Bubbles experiments

Small-scale experiments with fireballs have been carried out by a number of investigators, and can be roughly divided into two categories. The first includes experiments in which a spherical gas-air mixture contained by a thin envelope at ambient pressure was released, then ignited (soap bubble experiments). 

Although the single bubble experiment in Fig. 14.10b and the aforementioned multi-bubble work of Didenko et al. does support the hypothesis that thermal conductivity is a defining parameter of SL emission intensity, an alternative explanation attributes the trend in multi-bubble systems to the gas solubility, rather than the thermal conductivity. If the SL data from Fig. 14.9 is re-plotted as a function of the gas solubility, as shown below in Fig. 14.11, a very good correlation is found. This explanation is supported by several studies by Okitsu et al. [42, 59]. They found sonochemical activity to obey the same trend for the rare gases as for thermal conductivity, SL luminosity and temperature, as described above. This is evident in Fig. 14.12, which shows the sonochemical reduction of Au(III) to colloidal gold as a function of sonication time for different gas atmospheres. 

Therefore, the stability and lifetime of such thin films will be dependent on these different characteristics. This is evident from the fact that, as an air bubble is blown under the surface of a soap or detergent solution, it will rise up to the surface. It may remain at the surface if the speed is slow, or it may escape into the air as a soap bubble. Experiments show that a soap bubble consists of a very thin liquid him with an iridescent surface. But, as the huid drains away and the thickness decreases, the bubble approaches the equivalent of barely two surfactant molecules plus a few molecules of water. It is worth noting that the limiting thickness is of the order of two or more surfactant molecules. This means that one can see with the naked eye the molecular-size structures of thin liquid hlms (TLFs) (if curved). 

In Grahame (1957), the presence at a liquid surface of a quasi-ice structure was hypothesised. Moreover, study of droplets on inclined planes, and of bubbles clinging to vertical surfaces, reveals behaviour (contact angle hysteresis) which cannot be accounted for without such an ice film. On a vertical wall, a bubble experiences an upward buoyancy force, but in the absence of an ice film, a zero restraining force. The restraining force is made evident by the phenomenon of contact angle hysteresis, followed by film rupture as bubble growth occurs, and leads to bubble detachment. 

As a final point in this section, we should mention that as the bubble trains advance through the constricted channels, the capillary resistance will assume its maximum value (the mobilization pressure) only when the lamellae in the train assume their most unfavorable positions with respect to displacement. At other times, the capillary resistance will be below this maximum value with the result that the actual work required to maintain foam flow at a given rate will be below that which would be required if the mobilization pressure was operative at all times. This is easily understood if one pushes a bubble through a single constriction in a tube and notes that the pressure in the train builds up to the mobilization pressure as the drainage surface advances into the constriction and then rapidly falls as the front bubble experiences a Haines jump. To account for such effects in the present model, the Km term in Equation 63 would vary with time as the bubble train moved through the constricted channels. 

The air stability of PPB (6bvl was examined by an air-bubbling experiment. After the vigorous air-bubbling of the THF solution of 6by for 24h, no significant decrease in Mn was observed from the GPC measurements. The relatively high thermal stability is also expected due to the absence of a retro-hydroboration... 

The parameterisation has been tested on the city of Basel (Switzerland), Mexico City (Mexico), Copenhagen (Denmark), and verified versus the BUBBLE experiment (Basel Urban Boundary Layer Experiment Rotach et al., 2005 [549]). The verification results (Figure 9.11) show that the urban parameterization scheme is able to catch most of the typical processes induced by an urban surface Inside the canopy layer, the wind speed, the friction velocity and the atmospheric stability are reduced. In the other hand, even if the main effects of the urban canopy are reproduced, the comparison with the measurement seems indicates that some physical processes are still missing in the parameterization. In most of the cases, the model still overestimates the wind speed inside the canopy layer and it can have difficulties to simulate the maximum of the friction velocity which appears above the building roofs. 

Risso, F., Legendre, D. (2003) Velocity fluctuations induced by high-Reynolds-number rising bubbles experiments and numerical simulations. ERCOFTAC Bulletin. 56, 41 45. 

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)...

The bubble experiments described above show that silver and lead azide respond rapidly to the collapse of gas pockets as small as 50 fjm diam. Johannson and coworkers [35-37] pointed out that the temperature of the explosive surface will be lower than the temperature of the heated gas. However, the experiments described have been supported by calculations to show that sufficient heat reaches the explosive for initiation of fast reactions to take place [28]. For example, the energy in a 100-/xm air bubble compressed to its final volume is 300 J/m, and the required energy transfer to the crystal surface for initiation in 10" -10" sec is approximately 40 to 150 J/m. Bubbles much smaller than 50 /xm would probably not cause initiation because conditions during collapse would be increasingly isothermal, and the heat content would not be sufficient to exceed the hot spot requirements of temperature and size. 

