The Maximum Bubble Pressure Method

The maximum bubble pressure method. If a bubble is blown at the bottom of a tube dipping vertically into a liquid, the pressure in the bubble increases at first, as the bubble grows and the radius of curvature diminishes. It was shown in Chap. I, 13, that when the bubble is small enough to be taken as spherical, the smallest radius of curvature and the maximum pressure occurs when the bubble is a hemisphere further growth causes diminution of pressure, so that air rushes in and bursts the bubble. At this point the pressure in the bubble is 

This method is independent of the contact angle, provided that it is not so great (above 90°) that the liquid recedes to the outer edge of the tube if this occurs, r is the outer radius of the tube. 

This is the same equation as the approximate one for the rise in a capillary tube, as it must be, since the height of rise is a measure ofthe pressure effect of the curved surface of the meniscus. 

For larger tubes the surface cannot be taken as spherical, and the fundamental equation (5) must be applied. Numerous writers have given approximation formulae, of which the best is that of Schrodinger,1 

As with the rise in the capillary tube, all such formulae can only be accurate for moderately narrow tubes. A more satisfactory plan has been adopted by Sugden,2 who applied Bashforth and Adams s tables as follows. 

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The maximum bubble pressure method is good to a few tenths percent accuracy, does not depend on contact angle (except insofar as to whether the inner or outer radius of the tube is to be used), and requires only an approximate knowledge of the density of the liquid (if twin tubes are used), and the measurements can be made rapidly. The method is also amenable to remote operation and can be used to measure surface tensions of not easily accessible liquids such as molten metals [29]. 

Correction Factors for the Maximum Bubble Pressure Method (Minimum Values of Xjr for Values of r/a from 0 to 1.50)... 

Hsu and Berger [43] used the maximum bubble pressure method (MBP) to study the dynamic surface tension and surface dilational viscosity of various surfactants including AOS and have correlated their findings to time-related applications such as penetration and wetting. A recent discussion of the MBP method is given by Henderson et al. [44 and references cited therein]. 

Figure D3.5.6 Adsorption kinetics of a small molecule surfactant. Surface tension of polyoxyethylene (10) lauryl ether (Brij) at the air-water interface decreases as time of adsorption increases. Brij concentration is 0.1 g/liter, as measured by the drop volume technique and the maximum bubble pressure method (UNITD3.6).

In the Maximum-bubble-pressure method the surface tension is determined from the value of the pressure which is necessary to push a bubble out of a capillary against the Laplace pressure. Therefore a capillary tube, with inner radius rc, is immersed into the liquid (Fig. 2.9). A gas is pressed through the tube, so that a bubble is formed at its end. If the pressure in the bubble increases, the bubble is pushed out of the capillary more and more. In that way, the curvature of the gas-liquid interface increases according to the Young-Laplace equation. The maximum pressure is reached when the bubble forms a half-sphere with a radius r/s V(j. This maximum pressure is related to the surface tension by 7 = rcAP/2. If the volume of the bubble is further increased, the radius of the bubble would also have to become larger. A larger radius corresponds to a smaller pressure. The bubble would thus become unstable and detach from the capillary tube. 

Fundamental knowledge about the behavior of charged surfaces comes from experiments with mercury. How can an electrocapillarity curve of mercury be measured A usual arrangement, the so-called dropping mercury electrode, is shown in Fig. 5.2 [70], A capillary filled with mercury and a counter electrode are placed into an electrolyte solution. A voltage is applied between both. The surface tension of mercury is determined by the maximum bubble pressure method. Mercury is thereby pressed into the electrolyte solution under constant pressure P. The number of drops per unit time is measured as a function of the applied voltage. 

Methods. All experiments were performed at 25°C. Critical micelle concentrations were determined using the maximum bubble pressure method on a SensaDyne 6000 surface tensiometer. Dry nitrogen was used as the gas source for the process and was bubbled through the solution at a rate of 1 bubble/sec. Cmc s measured using the Wilhemy plate method were in agreement with those obtained from the bubble tensiometer however, the bubble pressure method was used since it is less susceptible to error due to impurities and the nitrogen environment makes pH control easier. 

The Young-Laplace equation forms the basis for some important methods for measuring surface and interfacial tensions, such as the pendant and sessile drop methods, the spinning drop method, and the maximum bubble pressure method (see Section 3.2.3). Liquid flow in response to the pressure difference expressed by Eqs. (3.6) or (3.7) is known as Laplace flow, or capillary flow. 

