coalescence of air bubbles at air–water interface

0263–8762/04/$30.00+0.00# 2004 Institution of Chemical Engineers

www.ingentaselect.com=titles=02638762.htm Trans IChemE, Part A, July 2004Chemical Engineering Research and Design, 82(A7): 849–854

COALESCENCE OF AIR BUBBLES AT AIR–WATER INTERFACE

P. GHOSH*

Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati, India

The rest time of air bubbles at flat air–water and water–organic interfaces is studied in thepresent work. Effects of cationic and anionic surfactants, alcohol, salts and bubble-sizeon rest time are investigated. Wide distributions in rest times are observed in all the

systems, which establishes the stochastic nature of the process. The stochastic model of Ghoshand Juvekar (2002; Chem Eng Res Des 80: 715–728) is used to fit the bubble rest timedistributions. The results show that the magnitude of the rest time is determined by the strengthof the interfacial repulsive force and the magnitude of surface diffusivity of the surfactantmolecules. Entanglement of surfactants by hydrophobic interaction is believed to be a majorfactor behind the high rest time in many of the systems studied, apart from the repulsiveelectrostatic double layer, hydration and steric forces. The nature of the repulsion differs fromsystem to system depending on the type of the adsorbed species. The work provides furthersupport to the viewpoint (Ghosh and Juvekar, 2002) that the hydrodynamic drainage of the thinliquid film trapped between the bubble and the flat interface is complete once the bubble comesto a rest on the interface and the lubrication force plays a negligible role in supporting theweight of the bubble.

Keywords: air–water interface; bubble; electrolyte; water–hydrocarbon interface; interfacialforce; surfactant; surface diffusion; stochastic modelling.

INTRODUCTION

Coalescence of bubbles is important in ore-flotation, firefighting, washing, cleaning, food processing, beverages,gas–oil separations, absorption and distillation. It is ofgreat importance in multiphase reactors. So far, most ofthe studies on coalescence of bubbles have been done usingtwo bubbles (binary coalescence). In most of these studies,coalescence time was very small, less than 1 s (Chaudhariand Hofmann, 1994). The rest time of air bubbles at a flatair–water interface has been studied by a few workers (e.g.Li and Slattery, 1988). However, few of these experimentalworks have presented the distribution of coalescence times.Recent work on coalescence of drops (Ghosh and Juvekar,2002) indicated the possibility that the process could bestochastic, and the present work demonstrates it to be so.

In this work, the coalescence of air bubbles is studied bymeasuring the rest times of air bubbles at a flat air–waterinterface. The rest times are presented in the form ofcumulative distributions. Experiments are performed byvarying the type and concentration of additives (surfactant,salt and alcohol) and size of the bubbles. The rest timedistributions are fitted by the stochastic model developed byGhosh and Juvekar (2002). The model parameters are

correlated with the measurable bulk and interfacial proper-ties of the system. Comparison of rest time of bubbles at air–water and water–hydrocarbon interfaces is also presented.

EXPERIMENTAL

The experiments were performed in an air-conditionedroom where the temperature was maintained at 27�C.Cylindrical glass cells of 70–150 mm diameter and 80–200 mm height with a teflon septum on the wall of thevessel near the bottom were used as coalescence cells. Asyringe inserted through the septum formed the air bubbles.They were released 5 cm away from the air–water interfaceto allow them to attain their terminal velocity before theystruck the interface. By suitable adjustment of flow, thebubbles were slowly formed at the tip of the needle. Thisallowed the new interface to equilibrate with the surround-ings. The bubbles generated in this method were uniform insize. The newly formed bubble was released a few minutesafter the previous bubble had coalesced. After striking at theinterface, the bubble and the bulk interface underwent anoscillatory up and down motion before coming to rest,similar to that shown by Ghosh and Juvekar (2002) fordrops. The bubbles were photographed with a video camerawith an internal clock. The clock had a minimum count of0.1 s. About 100 bubbles were photographed during anexperiment. The bubble rest time statistics were obtainedfrom these photographs. The water used in this study was

