Liquid maximum bubble pressure

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]. 

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

According to the simple formula, the maximum bubble pressure is given by f max = 27/r where r is the radius of the circular cross-section tube, and P has been corrected for the hydrostatic head due to the depth of immersion of the tube. Using the appropriate table, show what maximum radius tube may be used if 7 computed by the simple formula is not to be more than 5% in error. Assume a liquid of 7 = 25 dyn/cm and density 0.98 g/cm. ... 

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... 

Surface tension and density of liquid alloys have been studied by Moser et al. (2006). Measurements by maximum bubble pressure and dilatometric techniques were carried out in an extensive range of temperatures on liquid alloys close to the ternary eutectic Sn3 3Ag0 76Cu with different Sb additions, which decrease surface tension and density. The experimental data were discussed in comparison also with values calculated on the basis of different models. 

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). 

An almost overwhelmingly large number of different techniques for measuring dynamic and static interfacial tension at liquid interfaces is available. Since many of the commercially available instruments are fairly expensive to purchase (see Internet Resources), the appropriate selection of a suitable technique for the desired application is essential. Dukhin et al. (1995) provides a comprehensive overview of currently available measurement methods (also see Table D3.6.1). An important aspect to consider is the time range over which the adsorption kinetics of surface-active substances can be measured (Fig. D3.6.5). For applications in which small surfactant molecules are primarily used, the maximum bubble pressure (MBP) method is ideally suited, since it is the only... 

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. 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

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. 

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. 

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. 

Figure 1.18. Principle of the method of maximum bubble pressure. Cross-section of a vertical capillary in a wetting liquid. By applying an internal pressure p. the meniscus can be pushed down till at p = p(max) the bubble starts to grow spontaneously.

In the method of the Jailing meniscus a liquid-wetted tapering tube is placed vertically in a reservoir, as in fig. 1.26. Inside the tube liquid is held by the capillary pressure. The tube is now moved upwards - or the liquid in the vessel downwards - to increase the hydrostatic pressure head, and this is continued until the liquid in the capillary collapses. From the hydrostatic head the Laplace pressure is obtained and from that the surface tension. The method is very simple and may be considered as the counterpart of the maximum bubble pressure technique there are also similarities to the situation sketched in fig. 1.8a. The idea is rather old... 

A variant is the micro-pipette method, which is also similar to the maximum bubble pressure technique. A drop of the liquid to be studied is drawn by suction into the tip of a micropipette. The inner diameter of the pipette must be smaller than the radius of the drop the minimum suction pressure needed to force the droplet into the capillary can be related to the surface tension of the liquid, using the Young-Laplace equation [1.1.212). This technique can also be used to obtain interfacial tensions, say of individual emulsion droplets. Experimental problems include accounting for the extent of wetting of the inner lumen of the capillary, rate problems because of the time-dependence of surfactant (if any) adsorption on the capillary and, for narrow capillaries accounting for the work needed to bend the interface. Indeed, this method has also been used to measure bending moduli (sec. 1.15). 

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). 

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. 

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.

In theory, every surface tension measurement method can be used to determine the interfacial tension between two liquids. However, the accuracy of these methods is reduced when applied to liquid-liquid interfaces, or when one or both of the liquids is viscous. In practice, the maximum bubble pressure and pendant drop methods are the most suitable, giving consistent and reliable values for interfacial tensions, although there is sometimes the... 

In order to measure the surface tension of solutions containing surfactants, the maximum bubble pressure, pendant drop and Wilhelmy plate (immersed at a constant depth) methods are suitable capillary rise, ring, mobile Wilhelmy plate, sessile drop and drop weight methods are not very suitable. These methods are not recommended because surfactants preferably adsorb onto the solid surfaces of capillaries, substrates, rings, or plates used during the measurement. In a liquid-liquid system, if an interfacially active surfactant is present, the freshly created interface is not generally in equilibrium with the two immiscible liquids it separates. This interface will achieve its equilibrium state after the redistribution of solute molecules in both phases. Only then can dynamic methods be applied to measure the interfacial tension of these freshly created interfaces. 

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. 

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