized with nucleationwhere, the nuclei come into existence and grow through sponta-neous fluctuations in density of the liquid (Moore, 1959) (mainlydue to entrained/dissolved gas). The rate at which the vapourbubbles grow in superheated liquids is known to be stronglyaffected by inertial and thermal properties of the bulk andevaporating phase (Prosperetti and Plesset, 1978). For the case ofvapour bubbles growing in hot liquids, the growth rate is typicallyexpressed in terms of the vapour pressure of the phases at thebulk liquid temperature, and this may not be applicable for thesituation of immiscible liquid drop evaporating in hot bulk liquids.

Here, we report our observations of direct contact heat transferwhen the bulk liquid is significantly viscous than the slightlymiscible low boiling solvent. A phenomenological model is devel-oped for the prediction of droplet evaporation in slightly miscibleliquid and the predictions are compared with the experimentaldata. The approach helps to understand the transient variation inthe drag coefficient and the heat transfer coefficient, which willeventually be used for the design of a stirred or bubbled boilingreactor. In view of this, the current manuscript is organized asfollows: Followed by the above Introduction, in the next sectionwe focus on experimental set-up and the procedure. In Section 3we discuss the mathematical model in detail and in Section 4,we compare the model predictions with experiments and bringout variation in the observations for different parameters.

2. Experimental

2.1. Experimental set-up

The evaporation of injected the volatile solvent was visualizedusing a two dimensional (2D) experimental set-up (Fig. 1). Thesystem comprised of a polycarbonate 2D rectangular column(W¼40 mm, L¼200 mm and H¼500 mm) with a single inlet atthe bottom. The heat loss from the column during the experimentwas much smaller than the heat loss due to direct contactevaporation. Since injecting the low boiling liquid through a pre-existing hot needle can promote evaporation of solvent in theneedle itself, a pre-cooled needle (~10 1C) was inserted instanta-neously in the column as and when a drop was to be injected. Theneedle was inserted through a Teflon cylinder having bore sizealmost equal to the needle size. A circular diaphragmwas attachedat the top of the Teflon cylinder. The diaphragm thickness wasselected such that it withstands the pressure head of hot liquid inthe container and was flexible enough so that a needle of specificsize can be inserted in the tank instantaneously. Specific volume ofliquid was injected using a syringe pump (Longer Pump, China) togenerate a single drop at a time of desired volume.

A Sony digital camera (Cybershot) and a high speed camera(RedLake, USA) were used to capture the photographs of evapor-ating drop and its rise in the liquid while it grows due toevaporation and phase change. The liquid temperature wasmeasured online using several thermocouples (T-type thermocou-ples from Omega, 0.125 mm diameter, response time o0.1 s)installed along the rising path of evaporating drop and the datawas acquired online. The temperature of the bulk liquid in thevicinity of rising drop was monitored in time so that an effective

relationship between the extent of evaporation and the tempera-ture of bulk can be established.

2.2. Experiments

During the experiments, the rectangular column was filled with ahot viscous liquid (UCON90000 and UCON9500) with initial tem-perature in the range of 50–80 1C. Properties of fluids can be found inthe UCON Fluid and Lubricants Manual (DowChemicalCompany,2001). Typically, the viscosity of UCON90000 fluid was 9–10 timesthat of the UCON9500 fluid. n-pentane was used as the low boilingliquid (B.P.¼37.6 1C). The data was acquired in terms of the tem-perature variation in time and space and the drop behavior wascaptured using the high speed camera. In order to explore the waynucleation takes place, the frame rate was kept at 200 fps, while forunderstanding the phase change and rise of drop the images wereacquired at 25 fps. The low boiling liquid was cooled to 6–10 1Cbefore injecting in the column. Drops of different initial volumes(ranging from 0.01–0.2 mL) were created discretely. After the dropdetachment the needle was instantaneously removed from thebottom to prevent its heating and expansion of the liquid insidethe needle. This approach helped avoid attachment or spreading oflow boiling liquid on the diaphragm surface. During the experiments,a number of difficulties were faced, which were eventually sorted outto make a working system. For the benefit of the reader, here weenlist some of the issues which were encountered and resolvedduring the experiments:

(i)

Preventing the evaporation of the solvent in the metallicnozzle inserted in the system.

(ii)

Inducing the drop/bubble detachment. (iii) Controlling the initial drop size. (iv) Avoiding the bubble coalescence in the bulk. (v) Inducing the nucleation for phase change. (vi) Monitoring the bulk temperature continuously due to rapid

cooling of the liquid.