849

*Correspondence to: Dr P. Ghosh, Department of Chemical Engineering,Indian Institute of Technology Guwahati, Guwahati—781039, India.E-mail: [email protected]

triple distilled in all-glass apparatus. Its specific conductancewas 3 � 10�6O�1 cm�1 and the surface tension (g) was72 mNm�1. Surface tension was measured using a DuNouy ring tensiometer. The surfactants [sodium dodecylsulfate (SDS) and cetyl trimethyl ammonium bromide(CTAB)], aliphatic alcohol (ethanol and pentanol), poly-acrylic acid, CCl4 and the salts (NaCl, LiCl and tetraethylammonium bromide) were analysed reagent-grade and wereused without further purification. The surface tension curvesfor these surfactants are presented in the work of Ghosh andJuvekar (2003).

RESULTS AND DISCUSSION

The cumulative distribution of bubble rest time is givenby (Ghosh and Juvekar, 2002):

F(tR) ¼1

2erf

1

SGffiffiffi2

pPG

(1 þP1

i¼1 e�l2i tR )

� 1

!( )"

þ erf1

SGffiffiffi2

p

� �#(1)

where erf(x) is the error function defined as

erf (x) ¼

ffiffiffip

p

2

ðx0

e�y2

dy (2)

li are the roots of the Bessel function. tR is the dimension-less rest time, defined as (tR ¼ t=�tt) where �tt is the character-istic diffusion time given by

�tt ¼R2

b

DG(3)

DG is the surface diffusivity of the adsorbed surfactant atthe interface. Its value is taken to be equal to1 � 10�10 m2 s�1 for surfactants. For small amphiphiles(e.g. ethanol), DG ¼ 2 � 10�10 m2 s�1 is used. The radiusof the barrier ring, Rb, is estimated from the relation

Rb ¼ 2R2

ffiffiffiffiffiffiffiffiffiDrg3g

s(4)

where R is the radius of the bubble. PG is the dimensionlesscoalescence threshold, given by

PG ¼Gm

a �GGi

¼R

(wbfra) �GGi

ffiffiffiffiffiffiffiffiffiffiffiDrgg

3

r(5)

where Gm represents the minimum value of the adsorbateconcentration at the barrier ring required to support theweight of the bubble, �GGi is the mean value of Gibbs surfaceexcess, Gi, in the film. The bubble to bubble variation inGi is assumed to be described by normal distribution.a represents the fraction of the adsorbate that remains atthe barrier ring, after the bubble strikes at the interface. Thepossibility of loss of the adsorbate molecules when thebubble strikes with a high velocity at the interface is takeninto account through a. wb is the width of the barrier ringand fr is the repulsive force generated by one mole of theadsorbed molecules. Dr is the density difference betweenthe aqueous and air phases. g is acceleration due to gravity

and g is the surface tension. SG is the normalized standarddeviation in surface excess (Gi), given by

SG ¼sG�GGi

(6)

Effect of Surfactant Concentration

Increase in the concentration of SDS increased the resttime of bubbles (Figure 1). Similar effects are also reportedin the literature (Yang and Maa, 1984; Kim and Lee, 1987).The large increase in rest time with surfactant concentrationshown in Figure 1 may be attributed to the increase in thesurface potential as well as the viscosity of the air–waterinterface. With more ionized head groups adsorbed on theinterface, the surface potential increases (Chattoraj andBirdi, 1984). This increases the double layer repulsion thathinders coalescence. With increase in the amount of surfac-tant at the interface, the tails of the surfactant moleculesassociate with each other through hydrophobic interaction.This increases the interfacial viscosity. Increase in inter-action among the surfactant tails reduces the surface diffu-sivity of surfactant. The increase in surface viscositywith increase in surfactant concentration is well known(e.g. Edwards et al., 1991; Kao et al., 1992). Thus,the repulsive force generated by the condensed phase (seeGhosh and Juvekar, 2002) at the periphery of the film (the‘barrier ring’) takes longer time to deplete. This increasesthe rest time. An estimate of the reduction of DG withsurfactant concentration is made as follows. For the lowestconcentration of SDS, we take DG ¼ 1 � 10�10 m2 s�1. PGfor this concentration is obtained by fitting the model to theexperimental data. For the next higher concentration (i.e.200 ppm) of SDS, PG is obtained from the equation

