Influence of Surfactant Concentration and Chain Length on the

The mass transfer across the gas/liquid interface can be self-facilitated by the creation of surface tension and/or density gradients driving interfac...
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Ind. Eng. Chem. Res. 2000, 39, 1088-1094

Influence of Surfactant Concentration and Chain Length on the Absorption of CO2 by Aqueous Surfactant Solutions in the Presence and Absence of Induced Marangoni Effect G. Va´ zquez, G. Antorrena, and J. M. Navaza* Department of Chemical Engineering, University of Santiago, Avda. das Ciencias, s/n, E-15706 Santiago de Compostela, Spain

We studied the absorption of CO2 at a plane interface by aqueous solutions of anionic surfactants (sodium alkyl sulfates) or of the cationic surfactant cetyltrimethylamonium bromide in the presence and absence of induced Marangoni effect induced by deposition of the liquid of low surface tension on the gas-liquid interface. The surface velocity distributions generated by induced Marangoni effect in the absorption cell were determined for each of the various surfactant solutions by the stroboscopic technique. The resistance to mass transfer induced by the surfactants increased linearly with the logarithm of surfactant concentration, Cs. For the anionic surfactants used, the resistance also depended linearly on their alkyl chain length, n. In the presence of induced Marangoni effect, ≈87% of the total surfactant-induced resistance to absorption of CO2 were due to the effect of the surfactant on interfacial hydrodynamics. Introduction The mass transfer across the gas/liquid interface can be self-facilitated by the creation of surface tension and/ or density gradients driving interfacial turbulence (the Marangoni effect).1-4 Such turbulence (agitation at the interface) can alter both liquid flow patterns and the geometry of the interface itself. Both these aspects of turbulence driven by surface tension gradients are reduced if these gradients are reduced by the addition of surfactant, although extreme interfacial turbulence can reduce the effects of the surfactant by hindering its effective incorporation in the interface.5,6 The influence of surfactants on mass transfer across gas/liquid interfaces has been investigated in numerous studies.1-3,7-14 Even very low concentrations of surfactant generally reduce the mass transfer significantly, although increased mass transfer may occur with certain soluble surfactants3 or surfactant/polymer mixtures,13 or under certain special conditions.14 The reduction of mass transfer by surfactants is usually considered to be mediated by two main effects: the reduction or elimination of interfacial turbulence and the interposition of a surfactant barrier hindering transfer.2,3,7,12 However, it is often impossible to experimentally determine the individual contributions of these two effects.2,5,7 Spontaneous interfacial turbulence created by mass transfer as described above is random and extremely difficult to quantify, but convective flow induced by the deposition of a liquid of low surface tension at the interface is more amenable to experimental investigation and has the same effects on mass transfer as spontaneous turbulence. In previous work15 we used this approach to correlate interfacial area (determined by Danckwerts’ method) with measures of turbulence and of the physical properties of the system and to obtain an experimental determination of the mass-transfer * To whom correspondence should be addressed. E-mail: [email protected].

coefficient, kL, which in the absence of surfactants, agreed well with a theoretical coefficient calculated from the known surface velocity distribution16 by means of a penetration theory17-19 and corrected for the convectioninduced perturbation of interfacial area. In the work now reported on we used the same methods to compare theoretical and experimental masstransfer coefficients in the presence and absence of various concentrations of surfactants; because the theoretical coefficient accounts only for the hydrodynamic effects of the surfactant, not for its barrier effect, the discrepancy between the theoretical and calculated values of the mass-transfer coefficient allows calculation of the contributions of each kind of effect to the surfactant-induced resistance to absorption of CO2. The surfactants used were the cationic surfactant cetyltrimethylamonium bromide and a series of anionic surfactants (sodium alkyl sulfates) differing in alkyl chain lengths, the influence of which was also evaluated. Apparatus and Procedure The apparatus and the procedure employed have been described in detail elsewhere.20 Figure 1 shows the apparatus used for absorption measurements. Pure CO2 from a cylinder (1) is saturated with water vapor at the working temperature by passage through a thermostated humidifier (2) before entering the absorption cell (3). The rate of absorption of CO2 is calculated as the difference between the flow rates into and out of the cell, which are measured by bubble flowmeters (4). Absorbent liquid from a raised tank (5) is fed into the center of the base of the cell at constant pressure, the flow rate being controlled by a stopcock (6) and measured with a previously calibrated capillary (7) and the temperature being brought to 20 °C in a heat exchanger (8) through which water from the humidifier thermostat is circulated. The absorbent liquid leaves the cell through a lateral exit at its base (9). The ethanol is fed from a constant-flow buret (10). The absorption cell (Figure 2) consists of two concentric tubes with a common base plate. The inner tube is

