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Pulsation and Bouncing of a Bubble Prior to Rupture and/or Foam Film Formation M. Krzan,† K. Lunkenheimer,‡ and K. Malysa*,† Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Cracow, Poland, and Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, D-14476 Potsdam/Golm, Germany Received November 18, 2002. In Final Form: June 11, 2003 When a bubble rising in distilled water or in an aqueous pentanol-1 solution approached the air/water interface, rapid pulsations of its shape with a frequency of more than 1000 Hz were observed. In addition, the bubble bounced from the free surface, prior to its rupture or to the formation of a foam film. It is rather unexpected that the bubble’s shape and consequently its surface area can vary so rapidly. It shows straightforwardly that on such a rapidly distorted interface the adsorption coverage can be very different from that at equilibrium. This fact should be taken into account more appropriately in the discussion of the mechanism of formation and stabilization of various dispersed systems (e.g., foams, emulsions).
Introduction Drinking champagne, soft drinks, or beer, everyone can observe that bubbles are rising up and either rupture immediately at the liquid/gas interface or form a foam layer. Bubble motion is encountered in many processes, especially those aiming at separation of component(s) from a mixture as for example froth flotation, ion and precipitate flotation, foam fractionation, wastewater treatment, foam separation of proteins, and so forth. To generate foam, the gas phase is dispersed into bubbles, which, after their arrival at the solution’s surface, form foam films and consequently the foam. It is rather commonly assumed that the bubble bursts at once at the surface of clean water. Immediate rupture of the bubble at the water surface is the simple and commonly accepted criterion to check if the water is clean, that is, its surface does not contain any surface-active contaminants. A bubble lifetime of the order of a fraction of seconds is the indicator that the water surface is really clean. Bikerman stated in his textbook1 that “...When the bubble reaches the upper surface of the liquid, and the liquid has no foaming tendency, the bubble bursts at once; that is the film separating it from the bulk gas phase immediately ruptures. When the liquid contains a foaming agent, the above film has a significant persistence, and the bubble lifts a “dome”....” For foaming, a surface-active substance is required to stabilize the bubbles by forming an adsorption layer at the foam film interfaces. Considering the role of motion-induced nonequilibrium adsorption coverage in foam stability,2,3 we also shared the common understanding that the bubble is immediately stopped when arriving at the free solution surface. However, we have just observed that the real picture is much more complicated and the bubble pulsates * Corresponding author. Kazimierz MALYSA, Institute of Catalysis and Surface Chemistry Polish Academy of Sciences, ul. Niezapominajek 8, 30-239 Cracow, Poland. Phone: (+48 12) 6395133. Fax: (+48 12) 425 19 23. E-mail:
[email protected]. † Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences. ‡ Max-Planck-Institut fu ¨ r Kolloid- und Grenzfla¨chenforschung. (1) Bikerman, J. J. Foams; Springer-Verlag: Berlin, 1973; Chapter 2, p 57. (2) Malysa, K.; Lunkenheimer, K.; Miller, R.; Hempt, C. Colloids Surf. 1985, 16, 9. (3) Jachimska, B.; Warszynski, P.; Malysa, K. Colloids Surf., A 2001, 192, 177.
with high frequency and can bounce from the interface prior to rupture or the foam film formation. The paper presents fascinating pictures, in our opinion, showing straightforwardly that the bubble approaching the water surface can pulsate with high frequency and bounce backward. High-frequency pulsation means a rapid variation of the bubble’s surface area and, in the presence of surface-active substances, a disequilibration of adsorption coverage. Thus, it shows how rapidly the processes proceed that lead to the formation of various dispersed systems (e.g., foams, emulsions). As far as we know, nobody has reported pictures showing that the shape of the freely rising bubble can pulsate with such high frequency (above 1000 Hz) at an air/water surface. Bouncing of bubbles from water surfaces was already reported earlier,4,5 but probably the picture magnification was too small to notice that the bubble shape can also pulsate. Experimental Details Single bubbles were formed at a capillary orifice of inner diameter 0.07 mm using a Cole-Parmer syringe pump for highprecision control of the gas flow. To avoid optical distortions, a square glass column (40 × 40 mm) was used in the experiments. A high-speed camera Speedcam 512+ (with Cosmicar objective and rings for higher magnification) was used to record the behavior of the bubbles approaching the free surface. The camera maximum speed was 1182 frames per second. The entire setup was located on a vibration-isolated laboratory table with an automatic leveling system. To get absolute dimensions, an image of a nylon sphere of 7.85 mm diameter was recorded after each experiment. The movies obtained were transformed into BMP pictures and analyzed using a PC with SigmaScanPro Image Analysis Software. The distances between subsequent positions of the bubble and its vertical and horizontal diameters were measured as a function of time. Every measurement was performed at least three times, and mean values were calculated. Four-times-distilled water and high-purity pentanol-1 were used in the experiments. The experiments were carried out at room temperature (20 ( 1 °C).