(PG)200 ppm

(PG)100 ppm

¼(R

ffiffiffig

p)200 ppm

(Rffiffiffig

p)100 ppm

�( �GG)100 ppm

( �GG)200 ppm

(7)

Equation (7) is based on the assumption that (wb � a) doesnot change with concentration of SDS. With the value of PGknown for 200 ppm concentration using equation (7), thecharacteristic diffusion time, t, for the rest time distribution

Figure 1. Effect of concentration of SDS on rest time of air bubbles atair-water interface. (�), SDS concentration¼ 100 ppm; (m) SDS concentra-tion¼ 200 ppm; (j) SDS concentration¼ 350 ppm; (u) SDS concentra-tion¼ 500 ppm. The interfacial properties and model parameters are listedin Table 1.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A7): 849–854

850 GHOSH

at 200 ppm concentration is estimated by fitting the model tothe rest time distribution at this concentration. DG for thisconcentration is obtained from equation (3). The sameprocedure is repeated for the higher concentrations ofSDS. The values of DG are shown in Table 1. The valuesof �GGi in Table 1 are taken from the work of Adamson andGast (1997).

Effect of Salts in the Presence of Surfactant

Addition of certain electrolytes in the presence of surfac-tant significantly increased the rest time. The stability of thebubbles in aqueous CTAB solution increased tremendouslywhen NaCl was added to it. This is shown in Figure 2. Themagnitude of surface tension is nearly insensitive to the saltconcentration since the adsorption of CTAB is completeat this concentration of the surfactant (CMC ofCTAB� 0.034%) and no further adsorption is possiblebeyond this. Therefore, increase in the rest time is not dueto more adsorption of the surfactant. NaCl reduces therepulsion between the positively charged head groups ofCTAB. This favours aggregation of the tails of CTAB,which reduces the surface diffusivity of CTAB. It is worthnoting in Figure 2 that, with increase in the concentration ofNaCl beyond 0.1 M, the rest time is not affected by the saltconcentration any more. Steric hydration force may alsocontribute to the stability of the bubbles in this system(Israelachvili, 1997). The reduction of DG with the concen-tration of NaCl is presented in Table 2. Note that, sinceneither the size of the bubbles nor the surface tensionchange significantly with increase in concentration ofNaCl, the value of PG remains constant.

Similar effect was observed when tetraethyl ammoniumbromide (a quaternary ammonium salt) was added to a100 ppm solution of SDS. A striking effect was observedwith lithium chloride. When 1 M LiCl was added to a 200ppm solution of SDS, bubbles did not coalesce at all.Without LiCl, the bubbles coalesced within a few seconds.The associated surfactant molecules on the interfaces prob-ably cause steric repulsion when the bubble approaches theair–water interface. This prevented coalescence completely.Interestingly, at higher temperature (beyond 50�C), severalbubbles coalesced.

Effect of Alcohol

The effects of aliphatic alcohol on coalescence time havebeen studied by several workers (Sagert and Quinn, 1978a,b; Drogaris and Weiland, 1983). Alcohol acts as an amphi-phile and therefore it is expected that it will increase the resttime of the bubbles. Results with ethanol are shown inFigure 3. The results indicate that quite a few bubblescoalesced instantly, whereas many bubbles rested on theinterface for a much longer time. In ethanol, factors stabi-lizing the bubble can originate from either hydration force orhydrophobic interaction. Out of the two, the former must bethe dominant one, since the hydrophobic interaction isexpected to be weak for short ethyl groups. Repulsionoriginating from dipole–dipole interaction and double-layer force is expected to have negligible contribution instabilizing the bubbles. At very low concentrations of thealcohol (a few ppm), pentanol shows much higher resttime than ethanol. The magnitudes of hydration force forpentanol and ethanol are expected to be nearly the same.What differs between them is the length of their hydro-carbon tails.

