Effect of the Surfactant Concentration on the Rise of Gas Bubbles in

Jul 28, 2004 - Effect of the Surfactant Concentration on the Rise of Gas Bubbles in Power-Law Non-Newtonian Liquids. Aristotelis Tzounakos,Dimitre G...
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Ind. Eng. Chem. Res. 2004, 43, 5790-5795

Effect of the Surfactant Concentration on the Rise of Gas Bubbles in Power-Law Non-Newtonian Liquids Aristotelis Tzounakos, Dimitre G. Karamanev,* Argyrios Margaritis, and Maurice A. Bergougnou Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Canada N6A 5B9

The effect of the surfactant concentration on the terminal velocity, shape, and drag coefficient of freely rising bubbles in a non-Newtonian, pseudoplastic liquid was studied. It is known that surfactants affect the bubble terminal velocity by changing both the shape and surface mobility of the bubble. In this work we studied separately the effect of surfactants on the shape and surface mobility by using the recently obtained drag curves for freely rising bubbles with and without surface mobility. It was shown that, within the range of surfactant concentrations studied, the latter had no effect on the bubble shape. However, the effect on the bubble surface mobility was significant. It was shown that the transition from a bubble with an immobile surface to a bubble with a mobile one is a function of the surfactant concentration, terminal Reynolds number, and rheological properties of liquid. The values of these parameters at which transition occurs were determined. Introduction Gas-liquid and gas-liquid-solid systems containing non-Newtonian fluids as a continuous phase are very popular in different fields of human practice such as biotechnology, food industry, and chemical technology. In most of these multiphase systems, gas bubbles rise through the liquid. Typical examples are bubble columns, slurry bubble columns, airlift contactors, and mechanically agitated vessels. To understand the behavior of such systems and to develop their mathematical models, it is of significant importance to know the behavior, and in particular hydrodynamics, of the free rise of gas bubbles in non-Newtonian fluids. For example, computational fluid dynamics models of the above-mentioned reactors require the knowledge of the drag coefficient and terminal velocity of a single bubble in quiescent liquid.1,2 One of the important factors affecting the free rise, and the drag coefficient in particular, of rising gas bubbles is the presence and concentration of surface-active compounds in the continuous liquid. It has been recognized that molecules of surfactants, which tend to concentrate on the gas-liquid interface, influence the bubble rise dynamics mainly by affecting both the bubble surface mobility and bubble shape.3 A number of studies have been conducted on the hydrodynamics of rising gas bubbles in non-Newtonian fluids, especially those with power-law rheological properties.4-6 It has been shown that, in general, bubbles rising in pure liquids, containing no surfactants, have higher terminal velocities than bubbles rising in surfactant-containing liquids.7-10 When gas bubbles are released into a solution containing a surfactant, the latter will accumulate on the liquid-gas interface created by the bubble and solution. They found that the presence of a surfactant would decrease the bubble velocity. Surfactants affect in general both the bubble * To whom correspondence should be addressed. Tel.: +1 (519) 661 2111 (ext. 88230). Fax: +1 (519) 661 3498. E-mail: [email protected].

surface mobility and bubble shape. The effect of each of these parameters on the bubble rise will be studied in this paper. It has been shown that bubbles rising in surfactantcontaminated Newtonian liquids have the same terminal velocity and drag coefficient as freely rising rigid particles with similar size, shape, and particle-liquid density difference.11 This means that, in the absence of interfacial motion, gas bubbles act similarly to rigid bodies from the hydrodynamic point of view. However, bubbles rising in pure liquids have higher terminal velocities and smaller drag coefficients than bubbles (and rigid particles) rising in contaminated liquids, especially in the intermediate Reynolds numbers range.3 This is the range where the motion of the bubble interface affects most significantly the bubble rise. Thus, the comparison of the bubble drag to the drag of rigid particles with the same shape can be used to determine the effect of surface mobility on bubble motion. Previously, the light rigid particles having the shape and volume of gas bubbles were named “solid bubbles”.11,12 The drag curve (the relationship between the drag coefficient and Reynolds number) of rigid particles rising in power-law, pseudoplastic liquids was determined recently.13 It has been shown that this curve differs significantly from the drag curve of freely falling particles14 in the same type of liquid. However, freely rising rigid spherical particles had the same drag coefficient as freely rising “solid bubbles” with a wide variety of sizes and shapes, including spheroidal, ellipsoidal, and spherical cap.12 The study of the free rise of gas bubbles in “pure” pseudoplastic liquids, containing no surfactants, showed that the drag coefficients of bubbles are lower than those of “solid bubbles” having the same Reynolds number.12,15 The difference was by a factor of 16/24, or 33.3%. This finding was attributed to the effect of interface motion on bubble rise. The two drag curves were described by two semiempirical correlations (eqs 9 and 11), based on the model of a moving rigid particle for the case of particles without interface motion and on the model of a particle with a mobile

