Jets oscillating

As indicated above, all paturbations of a fluid cyhnder for which m 0 are stable. For w = 1, considraatiou of Equation 5.87 shows that the cross section remains circular with radius at all points but that the axis becomes sinuous. For /n = 2, the axis remains straight birt the cross section is pertorbed to a somewhat elliptical shape. It is this latt case that is of interest in this section. 

If a jet issues from an orifice of circirlar cross section, we suppose that it can experience pertorbatiorrs of the type specified by Equation 5.76 with all possible values of m and a. As shown in the previoirs section, an instabihty develops characterized by wavenirmba- and growth factor p. But if the orifice has a rather elliptical cross section, a praturbation characterized by w = 2 and a = 0 is imposed. Since Equation 5.93 is not conveniait to use for a = 0, we return to 

Equation 5.80 and solve directly for P r) in this limit. The solution, which remains finite for r = 0, is given by 

The remainder of the analysis proceeds in the same manner as before, the final resnlt being 

If the liquid moves along the jet with velocity K the distance A traveled during one cycle of oscillation is given by 

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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]. 

Howell, E. 2001. Dynamic surface tension measurements of liquid solder using oscillating jets of elliptical cross section. Mechanical and Industrial Engineering. University of Illinois at Chicago, Chicago, IL. pp. 75. 

Pressure leaf filters are supplied in a wide range of size and materials of construction. One typical design is the Verti-jet unit with a vertical tank and vertical leaf filter, as shown in Figure 7.12, with rectangular leaves mounted individually but connected to a common outlet manifold. For sluice cleaning either a stationary or oscillating jet system... 

An oscillated fuel flow was provided in the form of a central jet within the duct carrying the pilot stream. The dimensions of the tube carrying the oscillated flow implied that the mean velocity and equivalence ratio of the jet had to be larger than that of the pilot stream to enable the oscillation of at least 5% of the total fuel flow. An examination of the influence of the bulk mean velocities of the pilot stream and the central jet on the amplitude of oscillations in this flow arrangement showed that, for the present range of flow conditions, values of the bulk mean velocity of the pilot stream less than that of the annular flow had no effect on the amplitude of oscillations, although larger values led to a decrease in amplitude [20]. The amplitude was also insensitive to the bulk mean velocity of the oscillated jet for values up to 3.5 times... 

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 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.

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. 

Figure 1.29. Surface relaxation of pure water. Data from oscillating jet compared with those from falling meniscus (drawn curve). The different symbols refer to experiments with different capillaries. (Redrawn from N.N. Kochurova, Yu. A. Shvechenkov and A.I. Rusanov, Koll. Zhur. 36 (1974) 785, transl. 725.)...

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. 

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.. )...

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. 

Oscillating jet bad good small time interval, no commercial set-up... 

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... 

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 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). 

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 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. 

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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