The oscillating jet method

One of the oldest experimental methods for the measurement of dynamic surface tensions of surfactant solutions is the oscillating jet (OJ) method. The idea is based on the analysis of a stationary jet issuing from a capillary pipe into the atmosphere which oscillates about its 

The analysis of the jet geometry yields surface tension values at different distances from the orifice. The corresponding time t to each of the surface tension values results from the distance d and the mean linear velocity of the jet. 

The oscillating jet method provides dynamic surface tensions in a time interval from 3 ms-50 ms and has been used by many authors (for example Bohr 1909, Addison 1943, 1944, 1945, Rideal Sutherland 1952, Defay Hommelen 1958, Thomas Potter 1975a, b, Fainerman et al. 1993a, Miller et al. 1994d). 

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It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

Figure 3.11 Illustration of a magnified image of an oscillating jet of liquid that is being injected in front of a grid for measuring the jet s period. This is the oscillating jet method for surface tension measurement.

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. 

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. 

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. 

There is significant overlap in describing techniques for the measurement of equilibrium surface tension with those for dynamic surface tension, as discussed in the following chapter. Many of those dynamic surface tension methods can be used to measure equilibrium tension simply by performing the experiment over sufficiently long times. The time required for equilibration can range widely, from the practically instantaneous equilibration for pure liquids, to many hours or even days for dilute surfactant or polymer solutions. Thus, some of the dynamic techniques, particularly those that can only be used to study short times, such as the oscillating jet method, are not well suited for equilibrium measurements. 

Figure 12.5. Schematic of the set-up used for the oscillating jet method further details are given in the text (according to Joos (1))...

In addition to the methods discussed here and in Section 6.2, there are a few other methods for measuring surface tension that are classified as dynamic methods as they involve the flow of the liquids involved (e.g., methods based on the dimensions of an oscillating liquid jet or of the ripples on a liquid film). As one might expect, the dynamic methods have their advantages as well as disadvantages. For example, the oscillating jet technique is ill-suited for air-liquid interfaces, but has been found quite useful in the case of surfactant solutions. A discussion of these methods, however, will require advanced fluid dynamics concepts that are beyond our scope here. As our primary objective in this chapter is simply to provide a basic introduction to surface tension and contact angle phenomena, we shall not consider dynamic methods here. Brief discussions of these methods and a comparison of the data obtained from different techniques are available elsewhere (e.g., see Adamson 1990 and references therein). 

Figure 4.20. Surface potential relaxation of water and aqueous NaCl solutions. Oscillating Jet method. Temperature 24°C. The electrolyte concentration is indicated. (Redrawn from Kochurova et al.. )...

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. 

A method based on the comparison of experimental and calculated kinetic dependencies of the dynamic surface tension can be more precise in comparison with the use of Eq. (5.253) [77, 85, 89, 92, 93]. Mitrancheva et al. presented the most detailed data and compared calculated dynamic surface tension with results obtained for solutions of TRITON X-100 using three different experimental methods the inclined plate, the oscillating jet and the maximum bubble pressure methods [93]. The inclined plate method yielded values of i2 different from the results of the two other techniques. This discrepancy is probably connected with the differences in the attainable surface age. Thus the inclined plate method can be used only at relatively high surface life times when the surface tension tends asymptotically to equilibrium, and when the accuracy of determination of i2 decreases. In addition the insufficiently investigated peculiarities of the liquid flow along the inclined plane can be another source of experimental errors [93]. 

The characteristic times of the slow step of micellisation determined by the maximum bubble pressure and oscillating jet methods have the same orders of magnitude at low concentrations and agree with results of investigation of the bulk phase [139, 157] (Fig. 5.14). At higher... 