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for sodium lauryl sulfate (SLS) were also used in joint analysis of the results for all the anionic surfactants. The concentrations of all the surfactant solutions were below the corresponding critical micellization concentrations.22 In experiments to determine interfacial area under the same conditions as in previous work,15 the absorbent liquids were 0.5/0.5 M sodium carbonate/bicarbonate buffers containing various concentrations of NaAsO2 (all less than 8 × 10-3 M) and 10-5-10-3 wt % of CTMAB. Physicochemical Properties

Figure 1. Diagram of the apparatus.

The surface tensions of surfactant solutions were taken from previously published work16 as were the physical characteristics of the 0.5/0.5 M sodium carbonate/bicarbonate buffers used, the diffusivity and solubility of CO2 in these buffers and the first-order pseudoconstant, k1, for the reaction between CO2 and the buffers.15 Because the densities and viscosities of the surfactant solutions were found experimentally to be practically identical to those of pure water, the diffusivity and solubility of CO2 in these solutions were also assumed equal to their values for pure water: D ) 1.71 × 10-5 cm2/s;22 Ce ) 0.039 mol/L.23 Results and Discussion

Figure 2. Schematic diagram of the absorption cell.

of radius 6.6 cm and height 7 cm, and the outer tube is of radius 7.1 cm and height 14 cm. A methacrylate plate closes the cell above with openings for inflow and outflow of gas and for a capillary tube for deposition of the low surface tension liquid (ethanol). The absorbent liquid enters the center of the bottom of the inner tube, rises, and flows over the brim into the annular space between the two tubes (0.3 cm), from where it leaves the cell through the outlet at the base; making the absorbent liquid flow over a brim in this way prevents the accumulation of impurities at the interface and means that the radial surface motion generated by the induced Marangoni effect is not subject to the constraint of enclosing walls as it is in previous devices.21 The level of liquid in the annular space is about 2 cm of the inner tube border. The ethanol is deposited at the center of the interface through a capillary fed from a constantflow buret, and the tip of the capillary is located as close as possible to the surface of the absorbent liquid (0.15 cm) so as to minimize mechanical perturbation of the surface by falling droplets. Except in experiments to determine interfacial area, the absorbent liquids used were water or 10-5-10-3 wt % aqueous solutions of cetyltrimethylammonium bromide (CTMAB), sodium octyl sulfate (SOS), sodium dodecyl sulfate (SDS), sodium tetradecyl sulfate (STS), or sodium hexadecyl sulfate (SHS); previous findings17

Hydrodynamics. The surface velocity distributions generated by induced Marangoni effect in the absorption cell were determined for each of the various surfactant solutions. A stroboscopic technique, previously used for water,16 was used to follow and record photographically the motion of 0.5-mm polyethylene disks, employed as tracers, which could be added onto the interface along with the low surface tension liquid through a capillary. A camera placed above the capillary photographed the tracers, lighted with a stroboscopic lamp. The experiments performed for each of the systems were recorded photographically. From the positions of the tracer, surface velocities were obtained as the product of the interval between two consecutive images of the tracer and the flashing frequency of the stroboscope lamp. This value was assigned to the middle point between the two images. For the absorbent flow rate used (18 L/h), the surface velocity due to absorbent flow in the absence of induced Marangoni effect was less than 0.5 cm/s and was treated as negligible in comparison to the velocities of 10-60 cm/s induced by Marangoni effect (both velocities are purely radial in the cell used). Figure 3 shows the surface velocity distributions for the system ethanol-aqueous solutions of SLS; the effect of the surfactant is an inhibition of the interfacial turbulence induced. The velocities so measured were used to calculate the Reynolds number Re for quantification of convective flow.16 The Reynolds number is defined in eq 1 and combines, as usual, density, viscosity, a characteristic length, rc, and an average velocity:

Re )

rc

[∫r

Frc

0

u dr/rc

µ

]

∫rr u dr

F )

c

0

µ

(1)

The average velocity is obtained from the experimental data for the velocity distribution, according to the mean-value theorem between the values of rc and r0. Plotting Re against the surface tension difference driv-

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Figure 3. Distribution of surface velocities induced by depostion of ethanol on aqueous solutions of SLS. (-) water, (- -) SLS 10-5%, (‚‚‚) SLS 10-4%, (-‚-) SLS 5 × 10-4%, and (s) SLS 10-3%.