10.1021/ie049649t CCC: $27.50 © 2004 American Chemical Society Published on Web 07/28/2004

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5791

Figure 1. Drag curves of bubbles with rigid and moving surfaces.

surface for the case of gas bubbles. These curves are shown in Figure 1. Therefore, if one compares the drag coefficient of a freely rising single gas bubble in a quiescent power-law fluid to the curves on Figure 1, it is possible to determine the effect of bubble surface mobility on bubble rise. If the drag coefficient is close to that of the drag curve with internal circulation (lower curve in Figure 1 and eq 11), then the bubble has a significant interface motion. On the other hand, if the bubble drag coefficient is close to that representing a rigid particle rise (upper curve in Figure 1 and eq 9), that means that its surface is immobile. In addition to the effect on surface mobility, surfactants affect also the shape of the gas bubbles. Usually, by affecting surface forces, surfactants cause a decrease in the bubble aspect ratio; i.e., bubbles become “more spherical”.3 This can also cause a change in the terminal velocity. However, it is not known to what extent the change in the bubble shape, caused by the presence of surfactants, affects the bubble rise velocity. The main aim of this work is to study the effect of surfactants on the dynamics of free rise of single gas bubbles in quiescent non-Newtonian, pseudoplastic liquids. It will be determined if the effect is due to the change in the bubble shape, reduction of interface mobility, or both factors. The critical concentrations of the surfactant, at which the latter starts affecting the bubble rise, will be determined. Materials and Methods Experimental Setup. The apparatus that was used throughout this research is shown in Figure 2. The column used was acrylic and was approximately 240 cm × 30 cm × 30 cm. The largest bubble to column width ratio was less than 0.2, thus ensuring that there would be no wall effects affecting the data.16 The column was filled with solutions of carboxymethylcellulose (CMC) in deionized water, with different concentrations containing different amounts of surfactant, sodium dodecyl sulfate (SDS). The bubbles were released from the bottom of the column using a rotating cup. The air was delivered to the Teflon cup through a nozzle in the column, filling the cup. Once the liquid became quiescent and the desired amount of air was collected in the cup, the bubble was released into the solution by rotating the Teflon cup. The bubbles produced ranged in volume from 0.005 to 38 cm3. A high-resolution CCD video camera (Hitachi Ltd., Tokyo, Japan, model KP-M 1U) was mounted on a vertically moveable ledge, which was capable of being adjusted to the required height by

Figure 2. Experimental setup.

using an adjustable speed motor. The camera was adjusted by varying the shutter speed and light intensity. A mounting lamp (Fisher Scientific, Ottawa, Ontario, Canada, model 11-504-5V4) with two flood lamps was used as the light source. The video output from the camera was then fed into a high-resolution Super-VHS video-recording device (Sanyo Canada Inc., Concord, Ontario, Canada, model TLS-7000). The video signal from the Super-VHS recorder was digitized using a video capture-board (Miro Computer Products AG, Ro¨dermark, Germany, model DC-30), and thus the images were then available for treatment on the computer. The images had an approximate resolution of 570 lines; therefore, this produced a very clear and precise image. The camera was mounted sidewise (90° rotation to the horizontal plane). In that case, the image lines produced by the camera did not interfere with the image lines produced by the VCR because they were perpendicular to each other. The relevant datasvolume, area, equivalent diameter, aspect ratio, and velocityswere obtained by treating the images with an imaging software program (Sigma Scan 4.0, SPSS Inc., Chicago, IL). To ensure that the measured velocity was terminal (constant), we measured the local velocity as a function of the vertical coordinate. We assumed that the velocity was terminal when it remained constant (within 5%) in at least five consecutive frames. The experimental error in the bubble volume determination was 2%, while the velocities were measured with a 5% precision. Determination of Physical Properties of Liquids. The rheological properties of non-Newtonian solutions of CMC used were determined by a Brookfield RVDV-II programmable viscometer. It has been shown that the CMC solutions used in this study displayed a power-law behavior within the limits of shear rates used in this study. The surface tension of CMC solutions containing a surfactant (SDS) was measured using a Fisher Scientific Autotensiomat surface tension analyzer, model 215. Its accuracy was (2%. Materials Used. The non-Newtonian (pseudoplastic) liquid used was an aqueous solution of CMC (analytical grade, supplied by BDH, Toronto, Canada, and Arcos, Phoenix, AZ) having an average molecular weight of 500 000. The rheological properties (Table 1) of the solutionss0.2% and 0.1% (w/w) CMCswere measured with a programmable rheometer (Brookfield, Middle-