(vii) Temperature mapping in the system.

Although the needle was inserted through a Teflon rod, therapid heat transfer due to metallic needle still induced someevaporation in the needle itself. This caused ambiguity in estimat-ing the true initial drop size. The issue was sorted out by reducingthe drop formation time to less than 500 ms by adjusting thesyringe pump to deliver the required liquid volume in a very shorttime. This also helped control the initial drop size as well as thedetachment. At many instances the detachment was seen to getdelayed due to very small droplet which remains attached to theneedle surface due to dominant surface forces. In such cases dropwas injected in the form of a pulse in very short time. With purelow boiling liquid being used for the experiments no specificcontrol on on-set of nucleation was observed. This was overcomeby sparging air through the low boiling solvent before it was usedfor injection. The dissolved air helped achieve rapid nucleationwhich essentially helps follow the further evaporation componentof the phase change in a reproducible manner. Thermocouplesinserted in the column helped monitor the spatial variability in thefluid temperature.

The images were analyzed using ImagePro® Plus software andthe data in terms of (i) lateral and vertical bubble dimensions,(ii) distance of bubble center from the detachment point, (iii) heightof vapour and the liquid sections in the evaporating drop, and (iv) therise velocity of the evaporating drop were obtained. The drobble sizesobtained from ImagePro® Plus software were verified using an edgedetection algorithm in the entire sequence of images and the volumefraction was estimated on the basis of volume of revolution of theinterface assuming it to be axisymetric. The centroid was determined

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432 423

based on the volume fraction (i.e., the center of buoyancy) ofindividual phases.

3. Phenomenological model of evaporating drops in hot liquid

Consider that a small spherical drop of initial radius R0 at thetime of detachment is generated from the needle and it rises byvirtue of buoyancy due to difference in the density between thebulk fluid and the liquid in the drop phase. Let the bulk liquid is ata temperature T and is in sufficiently large quantity such that eventhe heat taken for complete evaporation of the drop does notaffect the overall bulk liquid temperature. The model considers theinterfacial heat transfer between the different phases and solves

Fig. 1. Schematic of the experimental set-up. (1: PP-column for holding hot viscousliquid, 2: high speed camera, 3: PC for online data acquisition, 4: back illuminationlight, 5: arrangement for insertion of low boiling liquid injection needle, 6: syringepump, 7: temperature multiple port data acquisition system, and 8: thermocouplesflushed to the inside of PP-column).

t1 t2

Viscous fluid T >>Tboil, Solve

Solvent vapor

Liquid solven

Fig. 2. (A) Schematic of the model formulation and interface variation, and (B) Schematiapproach is shown with dotted lines.

for the temperature of the bulk, temperature of the solvent,volume fraction and mass fraction of the solvent liquid and vapour.The unsteady equations yield the transient profiles of the variationof the bubble size and its rise velocity. The assumptions madewhile formulating the model are given below:

3.1. Assumptions

(i)

t3

nt

t

c of dr

Drop/drobble remains spherical during expansion and rise.

(ii) Drobble rises in rectilinear manner. (iii) The interfacial mass transfer between vapour–liquid and liquid–

liquid are negligible or the viscous liquid is well saturated withthe solvent. (n-pentane is soluble in UCON fluids and hencedissolution is always possible if the evaporation is not fast).

(iv)

The added mass coefficient is considered to remain constant(at ~0.5) independent of phase fractions (Ohl et al., 2003).

(v)

The local flow pattern has no effect on the drobble properties(i.e. the drobble shape does not change due to any flow in thebulk liquid).

(vi)

The phenomena of drop formation, phase transfer and rise ofcompound drop-bubble occurs in infinitely large pool ofstagnant viscous liquid.

(vii)

The drop/bubble remains spherical throughout and the inter-face of solvent liquid to solvent vapour remains flat.

The schematic of the phenomena of drop evaporation in aslightly miscible liquid is shown in Fig. 2A and the typical

evaporation sequence is shown in Fig. 2B and is analogous to theexperimental observations in the literature.

The detailed equations are given as follows

Force balance equation for drop/bubble rise velocity:

mDdUD

dt¼ gρCVD−gmD−

CDAPρCU2D

2−CmρCVD

dUD

dtð1Þ

Vapor

Liquid t4

R

op evaporation sequence. The solvent liquid–vapour interface assumed in the

Fig. 3. Time varying temperature variation in the bulk viscous liquid. Measure-ments were made using a set of 14 thermocouples located along the rise directionof the bubble.