Effect of Salt in Absence of Surfactant

In pure water, more than 80% bubbles coalesced at firststrike at the interface (Figure 4). The remaining bubblesshowed rest times of the order of 0.2–0.3 s. On the otherhand, when two bubbles were brought into contact in purewater, all bubbles coalesced instantly. In pure water, theconcentration of surface-active molecules can be expected tobe negligible. These molecules adsorb at the interface inpatches because a sufficient number of molecules is notavailable to form a monolayer. If the bubble happens to fallon such a patch it rests there for some time, otherwise itcoalesces instantly. With increase in concentration of NaCl,the fraction of bubbles coalescing at first strike reducedsignificantly. This happened because NaCl increases the areacoverage of the interface. At a threshold concentration ofNaCl (approximately 0.18 M), maximum coverage occurs.Beyond this concentration, no first-strike coalescence was

Figure 2. Effect of NaCl on bubble rest time in presence of 1000 ppmCTAB. R¼ 1.4 mm. (r) No NaCl; (u) 0.03 M NaCl; (s) 0.1 M NaCl;(m) 1 M NaCl. The interfacial properties and model parameters are listedin Table 2.

Table 1. Effect of SDS concentration on coalescence of air bubbles.

SDS concentration(ppm) R (mm) Rb (mm) Gi� 106 (mol m�2) g (mN m�1) t (s) PG SG

DG� 1010

(m2 s�1)

100 1.6 1.12 1.1 68.2 12,569 23.5 0.28 1.00200 1.6 1.14 1.7 66.5 23,000 15.0 0.37 0.56350 1.5 1.01 2.2 64.3 75,000 10.7 0.36 0.14500 1.5 1.03 2.7 62.1 285,000 8.6 0.16 0.04


COALESCENCE OF AIR BUBBLES 851

observed. This threshold value of NaCl concentration issimilar to that reported in the literature for binary coales-cence (Lessard and Zieminski, 1971; Prince and Blanch,1990). Repulsive hydration force has been suggested to be afactor in stabilizing the bubbles in electrolyte solution(Israelachvili, 1997).

When a large number of bubbles coalesce at first strikeand some bubbles take several seconds to coalesce, it isexpected that the distribution of Gi no longer remainsGaussian (the basic assumption on which the stochasticmodel was derived). A skewed distribution may be moreappropriate in such systems. In order to estimate the modelparameters, the bubble rest time distributions in Figure 4were normalized by removing the events involving instanta-neous coalescence. Figure 5 shows the normalized distribu-tions obtained from Figure 4. The values of PG did notchange appreciably with change in concentration of NaCl.SG reduced with addition of NaCl, indicating that the inter-face becomes more uniform with adsorption of hydratedsalt ions as the concentration of NaCl is increased.

Effect of Bubble Size

Bubble rest time increased with increase in size of thebubbles. Similar effect was observed by Li and Slattery (1988).Figure 6 shows the effect of size on rest time with CTABused as surfactant. Similar results were observed with SDS.The variation of PG with R was found to be linear, asexpected from equation (5). However, the straight linecorrelating PG and R does not pass through the origin aspredicted by equation (5). This may be due to the variationof wb with bubble-size.

Coalescence at Water–Organic andAir–Water Interfaces

A very interesting phenomenon was observed when airbubbles were released through the CCl4 phase towards theCCl4–water interface. All bubbles went through the CCl4–water interface instantly, as if they did not face any resis-tance at the interface. After passing through the CCl4–waterinterface, these bubbles rested on the air-water interface fora few seconds. The rest time distribution at the air–waterinterface is shown in Figure 7. On the other hand, thebubbles formed in the aqueous phase showed much higherrest times at the air–water interface than the previous case.This difference in behaviour can be explained as follows.The bubble formed in CCl4 phase carries a thin film of CCl4

Table 2. Effect of NaCl in the presence of CTAB on coalescence of air bubbles.