Figure 4. Dependence of Re on the surface tension difference driving convective flow. (0) ethanol solutions-water, (9) ethanolSOS solutions, (4) ethanol-SDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

ing convective flow ∆σ (∆σ ) σs - σe, σs dynamic surface tension of surfactant solution and σe surface tension of ethanol) shows that the presence of surfactant not only reduces ethanol-induced convective flow but also more than what would be predicted on the basis of the surfactant-induced reduction in surface tension (Figure 4). Mass Transfer. All the experimental absorption rates, N, that are presented in this paper are the ones corresponding to the flat surface of the cell,15,18 once the contribution of extreme effects (the absorption that is produced in the annular space and in the wetted wall of the inner tube, and that is determined in each case) has been eliminated from the total absorption rates. The absorption rates are determined for several heights of liquid in the annular space. Straight lines occur, with slopes practically independent of the induced turbulence; when the absorption rate, N′, is plotted versus the difference of heights between the border of the inner tube and the level of the liquid in the annular space, ∆h, the extrapolation of the lines permits one to know

Figure 5. Dependence of experimental kLA values on surfactant concentration in the presence of induced convective flow. (9) ethanol-SOS solutions, (4) ethanol-SDS solutions, (O) ethanolSLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, (3) ethanol-CTMAB solutions, and (- -) ethanolwater.

Figure 6. Dependence of experimental kLA values on surfactant concentration in the absence of induced convective flow. (9) SOS solutions, (4) SDS solutions, (O) SLS solutions, (b) STS solutions, (2) SHS solutions, (3) CTMAB solutions, and (- -) water.

N′ for ∆h ) 0, the absorption which takes place through the flat surface of the cell and in the annular space between the two cylinders.22 N, the rate of CO2 absorption measured in the presence or absence of induced Marangoni effect, was used to calculate kLA (where kL is the mass-transfer coefficient and A the surface area) from the equation

kLA )

N (C - C) e

(2)

where Ce is the solubility of CO2 in the absorbent and C the concentration of CO2 in the bulk liquid (calculated as recommended in the literature.21 kLA increased in the presence of induced Marangoni effect, decreased with increasing surfactant concentration, and among the anionic surfactants increased with the length of their alkyl chains (Figures 5 and 6). Furthermore, in the presence of induced Marangoni effect the relation-

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Figure 7. Dependence of the proportional inhibition of absorption, I, on π, the difference between the surface tensions of water and the surfactant solution. (9) ethanol-SOS solutions, (4) ethanolSDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

Figure 9. Plot of theoretical kLtAg values (see text) against experimental kLA values. (0) ethanol solutions-water, (9) ethanol-SOS solutions, (4) ethanol-SDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

Figure 10. Schematic diagram of the radial flow in an interfacial layer.

in the horizontal plane, regardless of any perturbation due to turbulence, and kLt was calculated, following Higbie, as

kLt ) 2

Figure 8. Dependence of experimental kLA values on Re in the presence of induced convective flow. (0) ethanol solutions-water, (9) ethanol-SOS solutions, (4) ethanol-SDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

ship between the surface tension difference, π ) σw σs, and I, the proportional inhibition of absorption (defined by I ) 1 - (kLA)s/(kLA)w, where “s” indicates the presence of surfactant and “w” pure water) was practically independent of the identity of the surfactant responsible for the decrease in surface tension (Figure 7). However, plotting kLA against Re (Figure 8) shows that the reduction in kLA due to the addition of surfactant in the presence of Marangoni effect was not due solely to surfactant-induced reduction of convection, and the same conclusion is implied by the 2-4% shortfall between the experimental values of kLA and theoretical values kLtAg that take only hydrodynamic effects into account (Figure 9). The “geometric” area, Ag ) πrc2, is appropriate because the measured surface velocity distributions upon which the value of kLt was based refer to velocities

x

D πte

(3)

where D is the diffusivity of CO2 and the average exposure time, te, is calculated from the surface velocity distributions. The application of penetration theory is valid because Beek and Bakker’s24 equation for mass transfer through a flowing interface is satisfied. The exposure time is calculated by taking into account the liquid elements that move from the addition point of the liquid solute, r0, origin of the movements, and also the contribution made by the liquid elements that reach the surface at r.17,18 The surface residence time, ter0, taken by a surface element to travel from r0 to rc is

ter0 )