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432424

Energy equation: Till drop temperature reaches saturationtemperature it will lose the sensible heat.

mDCpef fdTL

dt¼ hAl

HðT∞−TDÞ for TDoTS ð2Þ

When drop temperature reaches saturation temperature TD≡TS

there will be no further change in drop temperature and hencedTD=dt ¼ 0Equation for mass fraction: The growth of vapour phase will bedirectly proportional to the rate of evaporation.

mDdf Ldt

¼ hAlH

λðTD−T∞Þ ð3Þ

where f L is mass fraction of liquid in the drop.

mDdf Vdt

¼ hAVH

λðTD−T∞Þ or f Lþ f v ¼ 1 ð4Þ

After the complete evaporation of liquid portion of the drop,f L ¼ 0, the vapour formed will gain sensible heat from the

Fig. 4. Nucleation and phase change of low boiling solvent in hot viscous fluid.

surrounding continuous phase. Thus the equation for temperatureof vapour is

mDCpef fdTV

dt¼ hAV

HðT∞−TSÞ ð5Þ

mD¼total mass of the drop.

3.2. Approximations

The volumes occupied by liquid and vapour phase in the dropare given by

VL ¼mDf LρL

and VV ¼ mDf VρV

ð6Þ

The total volume of the drop at any instant is

VD ¼ VLþVV ð7ÞEffective heat capacity for the drop is

Cpef f ¼ f LCpLþ f VCpV ð8ÞArea of heat transfer to liquid portion of the drop is calculated

assuming the following relationship:

AlH ¼ πd2p � f L ð9Þ

Similarly, the area of heat transfer for the vapour portion isestimated using the following approximation:

AvH ¼ πd2p � f V ð10Þ

The instantaneous heat transfer coefficient was estimated fromthe correlation given by Sideman and Taitel (1964)

Nu¼ 3 cosβ−cos2βþ2π

� �0:5

Pe0:5, ð11Þ

where Pe¼Ud=α. The equations were solved simultaneously usingODEPACK® with suitable initial and boundary conditions.

4. Results and discussions

4.1. Experimental observations

In order to verify the temperature variation during bubble risein the hot liquid, temperature mapping was done. A typicaltemperature map over the column is shown in Fig. 3. It is evidentthat the temperature of the bulk liquid in the vicinity of drop/bubble continues to fall during its rise. The bubble motion was

confirmed from the images acquired using the camera. The imagesshowed that depending upon the possibility of nucleation (due topresence of dissolved air) low boiling liquid drop starts evaporat-ing immediately after entering the hot liquid. Typically, threephases (viz., low boiling liquid, nucleating vapour and vapour)can be seen until the liquid gets completely evaporated (Fig. 4).However, as a consequence of phase change and continuousreduction in the density of drop, it comprises of liquid as well asthe vapour and hence will be referred as ‘drobble’ throughout thismanuscript. With increasing vapour fraction the density of thedrobble continues to decrease while it rises and the evaporationcontinues until the liquid at the bottom of drobble gets completelyevaporated. Typical sequences of such a phase change are shownin Fig. 5A and B.

The low boiling liquid solvent was injected in the hot liquidusing a syringe. It was seen that most of the times; the evaporationbegan immediately after starting the injection. At the time ofdetachment, the drobble was seen to have a spherical top andconical bottom due to pendant liquid having relatively higherdensity was seen to have a tail at the bottom. Also, dependingupon the solubility of low boiling liquid in the surrounding viscousfluid the rate of dissolution of solvent in liquid phase in viscousfluid is likely to be more than that of the vapour in viscous fluid.As mentioned earlier, the presence of dissolved gas in the solventhelps to initiate nucleation. Once the nucleation starts, theevaporation of solvent happens very rapidly. On the other handas shown in the last few images in the sequence shown in Fig. 5B,in the absence of any nucleating air, the solvent drop rises withoutany evaporation for some distance. During this rise, the masstransfer of solvent in the viscous liquid takes place leading to

Fig. 5. Typical drop evaporation sequence (n-pentane in UCON9500) (A) do¼1 mm, T¼59 1C and (B) do¼0.8 mm, T¼60 1C. In (B), the second drop does not contain anydissolved gas and thus delays nucleation and also undergoes dissolution to some extent in the surrounding liquid.