Results and Discussion Figure 1 shows a sequence of frames illustrating the phenomena occurring when the rising bubble approached the surface of distilled water. Each subsequent picture (4) Kirkpatrick, R. D.; Lockett, M. J. Chem. Eng. Sci. 1974, 29, 2363. (5) Duinveld, P. C. Ph.D. Thesis, University of Twente, Enschede, Netherlands, 1994.
10.1021/la020919r CCC: $25.00 © 2003 American Chemical Society Published on Web 07/03/2003
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Figure 2. Variations of the velocity (top part) and the vertical diameter (bottom part) of the bubble rising to and bouncing from the water surface.
evidence that the bubble shape can pulsate with a frequency higher than 1180 Hz. A quantitative analysis of the variations of the bubble velocity and the vertical diameter (dv) is shown in Figure 2. The bubble’s equivalent diameter was 1.48 ( 0.03 mm, and its terminal velocity in distilled water was 34.8 ( 0.3 cm/s. As can be observed in Figure 1, the bubble had a nonspherical shape. Therefore, the equivalent diameter (deq), that is, the diameter of a sphere having identical volume as the distorted bubble, was determined on the basis of measurements of the bubble’s vertical (dv) and horizontal (dh) diameters as
deq ) (dvdh2)1/3 Figure 1. Sequence of frames showing the shape pulsation and the bouncing of the bubble approaching the free surface of distilled water. The time interval between each picture is 0.845 ms.
shows the bubble position and its shape after a time interval of 0.845 ms. It is clearly seen that the bubble approaching the solution surface neither ruptures immediately nor “stays” at the surface. After having formed a “dome”, the bubble started to move backward, that is, opposite to the direction of the buoyancy force. Simultaneously, the bubble started to pulsate very rapidly, as can be observed in Figure 1. As seen there, the bubble shape can be changed completely between two subsequent photos (see for example the third and fourth rows of the photos), that is, within a time shorter than 0.845 s. This is the
(1)
The obtained value of the equivalent diameter was in good agreement with the bubble diameter measured at the capillary orifice, immediately before the bubble was detached. The deformation from the spherical shape, determined as the ratio of the spherical and vertical diameters, was equal to 1.5. As seen in Figure 2 (top part), the velocity of the bubble approaching the interface was constant (ca. 35 cm/s) prior to deformation of the water surface (the dome formation). The local velocity U of the bubble at a given position was calculated as
U)
x(x2 - x1)2 + (y2 - y1)2 ∆t
(2)
where (x2, y2) and (x1, y1) are coordinates of the subsequent
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positions of the bubble, and ∆t ()0.845 ms) is the time interval between subsequent frames of the camera. After having formed the dome, the bubble started to move backward within a time period of ca. 1-2 ms. Simultaneously, the bubble shape started to pulsate very rapidly, changing its shape during time intervals shorter than 0.845 ms (see Figure 1). The ratio of the horizontal/ vertical diameter varied from 1.5 to 0.85 within milliseconds. Variations of the vertical diameter of the bubble during its bouncing from the water surface are shown in the bottom part of Figure 2. At the first “bounce”, the bubble reached the velocity of ca. 32 cm/s. This backward motion was stopped at a distance of ca. 2.9 mm (position of the bottom pole) from the interface, and the bubble started its second approach to the surface. Simultaneously, the bubble’s vertical diameter, that is, the bubble’s shape, varied rapidly and in a similar fashion (see Figure 2). The velocity of the bouncing bubble decreased with every bounce, as did the amplitude of the diameter variations. The coalescence occurred at the fourth approach (with a velocity of 10 cm/s) to the water surface. The problem of bubble coalescence in pure liquids was considered theoretically by Chesters and Hofman6 as a competition of two processes: (i) the thinning of the liquid between the bubbles and (ii) the increase of the free energy of the system resulting from the increase of the bubble’s surface area. According to them,6 the free energy of the system increases, at the expense of the kinetic energy and “...the bubbles therefore decelerate and eventually bounce apart...” if the thinning liquid layer did not reach earlier a critical thickness of rupture. We believe that generally their approach is correct and our data for distilled water are in good agreement with this approach. As can be observed in Figure 2, the bubble approach velocity to the water surface was decreasing with every bounce. Rupture occurred at the fourth bounce (approach velocity of 10 cm/s), from which it can be interpreted that during this approach the water layer above the top pole of the bubble reached a critical thickness and the bubble burst out. The presence of surfactant prolongs the lifetime of the bubbles as a result of formation of much more stable foam films.1,7 Depending on the type and concentration of the surfactant, the bubble lifetime can vary from a few seconds to hundreds of seconds and more. However, prior to the foam film formation there is always the stage of the bubble’s approach to and the deformation of the interface. The behavior of the bubble approaching the free surface of 0.001 mol/dm3 pentanol-1 solution is illustrated in Figure 3 where a sequence of frames showing the bubble pulsation and bouncing is presented. Qualitatively the picture is similar to that in distilled water; that is, the rapid pulsations of the bubble shape and the bouncing can be noticed. However, the bubble did not rupture immediately (within milliseconds) but lasted a few seconds as a result of the increased stability of the thin liquid film due to the pentanol-1 adsorption. Results of the quantitative analysis of variations of the bubble velocity and pulsations with time are presented in Figure 4. The bubble equivalent diameter in 0.001 mol/dm3 pentanol-1 solution was 1.44 ( 0.02 mm, that is, practically identical to that in distilled water. However, the terminal velocity of the bubble was 30 ( 0.03 cm/s, that is, lower than in distilled water. The decrease in the bubble terminal velocity is caused by adsorption of surfactant (pentanol-1 in our case) (6) Chesters, A. K.; Hofman, G. Appl. Sci. Res. 1982, 38, 353. (7) Exerowa, D.; Kruglyakov, P. M. Foam and Foam Films: Theory, Experiment, Application; Elsevier: Amsterdam, 1998.