∫rr dr u c

0

(4)

To take into account the volume elements that reach the surface between r0 and rc, note that the increase in radial flow (Figure 10) between r and (r + dr) in a surface film of depth δ is

2πδ[(r + dr)(u + du) - ur] ) 2πδ d(ur)

(5)

Because the surface residence time of an element reaching the surface at r and traveling to rc is

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Figure 11. Danckwerts plots obtained to determine effective interfacial area in the presence of induced convective flow and in the presence or absence of CTMAB. (b) buffer solution, ([) CTMAB 10-5%, (2) CTMAB 10-4%, (9) CTMAB (5 × 10-4)%, and (1) CTMAB 10-3%.

ter )

∫rr dr u c

(6)

the mean time of residence is given by

teth )

r dr ur d(ur) + 2πδ∫u r [∫r ∫rr dr u u] ur 2πδr0u0 + 2πδ∫u r d(ur)

2πδr0u0

c

c c

0

c

0 0

c c

(7)

which can be simplified to

teth )

ur r dr d(ur) + ∫u r [∫r ∫rr dr u u] c

0

c c

0 0

rcuc

22% greater than Ag, increasing with decreasing surfactant concentration (Figure 12). Because the physical properties of the solutions were virtually the same in the experiments with CTMAB as in those carried out previously with SLS, the data obtained with the two surfactants in the presence of induced convection were jointly correlated to afford the expression

A/Ag ) (3.26 × 10-3)Re0.7We-0.2

0 0

r0u0

Figure 12. Dependence of effective interfacial area A on surfactant concentration in the presence and absence of induced convective flow. (O) SLS solutions, (3) CTMAB solutions, and (s) geometric area.

c

(8)

where the first term in the numerator (and in the denominator of the expression (7)) takes into account volume elements reaching the surface at r0. For water as the absorbent liquid, the theoretical mass-transfer coefficients calculated from eq 3 using teth (eq 8) for the mean residence time are all within 4% of the experimental values.18 Interfacial Area. To obtain experimental values of kL from the values of kLA obtained as above, we calculated a relationship between A/Ag and the Reynolds and Weber numbers of the system using data for the effective interfacial area A obtained by Danckwerts’ method,25 which makes use of a moderately fast pseudofirst-order reaction between the absorbed gas and the absorbent liquid. In this work, as previously,15 we measured A in the presence and absence of induced convective flow by means of the reaction between CO2 and 0.5/0.5 M sodium carbonate/bicarbonate buffers containing various concentrations of NaAsO2 (all less than 8 × 10-3 M) and with or without 10-5-10-3 wt % of surfactant (previously15 SLS; CTMAB in this work). Figure 11 shows the Danckwerts plots obtained with CTMAB. In the absence of induced Marangoni effect the effective interfacial area never differed by more than 3% from the geometrical area, Ag, whereas in the presence of Marangoni effect the effective area was 11-

(9)

which was thereafter used to calculate the effective interfacial area, A, in the presence of induced convective flow. In systems with induced turbulence, the produced ripples can be visually observed and the change in the area could be attributed to the ripples caused in the surface plane of the cell. Surfactant-Induced Resistance to Mass Transfer. The values of A given by eq 9 allow the calculation of both experimental values of kL (from the measured values of kLA) and theoretical values kLcal that, unlike kLt, take the convection-induced perturbation of the interface into account: kLcal ) kLtAg/A. The experimental values may be used to define the experimental surfactant-induced resistance to mass transfer,11 R:

R ) 1/kLs - 1/kLw

(10)

where kLs and kLw are the values of kL respectively in the presence and absence of surfactant. In the presence of induced convective flow, R increases linearly with the logarithm of surfactant concentration (Figure 13) and, among the anionic surfactants, with the length of the alkyl chain: to within a 5% error,

R ) 2283.2 + 219.8n + 943.4 log Cs

(11)

However, substituting the theoretical value, kLcal, for the kL in eq 10 affords smaller values of Rcal, showing that the resistance due to the hydrodynamic effects of the surfactant, though predominant, is less than the total resistance. The resistance due to nonhydrodynamic effects of the surfactant, defined as the difference ∆R between R and Rcal, may be calculated as

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Figure 13. Dependence of total surfactant-induced resistance to mass transfer on surfactant concentration in the presence of induced convective flow. (9) ethanol-SOS solutions, (4) ethanolSDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