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432 425

reduction in the size of drops. However, after the drop reaches itscritical temperature, the whole drop was seen to undergo aninstantaneous evaporation. In such a case, the total heat removedfrom the bulk liquid at the location of evaporation is lower thanthat of the situation where nucleation is followed by evaporation.Thus, it is necessary to understand (i) the mechanism of nuclea-tion, (ii) can nucleation rate be used to achieve specific growth/evaporation rate, and (iii) quantify the liquid–liquid and gas–liquidheat transfer in this dynamic three phase system.

The above discussion implies that, depending upon the initialcondition at which the drop enters the hot liquid bath, severalpossible ways could be seen in which such a phase change occurs.The data was quantitatively analyzed to obtain the transientbubble size, phase fractions, mass fractions of vapour and liquid

phases and also their volume fractions. The experimental resultsare shown in Fig. 6. The experimentally obtained images wereanalyzed as mentioned before. The values of drop size, vapour andliquid volume fractions, the distance from the source and the risevelocity were estimated. Interestingly, although the trends forspecific variables are identical, the actual values differ. The mainreasons for these variations in the values are (i) inability to controlthe beginning of evaporation and hence the growth rate (ii)inability to predict the rate of nucleation and (iii) the bulk liquidis in batch mode and hence during the experiments the tempera-ture of bulk liquid falls, which makes it difficult to reproduce in theexisting system. Thus, every single solvent droplet formation inthe bulk liquid is considered as an independent experiment.However since the local temperature changes are continuously

0

2

4

6

8

10

12

14

16

0 30 60 90 120

Velo

city

(mm

/s)

Height (mm)

T66_Drop 1 T66_Drop 2 T66_Drop 3

0

5

10

15

20

25

30

0 50 100 150

Height (mm)

T68_Drop1 T68_Drop2 T68_Drop3 0

5

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25

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35

0 20 40 60 80 100

Height (mm)

T68_Drop2 T68_Drop3 T68_Drop4 T68_Drop5

0

20

40

60

80

100

120

0 2 4 6 8 10

Dis

tanc

e (m

m)

Time (s)

0

20

40

60

80

100

120

0 2 4 6 8 10

Time (s)

0

20

40

60

80

100

120

0 2 4 6 8

Time (s)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

Vapo

r pha

se m

ass

fract

ion

( - )

Time (s)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

Time (s)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

Time (s)

Fig. 6. Experimental observations with UCON9500–n-pentane system. The temperature of the hot fluid is given in the legends as T¼66 1C and T¼68 1C. Legends given forthe plot of velocity vs. height are applicable for other plots in the same column.

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432426

monitored the bulk properties during every experiment areknown. The interfacial mass transfer also affects the bubble sizeand its rise velocity, which makes the situation complex. This isevident from the bottom plot in the third column of Fig. 6, wherethe vapour phase mass fraction decreases after certain time.

Similar features were seen from the experiments carried out inUCON90000 fluid, which has higher viscosity and slightly lowerdensity than UCON9500. Extensive experiments were carried out tounderstand the phase change and motion of single evaporatingdrop in the liquid in the 2D system. Initial drop size was varied byusing two different needle sizes (0.2 and 0.5 mm) and theUCON9500 temperature was maintained at 70 1C and 80 1C whilethe injected n-pentane temperature was kept in the range of 6–30 1C. Inline temperature was measured for different situations tounderstand the rate of heat transfer from bulk fluid to theevaporating drop while it rises. In most of the experiments it wasobserved that the drobble size increases with time, however thetime required to initialize the evaporation depends upon the extentof dissolved gases and the initial size. Fig. 7 shows the experimentaldata in terms of drobble size as a function of time or distance fromthe orifice at different temperatures of the viscous liquid and thesolvent. In general different trends can be seen because of the local

temperature, initial temperature difference between the solventdrop and viscous liquid and the initial size of the drop. With lowertemperature difference, the evaporation rate was low. At identicaltemperatures, the bulk fluid viscosity played an important role suchthat the evaporation rate was governed by temperature differenceand the completion of evaporation before the drobble leaves thebulk liquid was governed by the viscous drag. Correspondingvelocity vs. drobble size plots are given in Fig. 8.

The experimental observations can be summarized as

(i)

The drobble diameter is a strong function of the initial liquidvolume, temperature difference between the hot fluid and thelow boiling solvent and the rate of initialization of thenucleation.