One of the reasons of the insufficient reliability of micellisation kinetics data determined from dynamic surface tensions, consists in the insufficient precision of the calculation methods for the adsorption kinetics from micellar solutions. It has been already noted that the assumption of a small deviation from equilibrium used at the derivation of Eq. (5.248) is not fulfilled by experiments. The assumptions of aggregation equilibrium or equal diffusion rates of micelles and monomers allow to obtain only rough estimates of the dynamic surface tension. An additional cause of these difficulties consists in the lack of reliable methods for surface tension measurements at small surface ages. The recent hydrodynamic analysis of the theoretical foundations of the oscillating jet and maximum bubble pressure methods has shown that using these techniques for measurements in the millisecond time scale requires to account for numerous hydrodynamic effects [105, 158, 159]. These effects are usually not taken into account by experimentalists, in particular in studies of micellar solutions. A detailed analysis of... 

While the above equations were draived for a plane interface, they may also be used for curved interfaces provided that the radii of curvature are much greato than the thickness of the layer in the bulk solution where the concentration deviates significantly from c. This thickness is, to an order of magnitude, and hence only about 0.1 mm for D = 5 x 10 cm /sec and t -20 sec. Thus interfacial tension data y(t) obtained with the oscillating jet technique described in Chapter 5 may be used with Equation 6.41 in many cases. Another method of measuring dynamic inteifacial tension is the falling meniscus method discussed in Problem 6.4. 

A third group of methods is the so-called dynamic methods, such as the oscillating jet, capillary wave, or oscillating drop/bubble methods. These methods are typically based on the evalnation of periodically applied interfacial stresses followed by interface relaxation and provide the means for determining the dilational rheology of the liquid-gas and liquid-liquid interfaces. 

Houcine et al. (64) used a non-intrusive laser-induced fluorescence method to study the mechanisms of mixing in a 20 dm CSTR with removable baffles, a conical bottom, a mechanical stirrer, and two incoming liquid jet streams. Under certain conditions, they observed an interaction between the flow induced by the stirrer and the incoming jets, which led to oscillations of the jet stream with a period of several seconds and corresponding switching of the recirculation flow between several metastable macroscopic patterns. These jet feedstream oscillations or intermittencies could strongly influence the kinetics of fast reactions, such as precipitation. The authors used dimensional analysis to demonstrate that the intermittence phenomenon would be less problematic in larger CSTRs. 

The dynamic methods depend on the fact that certain vibrations of a liquid cause periodic extensions and contractions of its surface, which are resisted or assisted by the surface tension. Surface tension therefore forms an important part, or the whole, of the restoring force which is concerned in these vibrations, and may be calculated from observations of their periodicity. Dynamic methods include determination of the wave-length of ripples, of the oscillations of jets issuing from non-circular orifices, and of the oscillations of hanging drops. Dynamic methods may measure a different quantity from the static methods, in the case of solutions, as the surface is constantly being renewed in some of these methods, and may not be old enough for adsorption to have reached equilibrium. In the formation of ripples there is so little interchange of material between the surface and interior, and so little renewal of the surface, that the surface tension measured is the static tension ( 12. ... 

The various dynamic methods give the surface tension of more or less recently formed surfaces, and may yield results different from the static methods, if adsorption occurs, and is incomplete at the moment when the tension is actually measured. One factor in dynamic measurements, which cannot be satisfactorily measured at present, is the time which has elapsed between the formation of the surface from the homogeneous interior liquid, and the actual measurement of the surface tension. If this could be varied, and measured with an accuracy of say 10 4 second, a valuable new weapon would be available for investigating the progress of adsorption. Bohr s work on oscillating jets is probably the best on any dynamic method. 

Table 1.5 reviews the capabilities of the most common (quasi-)static methods (we excluded the very fast oscillating jet and pulsating bubble), obtaining dynamic information. Some of these are intrinsically dynamic in that the measurement requires the extension of an interface (drop weight, maximum bubble pressure), so that y(t) data can in principle be obtained when the rate of extension can be varied in a controlled fashion. Others are basically static (shapes of sessile or pendent drops and bubbles), but can be rendered dynamic by disequilibratlon. 

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