5792 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 Table 1. Rheological Properties of Non-Newtonian Liquids Used CMC concn, % (w/w)

consistency index (m), Nsn/m2

flow index (n)

0.1 0.2

0.0658 0.0950

0.846 0.700

boro, MA, model RV DV 2+). The surfactant that was used throughout the research was SDS (analytical grade, supplied by BDH); the concentration of SDS ranged from 0 to 30 mg/L. The temperature of the liquid was kept at 21 °C. Equations Describing Free Motion of Bubbles and Fluid Rheology The most commonly encountered non-Newtonian fluid of the time-independent fluid behavior is the shearthinning type.4 This was the main reason to choose it for our research. Various mathematical models have been proposed to describe the rheological characteristics of shear-thinning fluids. One of the most precise ones is the model of Carreau,17 which describes very well not only the power-law behavior at intermediate shear rates but also the shear stress at very low and very high values of the shear rate. However, because in this work the shear rates are in the intermediate region, we decided to use the power-law model of Ostwald-de Waele:

τyx ) m(γyx)n

(1)

which combines simplicity and relatively good precision in the range of shear rates studied. The Reynolds number for particles moving in a powerlaw fluid was defined on the basis of the following approximation for the shear rate:18

γ ) Ut/d

(2)

CD )

24 (1 + 0.173Re0.657) Re

(3)

The drag coefficient can be calculated on the basis of the force balance on a freely rising sphere:

(9a)

for Re < 135 and

CD ) 0.95

(9b)

for Re > 135. It can be seen that the drag coefficient at Re approaching zero reaches the value of

CD ) 24/Re

(10)

which is the Stokes equation. A bubble with a moving surface, regardless of its shape (using eq 6), has a drag coefficient that can be determined from the following correlation:12

CD )

16 (1 + 0.173Re0.657) Re

(11a)

at Re < 60 and

CD ) 0.95

The Reynolds number was defined as18

Re ) FldnUt2-n/m

where de and dh are the equivalent diameter (diameter of a sphere having the same volume as that of the bubble) and the diameter of the bubble projection on a horizontal plane, respectively. Equation 7 has already been used to describe the drag coefficient of gas bubbles.11,19 The use of eqs 5-8 allows one to treat nonspherical bubbles as spherical ones and to use the same drag curve for spherical and nonspherical bubbles.11,19 The two drag curves of rising particles with and without internal circulation, respectively (Figure 1), were described mathematically as follows. The drag curve without interface mobility representing the rise of rigid bodies as well as bubbles with any shape having an immobile surface can be described by the following correlation:13

(11b)

at Re > 60. The value of the drag coefficient in eq 11a converges to

CD ) 16/Re

(12)

3

CD )

4gde ∆F 3Fldh2Ut2

(4)

Because gas bubbles are usually nonspherical, the following modifications of eqs 2-4 are proposed:

γ)

Re ) CD )

Ut E de

FldenUt2-n mEn 4gde∆F

E2 2

3FlUt

(5)

(6)

(7)

The aspect ratio (E), which is used in eqs 5-7, accounts for the nonsphericity of the bubble and is defined3 as

E ) de/dh

(8)

at very low values of Reynolds numbers, i.e., reaches the values predicted by the Hadamard-Ribczynky model20 of a bubble with a shear-free (completely mobile) interface. It should be noted that eqs 9a and 11a are simplified versions of the correlations proposed earlier.11,13 The drag coefficients were calculated by determining the bubble terminal velocity according to the procedure described in the Materials and Methods section and using eq 7. Results and Discussion Rheological Properties of Liquid. The rheological properties of aqueous CMC solutions, used in this study, were determined using the Brookfield viscometer. It has been shown that in the range of shear rates present in this work, as calculated from eq 2, rheological characteristics of liquids can be approximated very well by the power-law relationship between the shear rate and shear stress. The rheological constants are given in

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Figure 4. Terminal velocity versus equivalent diameter at a CMC concentration of 0.1% (w/w) and at different SDS concentrations.