∆R ) 1/kLs - 1/(kLcal)s

Figure 14. Influence of surfactant concentration on the resistance to mass transfer due to nonhydrodynamic effects of the surfactant, in the presence of induced convective flow. (9) ethanol-SOS solutions, (4) ethanol-SDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

(12)

(since kLw and (kLcal)w are practically identical), and proved to be, like R, linearly dependent on both log Cs (Figure 14) and, among the anionic surfactants, the chain length n: to within a 7% error,

∆R ) 306.1 + 29.6n + 123.4 log Cs

(13)

Writing eqs 11 and 13 as respectively

R ) 943.4(2.42 + 0.233n + log Cs)

(11′)

∆R ) 123.4(2.48 + 0.24n + log Cs)

(13′)

and

now shows that the ratio R/∆R may be approximately calculated as 943.4/123.4 ) 7.6, a value implying that in the presence of ethanol-induced convective flow about 87% of the total surfactant-induced resistance to mass transfer is due to the hydrodynamic effects of the surfactant. Similar calculations on the data obtained in the absence of induced convective flow show that under these conditions too (in which A may be taken equal to Ag) R depends linearly on log Cs (Figure 15) and n. The fact that the values of R for given Cs and n are now about twice those found in the presence of induced convection is in keeping with the hypothesis mentioned in the Introduction according to which interfacial turbulence tends to reduce the effects of surfactants by hindering their effective incorporation in the interface.6 The surface velocity distributions in all the systems in the absence of induced convective flow are practically equal, and the values of the surface velocities are much less than those in the systems with induced convective flow. These facts permit us to justify that the resistance to the mass transfer should also be to the existence of nonhydrodynamic effects. The influence of the surface agents on the mass transfer can be related to the surface surfactant concentration,6 that it is a function of the surfactant

Figure 15. Dependence of total surfactant-induced resistance to mass transfer on surfactant concentration in the absence of induced convective flow. (9) ethanol-SOS solutions, (4) ethanolSDS solutions, (O) ethanol-SLS solutions, (b) ethanol-STS solutions, (2) ethanol-SHS solutions, and (3) ethanol-CTMAB solutions.

concentration, Cs, and of the surface tension, σ. The surface tension decreases because the surface excess concentration increases when the bulk surfactant concentration increases below the cmc. In all the systems studied in this paper, for the same anionic surfactant concentration, the surface tension reduces upon increasing the chain length, n, and the resistance to mass transfer increases. Nomenclature A ) interfacial area Ag ) geometric area (πrc2) C ) concentration of the gas in the bulk of the liquid Ce ) solubility of the gas Cs ) concentration of surfactant D ) diffusivity of CO2 in the solution

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De ) diffusivity of convection-inducing liquid (solute) in the solution K1 ) rate constant (see Physicochemical Properties) kL ) mass-transfer coefficient in the liquid phase kLt ) mass-transfer coefficient in the liquid phase, calculated as 2xD/(πte) kLcal ) mass-transfer coefficient in the liquid phase, calculated as kLtAg/A kLs ) mass-transfer coefficient in the liquid phase, in the presence of surfactant kLw ) mass-transfer coefficient in the liquid phase, in the absence of surfactant N ) rate of absorption R ) resistance calculated from experimental values of kL Rcal ) resistance calculated from theoretical values of kLcal ∆R ) difference between experimental and calculated resistances (eq 11) rc ) radius of the absorption cell r ) distance to the axis of the cell r0 ) radius of the film of solute te ) time of exposure tero ) time of exposure, calculated from eq 3 ter ) time of exposure, calculated from eq 5 teth ) time of exposure, calculated from eq 7 u ) surface velocity uc ) velocity at the distance rc u0 ) velocity at the edge of the film of solute Greek Letters δ ) depth of an interfacial layer F ) density of the solution µ ) viscosity of the solution σ ) surface tension of the solution ∆σ ) surface tension difference between the convectioninducing liquid and the absorbent solution σw ) surface tension of water σe ) surface tension of the convection-inducing liquid (ethanol) σs ) surface tension of the surfactant solution π ) surface tension difference between water and the surfactant solution Dimensionless Numbers

∫rr Fu dr c

Re )

0

µ F

We )