Chiba and Kobayashi [21], Van Swaay and Zuiderweg [23] and de Vries et al. [24] found that Eq. 13.4-6, derived from single-bubble experiments, does not adequately describe the true bubble-rising velocity, probably because of interaction between the bubbles. The first authors therefore deriv empirical correlations for the bubble size. 

The vapor pressure of liquids can cushion the bubble collapse like a high gas content. Vapor in a transient bubble can be condensed in the compression cycle and lead to higher cavitation intensities than gas-filled bubbles. Experiments with different solvents show that small vapor pressures are necessary for a sufficiently high cavitation intensity. Higher vapor pressures, especially near the boiling point of the liquid, can dampen the cavitation efficiency to nearly zero. If a substrate is subject to treatment within the collapsing bubbles, then a certain number of its molecules must be present in the bubbles and exert an at least measurable vapor pressure. The existence of molecules inside the bubble can easily be proved by means of molecules that exist as ionic or molecular species at different pH values. Ionic species do not enter the bubbles, and high-temperature pyrolysis products can therefore not be created. 

The mechanism of liquid atomization has been systematically studied by several workers such as Lefebvre and Sojka and coworkers, e.g., [36-39]. At the right conditions, where a bubbly two-phase mixture forms in the mixing chamber and flows toward the exit orifice, the bubbles experience a sudden pressure relaxation and expand rapidly, thereby shattering the liquid into drops, as shown schematically in Fig. 24.22. 

This model has several limitations. The film model assumes that mass transfer is controlled by the liquid-phase film, which is often not the case because the interface characteristics can be the limiting factor (Linek et al., 2005a). The liquid film thickness and diffusivity may not be constant over the bubble surface or swarm of bubbles. Experiments also indicate that mass transfer does not have a linear dependence on diffusivity. Azbel (1981) indicates that others have shown that turbulence can have such a significant effect on mass transfer such that eddy turbulence becomes the controlling mechanism in which diffusivity does not play a role. In most instances, however, eddy turbulence and diffusivity combine to play a significant role in mass transfer (Azbel, 1981). 

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 dynamic surface tension of [3-casein solutions at three concentrations 5 10, 10 and 10 mol/1 are shown in Fig. 14. As one can see the results from the two methods differ significantly. For the bubble the surface tension decrease starts much earlier. The surface tensions at long times, and hence the equilibrium surface tension from the bubble experiment are lower than those from the drop. However, the establishment of a quasi-equilibrium for the drop method is more rapid at low (3-casein concentrations while at higher P-casein concentrations this process is more rapid for the bubble method. This essential difference between solutions of proteins and surfactants was discussed in detail elsewhere [50]. In brief, it is caused by simultaneous effects of differences in the concentration loss, and the adsorption rate, which both lead to a strong difference in the conformational changes of the adsorbed protein molecules. 

Fig. 14 Dynamic surface tension y of P-casein solutions as a function of time, 5 10 mol/1 (O ), 10" mol/1 ( ), 10" mol/l (AA), ( A) - drop experiments, (ODA) - bubble experiment, according to [50] Please note that at low initial concentrations and high adsorption activity, which is typical for proteins but also some surfactants, the final bulk concentration in the drop can become significantly lower than the initial value. By comparing the results obtained from drop and bubble experiments one can make use of this principle difference and estimate the value of the adsorption at the surface. Quantitative experiments are not known so far.

In drop/bubble experiments, either working with transient (aperiodic) procedure or with harmonic (periodic) procedure, there never is a continuous function g(t) to be analysed. There is instead a list of measurements of g(tj) for a discrete set of N time values ti, where g(t) represents the time-evolution of the inherent interfacial physical and geometrical properties (surface tension, differential pressure, interfacial area, et cetera). 

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. 

All these forces have to be cast into terms of the averaged quantities of the E-E model. For instance, the drag forces that a bubble experiences is, for a single bubble in a pool of liquid, formulated as... 

Hibiki and Ishii (2007) derived a model for the effect of bubble deformation that can be decomposed in a shear-induced and a deformation-induced part. Sankaranarayanan and Sundaresan (2002) correlated their lift coefficient at low shear conditions—obtained by means of numerical simulations—with the nondimensional Tadaki number Ta, which is a combination of Reynolds and Morton Ta = Mo Re they also found that highly distorted bubbles experience a much larger Hfi force than circular or spherical bubbles, accompanied by a change in the flow pattern around the bubble and eventually even leading to a negative lift coefficient. 

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