(ii)

The increase in drobble size was seen to go through twostages, in the first stage, rate of nucleation is the controllingparameters with slight surface evaporation, while in thesecond stage, the evaporation was very rapid thereby yieldinglarge drobbles with higher vapor phase volume fraction.

(iii)

The drobble rise velocity in viscous liquids showed behaviorsimilar to the rise of bubbles in stagnant viscous liquids(Kulkarni and Joshi, 2005). However, the behavior strongly

0

5

10

15

20

25

30

35

40

45

50

0 5 10

Dro

bble

siz

e (m

m)

Time (s)

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10

Dro

bble

siz

e (m

m)

Time (s)

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5

10

15

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30

35

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45

0 10 20 30

Dro

bble

siz

e (m

m)

Time (s)

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35

40

45

0 1 2 3 4 5

Dro

bble

siz

e (m

m)

Time (s)

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20

Dro

bble

dia

met

er (m

m)

Time (s)

Fig. 7. Drobble size variation during evaporation in the 2D set-up. (A) TUCON¼80 1C, Tsolvent¼10 1C, (B) TUCON¼80 1C, Tsolvent¼6 1C, (C) TUCON¼70 1C, Tsolvent¼20 1C,(D) TUCON¼80 1C, Tsolvent¼20 1C, and (E) TUCON¼54 1C, Tsolvent¼6 1C. (A–D: UCON9500, and E: UCON90000).

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432 427

depends on the extent of evaporation. In reality the system ofobserving movement of drobbles in hot liquids actuallyhelps to obtain the entire bubble rise velocity vs. size plot ina single experiment and the phenomena is be independentof temperature of bulk liquid as it rises.

(iv)

The extent of increase in the drobble size at the disengage-ment is independent of the time taken for nucleation.

(v)

For the case of delayed nucleation, the solvent drop getssuperheated continuously (Fig. 7C, ▲) as it rises slowly inthe hot liquid without any possibility of nucleation andbeyond its specific heat limit, the entire drop undergoesevaporation in a very short time. However, the relationship

between drobble velocity vs. size is independent of mode ofevaporation.

Upon plotting all the velocity vs. size data together (not shownhere) it was observed that the data does not overlap completely andthe points fall outside of the parity, mainly due the difference in theexperimental conditions for individual cases. The extent of variationwas 76.8%. The drobble shape map can be obtained from the datahowever the local viscosity is a function of local temperature and aquantitative relationship between them would help estimate therequired dimensionless numbers more accurately. This specific issuewill be discussed separately.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 10 20 30 40 50

Vel

ocity

(mm

/s)

Drobble size (mm)

Drop 1 Drop 2 Drop 3 Drop 4

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 10 20 30 40 50

Dro

bble

rise

vel

ocity

(m/s

)

Drobble size (mm)

0

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0 10 20 30 40 50

Dro

bble

rise

vel

ocity

(m/s

)

Drobble size (mm)

0

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0 10 20 30 40 50

Ris

e ve

loci

ty (

m/s

)

Drobble size (mm)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 10 20 30 40 50

Ris

e ve

loci

ty (

mm

/s)

Drobble diameter (mm)

T= 54.7

T= 52.4

Fig. 8. Drobble rise velocity vs. drobble size during evaporation in the 2D set-up. (A) TUCON¼80 1C, Tsolvent¼10 1C, (B) TUCON¼80 1C, Tsolvent¼6 1C, (C) TUCON¼70 1C,Tsolvent¼20 1C, (D) TUCON¼80 1C, Tsolvent¼20 1C, (E) TUCON¼54 1C, Tsolvent¼6 1C. (For A–D: UCON9500, and for E: UCON90000).

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432428

4.2. Simulation results

The equations were solved using ODEPACK® and initially testedagainst the results from literature. The properties of the fluids atdifferent conditions are given in the Supporting Information. Thedrag coefficient that is used in Eq. (1) was estimated usingcorrelations based on drobble size and its rise velocity, both ofwhich vary continuously till the evaporation is complete. Typically,the value of CD can be defined as a function of Re, assuming thatthe gas/vapour–liquid interface is clean. In the present experi-ments the interface of the viscous liquid (which contains manyadditives including traces of surfactant) and n-pentane (purged

with nitrogen to help nucleation) may not be clean and hence thefollowing correlations were used for the estimation of dragcoefficient (Mei and Klausner, 1992).