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Figure 3. Sequence of frames showing the shape pulsation and bouncing of the bubble approaching the free surface of 0.001 mol/dm3 pentanol-1 solution. The time interval between each picture is 0.845 ms.
at the bubble surface leading to a lowering of its fluidity, as discussed in detail in refs 8-10. As seen in Figure 4, during the first approach the bubble velocity was constant (ca. 30 cm/s) till the solution surface was deformed and the dome was formed. After having formed the dome, the bubble started to move backward within a time period of again ca. 1-2 ms. Simultaneously, the bubble shape (8) Levich, V. G. Physico Chemical Hydrodynamics; Prentice Hall: Englewood Cliffs, NJ, 1962; Chapter VIII. (9) Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops and Particles; Academic Press: San Diego, CA, 1978. (10) Krzan, M.; Malysa, K. Colloids Surf., A 2002, 207, 279.
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Langmuir, Vol. 19, No. 17, 2003 6589 Table 1.
concentration [mol/dm3]
surface tension [mN/m]
adsorption coverage θ [%]
terminal velocity [cm/s]
velocity of the 1st bouncing [cm/s]
period of the 1st bouncing [s]
no. of cycles recorded
0 0.001 0.004 0.005
72.75 71.7 69.9 69.3
0 4 17 22
34.8 29.6 14.5 14.6
-32.6 -25.8 -9.9 -9.5
0.030 0.027 0.015 0.014
4 & rupture 6 2 2
Figure 4. Variations of the velocity (top part) and the vertical diameter (bottom part) of the bubble rising to and bouncing from the surface of 0.001 mol/dm3 pentanol-1 solution.
started to pulsate rapidly; the bubble’s vertical diameter decreased from ca. 1.3 to 0.9 mm. The bubble’s maximum velocity of backward motion was 26 cm/s, and the backward motion was stopped at the distance of ca. 2.4 mm from the solution surface. Next, the bubble started its second approach to the surface, reaching the maximum approach velocity of 16 cm/s. Simultaneously, the bubble’s vertical diameter increased from 0.9 to 1.4 mm. As seen in Figure 4, we detected at least six such cycles. The amplitude of
the bubble’s shape pulsations and the velocity variations were decreasing with every cycle as a result of the energy dissipation. High-frequency pulsation of the bubble shape means a rapid variation of its surface area and as a consequence a lack of equilibrium adsorption coverage. It shows how rapid the processes are that occur during the formation of various dispersed systems (e.g., foams, emulsions). This fact should be taken into account appropriately. With increasing pentanol-1 concentration, the amplitude of the bubble shape pulsation and its bouncing velocity was decreasing. In Table 1 are some characteristic parameters showing the influence of pentanol-1 on (i) the solution surface tension, (ii) the degree of equilibrium adsorption coverage, (iii) the bubble’s terminal velocity, (iv) the bubble’s maximum bouncing velocity, (v) the period of the first bouncing cycle, and (vi) the number of the bouncing cycles recorded. The presence of a surface-active substance causes (i) a decrease of the bubble’s rising velocity, (ii) a diminishing of the bubble’s amplitude of bouncing and shape pulsations, and (iii) a prolongation of the bubble lifetime at the free surface, as a result of the increased stability of the thin liquid layer (foam film) separating the bubble from the atmosphere. Surface tension gradients induced at the bubble surface, as a result of its motion through the viscous medium,8,11,12 are the force lowering the mobility of the gas/solution interface, leading to a decrease of the bubble’s rising velocity.8-10 We think that also the induced gradients of the surface tension cause the damping of the bubble’s shape pulsations and prevent the bubble from rupturing by stabilizing the foam film being formed.3 The effect of the type of surfactant and its concentration on the bubble pulsation and bouncing prior to the foam film formation is currently under study. Acknowledgment. The authors are grateful to the Max-Planck-Institut fur Kolloid- und Grenzfla¨chenforschung for supporting the study and making available the SpeedCam512+. Technical support from Weinberger Deutschland GmbH is gratefully acknowledged. LA020919R (11) Dukhin, S. S.; Deryaguin, B. V.; Lisichenko, V. A. Zh. Fiz. Khim. 1959, 33, 2280. (12) Dukhin, S. S.; Deryaguin, B. V. Zh. Fiz. Khim. 1961, 35, 1246, 1453.