Figure 3. Effect of the bubble size and surfactant concentration on the bubble aspect ratio.

Table 1. It has already been shown that this type of solution does not show any significant elasticity.4 In addition, the effect of surfactant addition on the rheology of CMC solutions was studied. It was found that the addition of up to 200 mg/L SDS to both 0.1 and 0.2% CMC solutions had no effect on both consistency and flow indexes. Effect of the Surfactant Concentration on the Bubble Shape. As mentioned above, molecules of surfactant, accumulated on a bubble-liquid interface, affect both the interface motion and shape of the bubble; each of these factors can affect the bubble terminal velocity. To study these effects separately, we first studied the effect of surfactant on the bubble shape. The influence of both the bubble size and surfactant concentration on the bubble aspect ratio (as defined above) is shown in Figure 3. It can be seen that, while there is some spread of experimental data, SDS at concentrations below 30 mg/L did not affect significantly the bubble shape. Therefore, if there is an effect of surfactant on the terminal velocity of bubble rise, it will be mainly due to the reduction of interface mobility rather than the change in bubble shape. Terminal Velocity of the Bubble as a Function of Its Equivalent Diameter and Surfactant Concentration. The terminal velocity of bubbles was studied as a function of their equivalent diameter at different surfactant concentrations. The results for bubbles rising in a 0.1% CMC solution are shown in Figure 4. It can be seen that, as the surfactant concentration increases, the terminal velocity decreases. However, this increase is observed only at bubble equivalent diameters below approximately 0.8 cm. At higher values of the equivalent diameter, the curves representing different surfactant concentrations converge and no effect of the surfactant concentration was observed. This is due to the fact that the drag curves of bubbles rising in liquids containing different amounts of surfactant converge at higher Reynolds numbers because drag becomes predominant. In addition, it can be seen that, in the region of bubble diameters above 1.0 cm, the terminal velocity changes only slightly as a function of the bubble diameter. This confirms the previously reported results.5,15 The effects of the surfactant concentration and equivalent bubble diameter on the terminal velocity at a CMC

Figure 5. Terminal velocity versus equivalent diameter at a CMC concentration of 0.2% (w/w) and at different SDS concentrations.

concentration of 0.2% (Figure 5) were qualitatively similar to those at 0.1% CMC (Figure 4). However, the overall terminal velocities in the higher concentration of CMC (0.2%) were lower than those at 0.1% CMC because of the increase in the apparent viscosity of liquid (Table 1). For example, at a bubble equivalent diameter of 0.5 cm, Ut for 12.5 mg/L SDS is 12 cm/s and that for 1 mg/L SDS is 20 cm/s, which is 40% slower at the higher concentration of SDS. The terminal velocity of a bubble with an equivalent diameter of 0.5 cm in 5 mg/L SDS in 0.1% CMC was 36% higher than the one in 0.2% CMC. The relationship between the equivalent bubble diameter and terminal velocity reaches a local plateau, similar to the case of 0.1% CMC (Figure 4). Effect of the Surfactant Concentration on the Bubble Drag Coefficient. Most of our experimental data on bubble drag in liquids containing surfactant showed similar behavior and are illustrated in Figure 6. When the bubble size, respectively Reynolds number, was increased in a non-Newtonian liquid containing both CMC and SDS with certain concentrations, the experimental data usually followed the drag curve of a particle without surface motion (the upper curve in Figure 6) only at low Reynolds numbers. As Re increased, the bubble drag coefficient started following the drag curve of a bubble with a moving surface (the lower curve in Figure 6), following a brief transition between the two curves. The transition between the two drag curves, observed at 10 < Re < 30 in the example given in Figure 6, was attributed to the initiation of internal bubble circulation. The average value of Re corresponding to the transition between the two curves was referred to as the “transition Reynolds number” (Figure 6).