CD ¼ 24Re

, for Re≤1 ð12Þ

CD ¼ 24Re

1þ 1ð8=ReÞþð0:5ð1þð3:315=Re0:5ÞÞÞ

� �for Re41 ð13Þ

In our model we assume the drobble to have a spherical shapewith the unevaporated liquid in the form of pendent as shown in

0.02

0.023 0.027

0.035

0.06

0.1

0.2

0

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0 2 4 6 8

Dro

bble

vel

ocity

(m/s

)

Time (s)

0.0004 0.0003

0.00017 0.0001

0.00008

0

0.02

0.04

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Dro

bble

vel

ocity

(m/s

)

Time (s)

0

0.02

0.04

0.06

0.08

0.1

0 2 4 6 8 10

Vel

ocity

(m/s

)

Time (s)

Fig. 9. Simulated drobble rise velocity as a function of time for (A) effect of CFAP,values of CFAP were varied in the range of 0.02 to 0.2 and (B) effect of variation inCFHT (C) values of CFAP and CFHT obtained using Eqs. (14) and (15) for correcting thedrag coefficient and the heat transfer coefficient, respectively. (dispersed phase:Furan, continuous phase: aqueous glycerol 96.1 mass%, dB0¼1.45 mm, Tbulk¼313.7 K,¼304.65 K, Tdrop¼295.0 K, and height of the column¼58 mm).

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432 429

Fig. 2. This assumption is a slight deviation from the actual shapeas seen in Fig. 3 and as given in literature (Dammel and Beer,2003). While the pendent liquid actually does not affect theprojected area, it influences the transient wake dynamics whichchanges the projected area dynamically and thus affects the actualdrag experienced by the drobble. Hence, the drag coefficientvalues were modified by multiplying it with a correction factorwhich should depend upon the dynamic property of drobble.Reduction in the values of the correction factor for projected area(referred hereafter as CFAP) further reduces the drag force andhelps increase the drobble rise velocity. The simulation results areshown in Fig. 9A and it can be seen that, with increase in thecorrection factor from 0.02–0.2, the individual experimental datapoints were seen to fall on independent prediction lines as afunction of time. This implies that the drag coefficient for adrobble would always be smaller than that of a constant volumedrop or a bubble of the same size, thereby getting helped to risefaster than the actual rise velocity. The correction factor that yieldsgood parity with the experimental data could be correlated withthe temporal Re as

CFAP ¼ 0:0135� Re2–0:056� Reþ0:096 ð14Þ

Upon fitting the correction factor for drag coefficient with Re,further simulations were carried out to finalize the dependenceof heat transfer coefficient on the varying drobble properties.Similarly, the interfacial heat transfer area between solvent-bulk,vapour-solvent and vapour-bulk were corrected to take intoaccount dynamic variation in the interfacial areas. The interfacialheat transfer was corrected using a multiplication factor (CFHT)which actually helps to correct the rate of change in the tempera-ture of the solvent drop and the rate of change of liquid phasevolume fraction in the drop (due to temporal variation in the localvalues of physicochemical properties of both the fluids at differenttemperatures). Simulations were carried out at the drag coefficientestimated using the CFAP given in Eq. (14). Similar to the previouscase, the values of CFHT where the simulated velocity matcheswith the experimental data were also again correlated with the Reat that instant. The instantaneous Re was estimated using theinstantaneous size, velocity of drobble and the density andviscosity of the drobble based on the phase fraction (vapour,liquid) available at that instant. The relationship between CFHTand Re in the form of a third order polynomial based on Fig. 9B isgiven as follows:

CFHT ¼ 1e−5ð1:17Re3−7:91Re2 þ 17:4Re þ 4:09Þ ð15Þ

The simulated drobble rise velocity using both the correctionfactors is shown in Fig. 9C as a function of time. A good agreementcan be seen between the simulations and the experimental data.Since the Re is a function of the local physical properties of theliquid and the local drobble diameter, the transient values aretaken into account to estimate the correction factors at any time.Based on the above approach simulations were carried out for theprediction of various parameters corresponding to drobble growthand movement. Initially, the simulations were carried out forcomparison with the data for Furan in hot glycerol (not shownhere). Typical simulation results for different cases with UCONfluids are shown in Fig. 10. The difference in the experimental andthe simulated data is mainly due to the ambiguity in the choice ofinitial drop diameter. This was due to the instantaneous evapora-tion of the solvent in the hot liquid, which based on the imageanalysis does not give a clear idea about the possible initial drop

size. Hence, a few experiments were carried out with a constantknown initial volume of the solvent. Typical results for UCON90000fluid are shown in Fig. 11.