NaCl concentration (M) Rb (mm) g (mN m�1) t (s) PG SG DG� 1010 (m2 s�1)

0.00 1.332 28.3 17,755.5 6.7 0.19 1.000.03 1.332 28.3 60,100.0 6.7 0.23 0.300.10 1.337 28.1 195,000.0 6.7 0.26 0.091.00 1.339 28.0 220,000.0 6.7 0.21 0.08

Figure 3. Effect of ethyl alcohol on rest time of bubbles. R¼ 1.4 mm. (r)0.2% ethanol, g¼ 71.3 mN m�1, t¼ 3524, PG¼ 9.0, SG¼ 0.30; (s) 0.6%ethanol, g¼ 68.7 mN m�1, t¼ 3657, PG¼ 4.5, SG¼ 0.35; (m) 1% ethanol,g¼ 66.4 mN m�1, t¼ 3784, PG¼ 3.7, SG¼ 0.42.

Figure 4. Effect of NaCl on rest time of bubbles in absence of anysurfactant. R¼ 1.6 mm. (m) No NaCl; (�|) 0.1 M NaCl; (r) 0.12 M NaCl;(j) 0.14 M NaCl; (u) 0.16 M NaCl; (s) 0.18 M NaCl.

Figure 5. Effect of NaCl on rest time of bubbles in absence of anysurfactant. Three rest time distributions in Figure 4 are re-plotted, omittingthe instantaneous coalescence. (�|) 0.1 M NaCl, t¼ 5912, PG¼ 12.3,SG¼ 0.30; (r) 0.12 M NaCl, t¼ 5912, PG¼ 12.4, SG¼ 0.19; (s) 0.18 M

NaCl, t¼ 5887, PG¼ 13.8 and SG¼ 0.14.


852 GHOSH

with it when it passes through the aqueous phase. When thebubble enters the aqueous phase (where the water-solublesurfactant is present) with a high velocity, adsorption ofsurfactant on the CCl4 (film)–water interface is onlypartially complete. As a result, the rest time of the bubbleat the air–water interface is small. Similar results were alsoobserved in other water–hydrocarbon systems. Only verysmall bubbles (size < 1 mm) were supported on the water–organic interface at this surfactant concentration. Thesebubbles took a long time to pass through the liquid–liquidinterface once they rested on the interface. In the presence oflong chain molecules like polyacrylic acid, several bubblesrested at the water–hyzdrocarbon interface for a very longtime, presumably due to steric effect. Some of them did notdetach from the interface even after several days.

CONCLUSIONS

The present study demonstrates the stochastic nature ofbubble rest time and emphasizes the influence of surfaceforces of molecular origin on coalescence. It is shown that

the rest time distributions for air bubbles are quite similar tothose for drops. It can be concluded that the hydrodynamicdrainage time of the thin liquid film trapped between thebubble and the bulk air–water interface is much shortercompared with the total rest time. The bubble rests on theinterface supported mainly by electrostatic double layerrepulsion (DLVO), steric and solvation forces dependingon the nature of surface-active molecules. Entropic factorsinvolving the adsorbed molecules sterically hinder theapproach of the bubble towards the interface. Hydrophobicinteraction favours entanglement of the hydrocarbon tails ofthe surface-active molecules. The interface becomes veryviscous and the surface diffusivity of surfactant is reduced.Consequently higher rest time is observed. The stochasticmodel developed earlier is shown to fit the rest timedistributions of the bubbles quite well. The model para-meters are shown to correlate well with the bulk andinterfacial properties of the systems.

NOMENCLATURE

DG surface diffusivity, m2 s�1

fr repulsive force generated by one mole of the adsorbate at thebarrier ring, N mol�1

F(tR) cumulative probability distribution of bubble rest timeg acceleration due to gravity, m s�2

PG dimensionless coalescence thresholdR radius of bubble, mRb radius of barrier ring, mSG normalized standard deviationt rest time, st characteristic diffusion time, swb width of the barrier ring, m

Greek symbolsa fraction of Gi that remains at the barrier ring after the displace-

ment of adsorbate molecules to the barrier ringg surface tension, N m�1

G Gibbs surface excess of the adsorbate, mol m�2

Gi initial value of Gibbs surface excess of the adsorbate when thebubble strikes at the interface, mol m�2

�GGi mean value of Gi, mol m�2

Gm minimum value of the adsorbate concentration at the barrier ringrequired to support the weight of the bubble, mol m�2

Dr density difference between the aqueous and air phases, kg m�3

li roots of the Bessel function of the first kind and of order 1sG standard deviation in the distribution of Gi

tR dimensionless bubble rest time

REFERENCES

Adamson, A.W. and Gast, A.P., 1997, Physical Chemistry of Surfaces(Wiley, New York, USA), p 68.

