Maximum bubble-pressure method

In this method, the surface tension of a liquid is determined from the value of the maximum pressure needed to push a bubble out of a capillary into a liquid, against the 

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. 

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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)... 

A number of experimental studies have supplied numerical values for these, using either the classical maximum bubble pressure method, in which tire maximum pressure requhed to form a bubble which just detaches from a cylinder of radius r, immersed in tire liquid to a depth jc, is given by... 

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]. 

There are numerous other methods for measuring surface tension that we do not discuss here. These include (a) the measurement of the maximum pressure beyond which an inert gas bubble formed at the tip of a capillary immersed in a liquid breaks away from the tip (the so-called maximum bubble-pressure method) (b) the so-called drop-weight method, in which drops of a liquid (in a gas or in another liquid) formed at the tip of a capillary are collected and weighed and (c) the ring method, in which the force required to detach a ring or a loop of wire is measured. In all these cases, the measured quantities can be related to the surface tension of the liquid through simple equations. The basic concepts involved in these methods do not differ significantly from what we cover in this chapter. The experimental details may be obtained from Adamson (1990). 

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).

Bendure, R.L. 1971. Dynamic surface tension determination with maximum bubble pressure method. J. Colloid Interface Sci. 37 228-238. 

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. 

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... 

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. 

Figure 1.30. Surface tension of a 6.2 mM solution of purified sodium dodecyl sulfate. Maximum bubble pressure method. (Redrawn from K.J. Mysels, Colloids Surf. 43 (1990) 241.) Discussion of the regions I and II in the text.

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%. 

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