Reynolds number

∫rr u2 dr c

0

σ

Weber number

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(5) Llorens, J.; Mans, C.; Costa, J. Discrimination of Effects of Surfactants in Gas Absorption. Chem. Eng. Sci. 1988, 43, 443450. (6) Va´zquez, G.; Cancela, A.; Varela, R.; Alvarez, E.; Navaza, J. M. Influence of Surfactants on Absorption of CO2 in a Stirred Tank with and without Bubbling. Chem. Eng. J. 1997, 67, 131137. (7) Frey, D. D.; King, C. J. Effects of Surfactants on Mass Transfer During Spray Drying. AIChE J. 1986, 32, 437-443. (8) Hikita, H.; Asai, S.; Katsu, Y.; Ikuno, S. Absorption of Carbon Dioxide into Aqueous Monoethanolsamine Solutions. AIChE J. 1979, 25, 793-800. (9) Asolekar, S. R.; Desai, D.; Deshpande, P. K.; Kumar, R. Effect of Surface Resistance on Gas Absorption Accompanied by a Chemical Reaction in a Gas-Liquid Contactor. Can. J. Chem. Eng. 1985, 63, 336-339. (10) Biswas, J.; Asolekar, S. R.; Kumar, R. Effect of Surface Resistance Arising Due to Surfactant on Gas Absorption Accompanied by a Chemical Reaction in a Foam-Bed-Reactor. Can. J. Chem. Eng. 1987, 65, 462-469. (11) Lindland, K. P.; Terjesen, S. G. The Effect of a Surface Active Agent on Mass Transfer in Falling Drop Estraction. Chem. Eng. Sci. 1956, 5, 1-12. (12) Mudge, L. K.; Heideger, W. J. The Effect of Surface Active Agents on Liquid-Liquid Mass Transfer Rates. AIChE J. 1970, 16, 602-608. (13) Mashelkar, R. A.; Soylu, M. Absorption in Mixed Surfactant-Polymeric Films: A Novel Phenomenon. AIChE J. 1984, 30, 688-691. (14) Albal, R. S.; Shah, Y. T.; Schumpe, A.; Carr, N. L. Mass Transfer in Multiphase Agitated Contactors. Chem. Eng. J. 1983, 27, 61-80. (15) Va´zquez, G.; Antorrena, G.; Navaza, J. M.; Santos, V. Effective Interfacial Area in Presence of Induced Turbulence. Int. Chem. Eng. 1994, 34, 247-254. (16) Va´zquez, G.; Antorrena, G.; Navaza, J. M. Estimation of the Turbulence Induced by the Marangoni Effect at a Gas-Liquid Interface. Int. Chem. Eng. 1990, 30, 228-235. (17) Va´zquez, G.; Antorrena, G.; Navaza, J. M.; Rodrı´guez, T.; Santos, V. Interpretacio´n de la absorcio´n de gases con conveccio´n interfacial. Rev. R. Acad. Cienc. Madrid 1990, 84, 525-529. (18) Va´zquez, G.; Antorrena, G.; Navaza, J. M.; Santos, V. Absorption of CO2 by Water and Surfactant Solutions in the Presence of Induced Marangoni Effect. Chem. Eng. Sci. 1996, 51, 3317-3324. (19) Lu, H.; Yang, Y.; Maa, J. Effect of Artificially Provoked Marangoni Convection at a Gas-Liquid Interface on Absorption. Ind. Eng. Chem. Res. 1996, 35, 1921-1928. (20) Va´zquez, G.; Antorrena, G.; Navaza, J. M.; Santos, V.; Rodrı´guez, T. Absorption of CO2 in Aqueous Solutions of Various Viscosities in the Presence of Induced Turbulence. Int. Chem. Eng. 1993, 33, 649-655. (21) Smigelschi, O.; Suciu, D. G.; Ruckenstein, E. Absorption under the Action of Artificially Provoked Marangoni Effect. Chem. Eng. Sci. 1969, 24, 1227-1234. (22) Navaza, J. M. Estudio de las velocidades superficiales inducidas por efecto Marangoni y su influencia en procesos de absorcio´n. Ph.D. Thesis, University of Santiago, Santiago, Spain, 1986. (23) Danckwerts, P. V.; Sharma, M. M. The Absorption of Carbon Dioxide into Solutions of Alkalis and Amines. Chem. Eng. (London) 1966, 44CE, 244-280. (24) Beek, W. J.; Bakker, C. A. P. Mass Transfer with a Moving Interface. Appl. Sci. Res. 1961, 10A, 241-252. (25) Roberts, D.; Danckwerts, P. V. Kinetics of CO2 Absorption in Alkaline Solutions. Chem. Eng. Sci. 1962, 17, 961-969.

Received for review August 27, 1999 Revised manuscript received January 6, 2000 Accepted January 11, 2000 IE990644J