Chattoraj, D.K. and Birdi, K.S., 1984, Adsorption and the Gibbs SurfaceExcess (Plenum Press, New York, USA), pp 101–102.

Chaudhari, R.V. and Hofmann, H., 1994, Coalescence of gas bubbles inliquids, Rev Chem Eng, 10: 131–190.

Drogaris, G. and Weiland, P., 1983, Coalescence behaviour of gas bubblesin aqueous solutions of n-alcohols and fatty acids, Chem Eng Sci, 38:1501–1506.

Edwards, D.A., Brenner, H. and Wasan, D.T., 1991, Interfacial TransportProcesses and Rheology (Butterworth-Heinemann, Boston, MA, USA),p 224.

Ghosh, P. and Juvekar, V.A., 2002, Analysis of the drop rest phenomenon,Chem Eng Res Des, 80: 715–728.

Ghosh, P. and Juvekar, V.A., 2003, Effect of temperature on permeation ofair through thin liquid films, J Chem Eng Jpn, 36: 711–715.

Israelachvili, J.N., 1997, Intermolecular and Surface Forces (AcademicPress, London, UK), pp 276, 281.

Figure 6. Effect of bubble-size on rest time. CTAB concentra-tion¼ 1000 ppm. g¼ 28.3 mN m�1. (r) R¼ 1 mm, t¼ 4622, PG¼ 4.9,SG¼ 0.13; (j) R¼ 1.9 mm, t¼ 60233, PG¼ 15.4, SG¼ 0.14; (m)R¼ 3.2 mm, t¼ 484643, PG¼ 36.5, SG¼ 0.14.

Figure 7. Comparison of rest time of air bubbles at CCl4–water interfaceand air-water interface. SDS concentration¼ 500 ppm. NaCl¼ 0.1 M.R¼ 1.5 mm. gCCl4

–water¼ 6.8 mN m�1. gair–water¼ 55.6 mN m�1. (u) Resttime of bubbles at CCl4–water interface. (m) Rest time distribution whenthe bubbles are formed in the organic phase, t¼ 11909.6, PG¼ 15.5,SG¼ 0.37. (s) Rest time distribution when the bubbles are formed in theaqueous phase, t¼ 11909.6, PG¼ 2.65, SG¼ 0.23.


COALESCENCE OF AIR BUBBLES 853

Kao, R.L., Edwards, D.A., Wasan, D.T. and Chen, E., 1992, Measurement ofinterfacial dilatational viscosity at high rates of interface expansion usingthe maximum bubble pressure method. I. Gas–liquid surface, J ColloidInterface Sci, 148: 247–256.

Kim, J.W. and Lee, W.K., 1987, Coalescence behaviour of two bubbles instagnant liquids, J Chem Eng Jpn, 20: 448–453.

Lessard, R.R. and Zieminski, S.A., 1971, Bubble coalescence and gastransfer in aqueous electrolyte solutions, Ind Eng Chem Fundam, 10:260–269.

Li, D. and Slattery, J.C., 1988, Experimental support for analysis ofcoalescence, AIChE J, 34: 862–864.

Prince, M.J. and Blanch, H.W., 1990, Transition electrolyte concentrationsfor bubble coalescence, AIChE J, 36: 1425–1429.

Sagert, N.H. and Quinn, M.J., 1978a, The coalescence of gas bubbles indilute aqueous solutions, Chem Eng Sci, 33: 1087–1095.

Sagert, N.H. and Quinn, M.J., 1978b, Surface viscosities at high pressuregas–liquid interfaces, J Colloid Interface Sci, 65: 415–422.

Yang, Y.M. and Maa, J.R., 1984, Bubble coalescence in dilute surfactantsolution, J Colloid Interface Sci, 98: 120–125.

The manuscript was received 27 May 2003 and accepted for publicationafter revision 28 April 2004.


854 GHOSH

coalescence of air bubbles at air–water interface

Documents