5794 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

Figure 6. Typical profile of bubble drag vs Re in a surfactantcontaining non-Newtonian solution.

Figure 7. Effect of the particle Reynolds number and surfactant (SDS) concentrations on the drag coefficient. CMC concentration ) 0.1% (w/w).

The relationship between the drag coefficient and Re of bubbles rising in a solution containing 0.1% CMC and different concentrations of surfactant is shown in Figure 7. It can be seen that, in the absence of surfactant, the bubble drag follows the drag curve for a moving bubble surface in the entire range of Reynolds numbers studied. In the case of the highest surfactant concentration studied (12.5 mg/L), the bubble drag coefficients were close to the drag curve for an immobile bubble surface within the entire range of Reynolds numbers studied. In the case of intermediate SDS concentrations (between 1 and 5 mg/L), the bubble drag was close to the drag curve for a fixed interface only at lower Re numbers, similar to the example shown in Figure 6. A transition from a fixed bubble surface to a mobile surface occurs at different transition Reynolds numbers; the increase in the SDS concentration results in an increase in the transition Reynolds number. Similar results were observed when bubbles rose in a 0.2% CMC solution (Figure 8). The transition Reynolds numbers as a function of both the surfactant and CMC concentration are shown in Figure 9. The increase in each of these concentrations results in an increase in the transition Reynolds number. The effect of the surfactant concentration on the transition Re number can be explained by the fact that higher bubble velocity (respectively higher Re) is required to induce internal bubble circulation when the amount of surfactant molecules on the bubble surface is higher. The effect of the CMC concentration on the transition Re number can be explained by the competition of the molecules of CMC and SDS on the bubble

Figure 8. Effect of the particle Reynolds number and surfactant concentrations on the drag coefficient. CMC concentration ) 0.2% (w/w).

Figure 9. Reynolds number of the transition between fixed and moving bubble surfaces as a function of the SDS concentration at various CMC concentrations.

surface: a higher concentration of CMC allows less surfactant molecules to reach the bubble surface.21 The surface tension of solutions used was also measured. The effect of both CMC and surfactant (SDS), within the range of concentrations used in this study, on the surface tension was negligible. The average value of the surface tension was 0.063 N/m. These results agree well with previously published data8 and show that the surfactant concentrations used are well below the critical micelle concentration. Conclusions 1. The addition of surfactant (SDS) at concentrations below 12.5 mg/L does not affect the shape of the gas bubbles rising in power-law liquids. 2. Comparisons of the experimental bubble drag coefficient to two different drag curves (those representing the free rise of “solid bubbles”, i.e., bubbles with an immobile surface and bubbles with free surface motion) were used to determine the effect of bubble surface motion on the terminal velocity. 3. It has been shown that the addition of surfactant to a power-law fluid (an aqueous CMC solution) results in the reduction of the terminal velocity of freely rising bubbles. This reduction is due to the significant decrease in surface mobility and not due to the change in the bubble shape. The velocity reduction is caused by the accumulation of surfactant molecules on the bubbleliquid interface, which causes immobilization of the surface.

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4. It has been shown that the transition from a bubble without internal circulation to a bubble with internal circulation is a function of the surfactant concentration, Reynolds number, and rheological properties of the liquid. Specific values of these parameters at which bubble circulation is initiated are reported. 5. The bubble surface motion is hindered at surfactant concentrations much lower than the critical micelle concentration. Acknowledgment This work was supported by the Natural Sciences and Engineering Research Council of Canada and by the Academic Development Fund of the University of Western Ontario. Nomenclature CD ) drag coefficient d ) particle diameter (spherical shape), m de ) equivalent particle (bubble) diameter, m dh ) diameter of the horizontal bubble projection, m E ) aspect ratio (defined by eq 8) g ) gravity acceleration, m/s2 m ) consistency index, Nsn/m2 n ) flow index Re ) terminal Reynolds number (defined by eqs 3 and 6) Ut ) terminal velocity, m/s Greek symbols ∆F ) density difference between a continuous fluid and particle, kg/m3 γyx ) one-dimensional shear rate, s-1 Fl ) density of a continuous liquid, kg/m3 τyx ) one-dimensional shear stress, N/m2

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Received for review April 29, 2004 Revised manuscript received June 25, 2004 Accepted July 2, 2004 IE049649T