0

0.05

0.1

0.15

0.2

0 2 4 6

Vap

or p

hase

mas

s fra

ctio

n ( -

)

Time (s)

0

0.02

0.04

0.06

0.08

0.1

0 2 4 6

Ris

e ve

loci

ty (m

/s)

Time (s)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6

Hei

ght (

m)

Time (s)

50

70

90

110

130

150

170

190

0 0.2 0.4 0.6 0.8 1

Ang

le (d

egre

e)

Liquid phase volume fraction (-)

0.0

0.2

0.4

0.6

0.8

1.0

0.00001 0.001 0.1

Liqu

id p

hase

vol

ume

fract

ion

(-)

Height (m)

0

100

200

300

400

500

600

0 2 4 6

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 k)

Time (s)

V-L HTC

L-L HTC

Fig. 10. Comparison of the simulated data with the experimental measurements for various parameters observed in the evaporation of a low boiling n-pentane in hotglycerol at 76 1C. The experimental data (symbols) are from Dammel and Beer (2003).

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432430

The observations show that the approach of using phenomen-ological model for prediction of growth due to direct contact heattransfer thus helps to predict the drobble size, rise velocity anddynamics of variation in the three phase contact angle. This data isuseful for the prediction of dynamic variation in heat transfercoefficient and drag coefficient, which are essential for the designof reactors.

5. Conclusions

This work brings out a simple approach based on phenomen-ological model for the interfacial heat transfer and rise of lowdensity drop-bubble (drobble) in a hot viscous liquid. The experi-mental system comprised of n-pentane as low boiling liquidwhich was injected into hot viscous liquid using a syringe pump

to generate the drop of desired volume. The videos were used toestimate bubble dimensions, its rise velocity, distance from thedetachment point, and fraction of vapour and the liquid phases inthe evaporating drop. The model was found to predict the volumefraction, mass fraction of the solvent liquid and vapour, thetransient drobble size, interfacial area for heat transfer, variationin the three phase contact angle, etc. Accuracy in predictions wasseen to depend a lot on the initial drop size, initial temperaturedifference between the hot fluid and the low boiling solvent,accurate estimation of the transient interfacial heat transfer area,and local values of physicochemical properties. The approach isuseful for rapid estimation of extent of direct contact heat transferand the time scales associated with this evaporation. More workon understanding (i) the nucleation rates and dynamics associatedwith and (ii) the role of interfacial tension between various phasesthat decides the shape of the drobble is in progress.

0

0.2

0.4

0.6

0.8

1

1.2

0 3 6 9 12

Vap

or p

hase

mas

s fra

ctio

n ( -

)

Time (s)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10

Hei

ght (

m)

Time (s)

0

0.02

0.04

0.06

0.08

0 0.01 0.02 0.03 0.04

Ris

e ve

loci

ty (m

/s)

Drop size (m)

Fig. 11. Experimental data and simulation results for various parameters observed in the evaporation of a low boiling n-pentane drop (1 mL) in hot UCON90000 viscousliquid.

A.A. Kulkarni, V.V. Ranade / Chemical Engineering Science 100 (2013) 421–432 431

Nomenclature

AH heat transfer area (m2)AP area of projection (m2)CD drag coefficient (−)Cm factor for added mass (−)Cpef f effective specific heat (J/kg K)dp total diameter of the drop (m)f mass fraction (–)g acceleration due to gravity (m/s−2)h heat transfer coefficient (W/m2 K)mD total mass of the drop (kg)TB Boiling temperature (K)TD temperature of the volatile liquid (K)TS saturation temperature of the volatile liquid (K)T∞ Temperature of the surrounding medium (K)UD Rise velocity of the drop (m/s)V volume (m3)

Greek symbols

εG fractional gas/vapor hold-up (–)λ latent heat of vaporization (J/kg K)ρc density of continuous medium (kg/m3)ρl density of volatile liquid (kg/m3)ρv density of vapour (kg/m3)

Subscripts

D dropL,l volatile liquidV ,v vapor

Superscript

l volatile liquidv vapor

Acknowledgments

Authors are thankful to Dow Chemicals (India) Ltd. for financialsupport (SSP269126, 2008–09) for this work.

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