Bubble methods equilibrium surface tension

A number of methods are available for the measurement of surface and interfacial tension of liquid systems. Surface tension of liquids is determined by static and dynamic surface tension methods. Static surface tension characterises the surface tension of the liquid in equilibrium and the commonly used measurement methods are Du Notiy ring, Wilhelmy plate, spinning drop and pendant drop. Dynamic surface tension determines the surface tension as a function of time and the bubble pressure method is the most common method used for its determination. 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

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... 

Pendant or Sessile Drop Method The surface tension can be easily measured by analyzing the shape of a drop. This is often done by optical means. Assuming that the drop is axially symmetric and in equilibrium (no viscous and inertial effects), the only effective forces are gravity and surface or interfacial forces. In this case, the Young-Laplace equation relates the shape of the droplet to the pressure jump across the interface. Surface tension is, then, measured by fitting the drop shape to the Young-Laplace equation. Either a pendant or a sessile drop can be used for surface tension measurement. The pendant drop approach is often more accurate than the sessile drop approach since it is easier to satisfy the axisymmetric assumption. Similar techniques can be used for measuring surface tension in a bubble. 

The dynamic surface tension of [3-casein solutions at three concentrations 5 10, 10 and 10 mol/1 are shown in Fig. 14. As one can see the results from the two methods differ significantly. For the bubble the surface tension decrease starts much earlier. The surface tensions at long times, and hence the equilibrium surface tension from the bubble experiment are lower than those from the drop. However, the establishment of a quasi-equilibrium for the drop method is more rapid at low (3-casein concentrations while at higher P-casein concentrations this process is more rapid for the bubble method. This essential difference between solutions of proteins and surfactants was discussed in detail elsewhere [50]. In brief, it is caused by simultaneous effects of differences in the concentration loss, and the adsorption rate, which both lead to a strong difference in the conformational changes of the adsorbed protein molecules. 

The profiles of pendant and sessile bubbles and drops are commonly used in determinations of surface and interfacial tensions and of contact angles. Such methods are possible because the interfaces of static fluid particles must be at equilibrium with respect to hydrostatic pressure gradients and increments in normal stress due to surface tension at a curved interface (see Chapter 1). It is simple to show that at any point on the surface... 

From this fit the surface tension is obtained. The same method is applied with a pendant or sessile bubble. Using a bubble ensures that the vapor pressure is 100%, a requirement for doing experiments in thermodynamic equilibrium. Often problems caused by contamination are reduced. 

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. 

Dynamic surface tension is the time trajectory of surface tension before equilibrium is reached. Dynamic surface tension tracks the changes during surface formation when surfactants are added. The bubble pressure method is the one most commonly used for the determination of dynamic surface tension. The details of this method are described in ASTM D3825-90 (2000) [ 19]. In this method a capillary tube is immersed in a sample liquid and a constant flow of gas is maintained through the tube forming bubbles in the sample liquids. The surface tension of the sample is calculated from the pressure difference inside and outside the bubble and the radius of the bubble. 

The oscillating bubble method proves to be very convenient and precise for the evaluation of the non-equilibrium elasticity of surfaces in a wide range of frequencies of external disturbances and surface coverage (adsorption of surfactant) [103-105]. It is based on registration of the sinusoidal variation of bubble volume. The bubble is situated in a capillary containing surfactant solution in which oscillations of different frequencies and amplitudes are created. The treatment of the U = f(ft)) curves (where U is the tension needed to initiate oscillations of constant amplitude) allows the determination of Marangoni elasticities [105]. 

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 static methods are based on studies of stable equilibrium spontaneously reached by the system. These techniques yield truly equilibrium values of the surface tension, essential for the investigation of properties of solutions. Examples of the static methods include the capillary rise method, the pendant and sessile drop (or bubble) methods, the spinning (rotating) drop method, and the Wilhelmy plate method. 

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 two methods maximum bubble pressure and profile analysis tensiometry complement each other experimentally and cover a total time range of nine orders of magnitude from about lO" seconds up to 10 seconds (many hours). The example given in Fig. 33 shows the dynamic surface tension of two Triton X-100 solutions measured with the instruments BPA and PAT (SINTERFACE Technologies) over the time interval of 7 orders of magnitude. As one can see, the experiments cover the beginning of the adsorption process and the establishment of the equilibrium state. 

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