The oscillating bubble method

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. 

The principle of the experiment is shown in Fig. 6.5. A small air bubble is formed at the tip of a capillary which is immersed in the solution. Via an electrodynamic excitation system and a membrane, a gas volume directly connected with the capillary is excited to harmonic oscillations. From the excitation voltage of the system in dependence on frequency, while keeping the bubble oscillation amplitude constant, the dilational elasticity and the exchange of matter can be calculated. The comparatively complex theory for data interpretation was described recently by Wantke et al. (1980, 1993). The method can be applied in a frequency interval from 5 Hz up to about 150 Hz. 

Schematic of a pulsating bubble method according to Lunkenheimer Kretzschmar (1975) and Wantke et al. (1980) 

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The oscillating bubble method proves to be very convenient and precise for the evaluation of the non-equilibrium elasticity of surfaces in a wide range of frequencies of external disturbances and surface coverage (adsorption of surfactant) [103-105]. It is based on registration of the sinusoidal variation of bubble volume. The bubble is situated in a capillary containing surfactant solution in which oscillations of different frequencies and amplitudes are created. The treatment of the U = f(ft)) curves (where U is the tension needed to initiate oscillations of constant amplitude) allows the determination of Marangoni elasticities [105]. 

Various experimental methods for dynamic surface tension measurements are available. Their operational timescales cover different time intervals. - Methods with a shorter characteristic operational time are the oscillating jet method, the oscillating bubble method, the fast-formed drop technique,the surface wave techniques, and the maximum bubble pressure method. Methods of longer characteristic operational time are the inclined plate method, the drop-weight/volume techniques, the funnel and overflowing cylinder methods, and the axisym-metric drop shape analysis (ADSA) " see References 54, 55, and 85 for a more detailed review. 

One of the more recently developed methods to investigate the surface relaxation of soluble adsorption layers due to harmonic disturbances is the oscillating bubble method. The technique... 

Let us consider another example in order to emphasise the extraordinary importance of the dilational elasticity for the understanding of the adsorption state of surfactant molecules. The experimental values of the viscoelasticity for two homologues of alkyl dimethyl phosphine oxides (C 4 and Cio) measured using the oscillating bubble method [96] are presented in Fig. 2.12. The existence of the maxima in the experimental curves are due to the finite magnitude of the oscillations of the bubble surface (-10%) resulting in an over-saturation of the surface layer at higher surfactant concentrations in the bulk phase and at the interface. 

Interfacial dilatational stress is measured in processes of isotropic expansion (compression) of an interface. Such processes are realized in the maximum bubble pressure method [176-180], the oscillating-bubble method [181-183], the pulsed-drop method [184], and the drop-expanding method [39,83,84,185-187]. Because of the simple spherical sjrmmetry equation (81), together with the projection of Eq. (80) along n, yields... 

Herein, our concern is to assess the suitability of the oscillating bubble tensiometer for marine purposes. Essentially, we conducted the present investigation with the aim of estimating the sensitivity of the measurement method, with respect to oceanographic studies and monitoring. In this paper we illustrate preliminary experimental results, obtained with a typical apparatus, working in an onshore laboratory. 

A comparison of the bubble pressure method with the oscillating jet method was also performed with aqueous Triton X-100 solutions. Some results are given in Fig. 5.29 as a y/log X3 - plot. In contrast to the inclined plate, the oscillating jet only yields data in the time interval of few milliseconds. Also in this time interval the agreement with the maximiun bubble pressure method is excellent and shows deviations only within the limits of the accuracy of the two methods. 

The most recently developed methods to investigate the surface relaxation of soluble adsorption layers due to harmonic disturbances is the oscillating bubble or drop method. The technique involves the generation of radial oscillations of a gas bubble or a liquid drop at the top of a capillary immersed into the solution under study. The first set-up was described by Lunkenheimer Kretzschmar [150] and Wantke et al. [151] followed by a number of new designs of apparatus using novel pressure transducers to monitor the pressure changes inside a bubble or a drop [67, 152, 153, 154]. 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

It has been already indicated (Fig. 7) that micelles can lead to an essential acceleration of the adsorption process. Therefore, special experimental techniques are necessary for its investigation, allowing measurements of the dynamic surface tension in a time interval of milliseconds. The maximum bubble pressure method [78, 81, 83, 89,90,93] and the oscillating jet method [77, 82, 86, 87, 88, 90, 92, 93, 156] are most frequently used for these purposes. The inclined plate method [83, 89, 90, 93], the method of constant surface dilation [85] and the drop volume method [84] have been used also for slow adsorbing surfactants. 

These two equations allow the understanding of the measuring principle of the oscillating bubble or drop method. Oscillation can be generated either by external pressure variation 8 , or by volume variation in the cell, while the measured signal is the meniscus volume 5V (which is equivalent to the volume passing through the capillary 6V = ) or the... 

Only the two first methods allow measurement of the temperature coefficient of the surface energy. The maximum bubble pressure technique is well-adapted for metals with low and intermediate melting points and specially for oxidizable metals, while the sessile drop technique has been applied with success to measure ctlv values up to 1500°C. The drop weight method is particularly useful for very high melting-point metals because it avoids liquid contact with container materials. This is also true for the recently developed levitation drop technique that analyses the oscillation spectrum of a magnetically levitated droplet. 

D. O. Johnson, and K. J. Stebe, Oscillating bubble tensiometry A method for precisely measuring the kinetics of surfactant adsorptive-desorptive exchange. J. Colloid Int. Sci. 168 526-538 ( 994). 

Another recently developed method for determining surface rheological properties is the damping of a radial oscillating bubble, firstly described by Lunkenheimer Kretzschmar (1975) and established theoretically by Wantke et al. (1980). This technique is described in more detail in Chapter 6. It is based on damping effects and yields dilational rheological... 

The maximum bubble pressure method, realised as the set-up discussed above, allows measurements in a time interval from 1 ms up to several seconds and longer. At present, it is the only commercial apparatus which produces adsorption data in the millisecond and even sub-millisecond range (Fainerman Miller 1994b, cf. Appendix G). Otherwise data in this time interval can be obtained only from laboratory set-ups of the oscillating jet, inclined plate or other, even more sophisticated, methods. The accuracy of surface tension measurements in... 

In a recent paper Miller et al. (1994d) discussed parallel experiments with a maximum bubble pressure apparatus and a drop volume method (MPTl and TVTl from LAUDA, respectively), and oscillating jet and inclined plate instruments, performed with the same surfactant solutions. As shown in Fig. 5.27, these methods have different time windows. While the drop volume and bubble pressure methods show only a small overlap, the time windows of the inclined plate and oscillating jet methods are localised completely within that of the bubble pressure instrument. 

Fig. 5.29 Dynamic surface tension of four TRITON X-100 solutions measured using the maximum bubble pressure ( OA) and oscillating jet ( A) methods c = 0.2 (AA), 0.5 ( 0), 2.0 ( ), 5.0 ( 9-) g/1 according to Fainerman et al. (1994a)...

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