Oscillating bubble experiments

As one can see the experimental set-up allows to register the initial stage of the bubble oscillation. Here a transient regime of non-established harmonic oscillations is clearly observed for larger frequencies and the measured pressure oscillation is a sum of a non-damped oscillation of the externally applied frequency and a damped oscillation with the meniscus eigenfrequency (for details cf. [208]). At larger frequencies the damped oscillation contribution as shown in Fig. 4.46c is practically absent as the damping time is sufficiently small. 

The comparison of the two figures shows that the characteristic bubble frequency for ground conditions is two times smaller than that for microgravity conditions. The most probable reason for the decrease of the characteristic bubble frequency under ground conditions is the bubble shape deformation due to gravity on which the characteristic frequency strongly depends. 

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Fig. 6.13 Dilational elasticity modulus of n-dodecyl dimethyl phosphine oxide determined for oscillating bubble experiments ( ), and calculated from the adsorption isotherm ( ) according to Wantke etal.(1993)...

Fig. 6.19 Effective dilational elasticity determined from oscillating bubble experiments of gelatine solutions at different concentration c = 0.01 wt%(B), 0.1 wt%(D), 0.5 wt%( ), 1 wt%(0), according to Hempt et al. (1985)...

These results were in contrast to the previous experiments described above, where nucleation was always observed. It is thought that as nucleation is a stochastic process, a single oscillation of a laser-induced bubble may not always lead to the nucleation. The probability of nucleation is increased by the continuously oscillating bubble produced by the standing wave system, and it is increased further by the multicavitation events produced by the ultrasonic horn. 

It is widely thought that the high pressure emitted from a "transient" cavitation bubble is responsible for the nucleation process (Hickling, 1994) however, experiments utilizing a single oscillating bubble have shown that ice can be initiated by a "stable" cavitation bubble. The mechanism of nucleation may be related to the asymmetric bubble shape, the flow field associated with the cavitation bubble, or the production of microbubbles. 

Kovalchuk VI, Miller R, Fainerman VB and Logho G (2005). Oscillating bubble pressure experiments for dilational rheology studies. Adv Colloid Interface Sci 114-115 303-313... 

Beside the capillary wave techniques, the oscillating bubble method belongs to the first experiments for measuring the surface dilational elasticity (Lunkenheimer Kretzschmar 1975, Wantke et al. 1980, 1993). For soluble adsorption layers it allows of the exchange of matter at a harmonically deformed bubble surface to be determined. 

We want to give only two examples of interfacial relaxation methods. The whole field of interfacial relaxations and rheology is so broad and of strong practical relevance that this topic deserves a whole book. At first, two examples, a harmonic and a transient experiment will be shown as example for slow relaxation experiments, while as second we will present results of experiments performed under ground and microgravity conditions, respectively, based on the principle of oscillating bubbles. 

The instrument shown schematically in Fig. 26 is suitable for slow oscillation experiments, as it was performed for the first time by Miller et al. in 1993. The frequency limit of the oscillations is given by the condition for the liquid meniscus shape, which has to be Laplacian. Under too fast deformations this condition is not fulfilled and hence the method does not provide reliable results. To reach higher frequencies of oscillation, the above mentioned oscillating drop or bubble experiments are suitable, because the shape of the menisci is spherical due to the small diameter. The instrument of Fig. 26 can be designed such that a pressure sensor and piezo translator are built in and the video system serves as optical control and determines the drop/bubble diameter accurately. 

The results up-to-now obtained with the DFT algorithm, in the reduced form for the oscillating drop/bubble experiments, appears more reliable than the results obtained by DFT / FFT standard routines. In Fig. 21 an example plot is reported, as obtained from raw experimental data, showing the time evolution of surface tension and of drop volume, relevant to a dilute aqueous surfactant solution. 

Figure 12.16. Experimental data obtained from oscillating bubble studies performed under micro-gravity at 450 Hz with water at 15°C, where the different symbols correspond to three runs of the experiment...

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

Arriola (8) and Ni (5) have observed a second mechanism for snap off in strongly constricted square capillaries. At low liquid flow rates, a bubble is trapped in the converging section of the constriction and liquid flows past the bubble. As liquid flow rate increases, waves developed in the film profile and at some critical liquid flow rate these oscillations become unstable and bubbles snap off. In these experiments, the bubble front is located upstream of the constriction neck. Therefore, no driving force for the drainage mechanism exists. Bubbles formed by this mechanism are produced at a high rate and have a radius on the order of the constriction neck. No attempt has previously been made to model snap-off rate by this mechanism in noncircular constrictions. 

Tartan and Gidaspow (29) have recently developed an experimental kinetic theory based particle image velocity technique for measuring particle and Reynolds stresses in gas-solid risers. They have shown that for gas-solid flow that are two types of turbulence in the risers random oscillations of the individual particles and oscillations of clusters measured by the Reynolds stresses of die particles. Earlier Mudde et al (30) have obtained similar measurements for bubble columns. Pan et al (72) have compared Mudde et al (30) experiments to simulations using the Los Alamos CFD code. Figure 4 shows typical Reynolds stress computations to the experiments. 

Bashforth F and Adams JC (1883) An attempt to test the capillary action, Cambridge University Press and Deighton Bell Co., Cambridge Chen P, Kwork DY, Prokop RM, del-Rio 01, Susnar SS and Neumann AW (1998) Axisymmetric drop shape analysis (ADSA) and its applications , in Drops and bubbles in interfacial research, D. Moebius and R. Miller Eds., Studies in Interface Science Series, Vol. 6, Elsevier, Amsterdam Dukhin SS, Kretzschmar G and R. Miller R (1995) Dynamic of adsorption at liquid interfaces. Theory, experiments, applications, D. Moebius and R. Miller Eds., Studies in Interface Science Series, Vol. 1, Elsevier, Amsterdam Joos P (1999) Dynamic Surface Phenomena, VSP, Utrecht, 1999 Kovalchuk VI, Zholkovskij EK, Kragel J, Miller R, Fainerman VB, Wiistneck R, Loglio G and Dukhin SS (2000) Bubble Oscillations in a Closed Cell. J Colloid Interface Sci 224 245-254... 

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