For foams, it is the surface tension of the foaming solution that is usually of most interest. For this, the most commonly used methods are the du Noiiy ring, Wilhelmy plate, drop weight or volume, pendant drop, and the maximum bubble pressure method. For suspensions it is again usually the surface tension of the continuous phase that is of most interest, with the same methods being used in most cases. Some work has also been done on the surface tension of the overall suspension itself using, for example, the du Noiiy ring and maximum bubble pressure methods (see Section 3.2.4). 

Hogness,1 Burdon,2 Bircumshaw, and Sauerwald have done a great deal to render accurate measurements possible the best method is probably the maximum bubble pressure method, but the measurement of sessile drops (see Chap. IX), and of drop volumes, are also useful. Metals always have a very high surface tension. Table X gives typical results. 

There are static and dynamic methods. The static methods measure the tension of practically stationary surfaces which have been formed for an appreciable time, and depend on one of two principles. The most accurate depend on the pressure difference set up on the two sides of a curved surface possessing surface tension (Chap. I, 10), and are often only devices for the determination of hydrostatic pressure at a prescribed curvature of the liquid these include the capillary height method, with its numerous variants, the maximum bubble pressure method, the drop-weight method, and the method of sessile drops. The second principle, less accurate, but very often convenient because of its rapidity, is the formation of a film of the liquid and its extension by means of a support caused to adhere to the liquid temporarily methods in this class include the detachment of a ring or plate from the surface of any liquid, and the measurement of the tension of soap solutions by extending a film. 

Measurements on molten metals. The maximum bubble pressure method has proved one of the most satisfactory, but sessile drops, and drop-volumes have also been used with success.2 The principal difficulty lies in the proneness of metals to form skins of oxides, or other compounds, on their surfaces and these are sure to reduce the surface tension. Unless work is conducted in a very high vacuum, a freshly formed surface is almost a necessity if the sessile bubble method is used, the course of formation of a surface layer may, if great precautions are taken, be traced by the alteration in surface tension. Another difficulty lies in the high contact angles formed by liquid metals with almost all non-metallic surfaces, which are due to the very high cohesion of metals compared with their adhesion to other substances. 

For rapid work, requiring an accuracy of about three-tenths per cent., Sugden s modification of the maximum bubble-pressure method is probably the most convenient very little apparatus is required, and a complete measurement can easily be made in 15 minutes. Two or three cubic centimetres of the liquid are all that is necessary. The drop-weight method (using Harkins s indispensable corrections) is also simple and equally accurate. 

Equipment. A Brookfield synchro-lectric viscometer, serial no. 758, is used to measure viscosity in the range of 0-100,000 cP. Sugden s double capillary modification of the maximum bubble pressure method is used to determine surface tensions. The apparatus is calibrated with benzene and is checked by determining the surface tension of chloroform at 25°C, which is found to be 23.5 dyn cm"1 (26.5 dyn cm 1) (35). 

In the maximum bubble pressure method, the interval between two bubbles ( the lifetime of one bubble) is the only measure of the age of the growing surface. Such intervals can nowadays be varied between milliseconds and several hours. Modem pressure transdueers allow small pressures to be measured rapidly and accurately. The trend is that the mcudmum pressure increases with increasing flow rate, as expected. 

Fedor (1990), and Fedor et al. (1991). The density, surface tension, electrical conductivity, and viscosity have been measured at the temperature of 1573 K and in a relatively wide concentration range. The density and surface tension were measured by means of the maximum bubble pressure method using a device similar to that described in Section 6.2.2. The viscosity was measured using the rotational method, and the electrical conductivity, by means of the two-electrode method. 

There are only a few suitable methods for high-temperature density measurement. The reason is the corrosive nature of molten salts and the thermal dilatation of the materials used for measurement. Most convenient for molten salts are the methods of hydrostatic weighing and the maximum bubble pressure method. For more viscous liquids, such as some silicate melts, the falling body method is suitable. These three methods will be described in detail here. For further study the reader is referred to an excellent book by Mackenzie (1959). 

The surface tension of this system was measured by Lubyova et al. (1997) using the maximum bubble pressure method. The values of constants a and b of the temperature dependency of surface tension, a = a —bt, obtained using the linear regression analysis, together with the values of the standard deviations of approximation, and the values of the surface tension at 823°C for the investigated KF-KBF4 melts are given in Table 6.1. 

In surface tension measurements using the maximum bubble pressure method several sources of error may occur. As mentioned above, the exact machining of the capillary orifice is very important. A deviation from a circular orifice may cause an error of 0.3%. The determination of the immersion depth with an accuracy of 0.01 mm introduces an error of 0.3%. The accuracy of 1 Pa in the pressure measurement causes an additional error of 0.4%. The sum of all these errors gives an estimated total error of approximately 1%. Using the above-described apparatus, the standard deviations of the experimental data based on the least-squares statistical analysis were in the range 0.5% < sd > 1%. 

On the basis of the GAI, it is clear that the interfacial tension y is the most important experimental quantity. Three methods are commonly used to determine y at liquid liquid interfaces, namely, the capillary electrometer method, the maximum bubble pressure method, and the drop weight or drop time method. 

Under certain circumstances, the contact angle between Hg and the solution can change with applied potential. For this reason, the maximum bubble pressure method which is independent of contact angle is preferred (see section 8.2). This technique is easily adapted to computer-controlled experiments. 

The most suitable technique for studying adsorption kinetics and dynamic surface tension is the maximum bubble pressure method, which allows measurements to be obtained in the millisecond range, particularly if correction for the so-called dead time, t. The dead time is simply the time required to detach the bubble after it has reached its hemispherical shape. A schematic representation of the principle of maximum bubble pressure is shown in Figure 18.14, which describes the evolution of a bubble at the tip of a capillary. The figure also shows the variation of pressure p in the bubble with time. 

The surface tension value in the maximum bubble pressure method is calculated using the Laplace equation. 

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. 

Figure 6.3 Liquid surface tension determination by the maximum bubble pressure method. The maximum pressure, P needed to push a bubble out of a capillary into a liquid is determined just prior to the detachment of the bubble hL is the distance below the surface of the liquid to the tip of the tube. The value of Pmax is usually found by measuring the height of a water column, hc. a. If the tube is completely wetted by the liquid, then the radius, r, is its internal radius, b. If the liquid is non-wetting towards the tube, then the radius, r, is its external radius. The bubble becomes fully hemispherical, as can be seen in the middle shapes of a and b.

If the radius of the capillary is large, so that (r/a) > 0.05, then the Basforth-Adams equation (Equation (481)) or the Lane equations (Equations (482) and (483)) can also be used in the surface tension calculation from the maximum bubble pressure method. This method can also be used to determine the surface tension of molten metals. It has been a popular method in the past, but now it is not very common in surface laboratories because of its poor precision. 

Figure 3 contains dynamic data for ff-LG received by three methods the maximum bubble pressure method in the time range 0.001 s to 100 s, the drop volume method for times in the range 5 s to 500 s, and the profile analysis tensiometer PAT l in the time range from 10 s up to several hours. 

The aim of this chapter is to present the fundamentals of adsorption at liquid interfaces and a selection of techniques, for their experimental investigation. The chapter will summarise the theoretical models that describe the dynamics of adsorption of surfactants, surfactant mixtures, polymers and polymer/surfactant mixtures. Besides analytical solutions, which are in part very complex and difficult to apply, approximate and asymptotic solutions are given and their range of application is demonstrated. For methods like the dynamic drop volume method, the maximum bubble pressure method, and harmonic or transient relaxation methods, specific initial and boundary conditions have to be considered in the theories. The chapter will end with the description of the background of several experimental technique and the discussion of data obtained with different methods. 

Adsorption Kinetics Model for the Maximum Bubble Pressure Method... 

The maximum bubble pressure technique is a classical method in interfacial science. Due to the fast development of new technique and the great interest in experiments at very small adsorption times in recent years, commercial set-ups were built to make the method available for a large number of researchers. Rehbinder (1924, 1927) was apparently the first who applied the maximum bubble pressure method for measurement of dynamic surface tension of surfactant solutions. Further developments of this method were described by several authors (Sugden 1924, Adam Shute 1935, 1938, Kuffiier 1961, Austin et al. 1967, Bendure 1971,... 

The surface tension value in the maximum bubble pressure method is calculated via the Laplace equation. For the instrument under discussion, the capillary radius is small and the bubble shape is thus assumed to be spherical. Thus the deviation of the bubble shape from a spherical one can be neglected and needs no correction. Hence, the following equation results. 

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... 

Fig. 5.32 Dynamic surface tension as a function of the square root of surface age for four pt-BPh-EOlO solutions measured using the maximum bubble pressure method Cg= 0.0001(B) 0.0005 ( ) 0.001 (A) 0.0025 ( ) mol/1 according to Miller et al. (1994d)...

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