Pendent drop technique

The Gauss-Laplace equation describing liquid menisci in general was discussed in detail by Padday Russel (1960) and Padday et al. (1975). The profile of an axisymmetric drop can be calculated in dimensionless co-ordinates from the following equation (Rotenberg et al. 1983), 

Beside the fitting of drop profile co-ordinates to the Gauss-Laplace equation, based on least square algorithms, a relation exists which allows the surface tension to be calculated from the characteristic diameters and Dj (Andreas et al. 1938, Girault et al. 1984, Hansen Rodsrud 1991). 

Girault et al. (1984) derived the following relation to calculate y from the ratio Ds/D,  

using Eqs (5.27) and (5.28) the surface tension y can directly be calculated from the two drop diameters Dg and Dg. 

Calculations with the characteristic diameters is fast but is less precise than with the fitting procedure. The latter is much more accurate and therefore the more commonly used. The graphs in Fig. 5.16 shows how the principle of the fitting procedure works. 

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Perhaps the most striking property of a microemulsion in equilibrium with an excess phase is the very low interfacial tension between the macroscopic phases. In the case where the microemulsion coexists simultaneously with a water-rich and an oil-rich excess phase, the interfacial tension between the latter two phases becomes ultra-low [70,71 ]. This striking phenomenon is related to the formation and properties of the amphiphilic film within the microemulsion. Within this internal amphiphilic film the surfactant molecules optimise the area occupied until lateral interaction and screening of the direct water-oil contact is minimised [2, 42, 72]. Needless to say that low interfacial tensions play a major role in the use of micro emulsions in technical applications [73] as, e.g. in enhanced oil recovery (see Section 10.2 in Chapter 10) and washing processes (see Section 10.3 in Chapter 10). Suitable methods to measure interfacial tensions as low as 10 3 mN m 1 are the sessile or pendent drop technique [74]. Ultra-low interfacial tensions (as low as 10 r> mN m-1) can be determined with the surface light scattering [75] and the spinning drop technique [76]. 

Wilhelmy plate used by Wei et al. 1990, pendent drop technique used by Miller et al. 1993a), is not understood so far. 

Transient relaxation experiments of protein adsorption layers were published by Miller et al. (1993a, c, d). The experiments were performed using a modified pendent drop technique described in Section 6.3.4. The surface tension response to three subsequent square pulse perturbations of 0.1 mg/ml HA adsorbed at the aqueous solution/air interfaces (Miller et al. 1993a) are shown in Fig. 6.21. 

In a very recent development the pendent drop technique was used to study the static and dynamic behaviour of insoluble monolayers. Kwok et al. (1994a) were the first who performed measurements of surface pressure - area isotherms of octadecanol monolayer by using a pendent water drop and ADSA (cf Section 5.4) as a film balance. Consistent results with classical Langmuir-Wilhelmy film balance measurements reveal ADSA as a powerful tool also for monolayers. 

The pendent drop technique has also been extended to studies of insoluble monolayers of phospholipids at the water/n-dodecane interface (Li et al. 1994b). In these experiments first a monolayer is produced on a water drop surface as described above. Then, the water drop is gently immersed into the second liquid, for example n-dodecane. Then the change of the drop size enables one to compress and expand the interfacial film. Again, the isotherm obtained with ADSA shows the same type of dynamic behaviour as measured with the classic Langmuir-Blodgett trough technique (Thoma Mohwald 1994). 

In the pendent drop experiments, the surrounding temperature is easily controlled by using a small quartz cuvette. The cuvette can be sealed during the measurements to avoid evaporation effects. This makes the pendent drop technique particularly suited for measurements of very... 

When a pendant drop forms slowly at the lower end of a capillary tube it ultimately falls and stretches the filament (which remains attached to the drop). For a Newtoiuan flmd the filament qmckly thins and breaks but long filaments can be formed from visco-elastic liqmds [Jones et al., 1990]. The forces acting on the falling drop are determined using a force balance, and the extensional stress determined as a function of time [Jones and Rees, 1982], The falling pendent drop technique is simple to set up and analyse, and provides consistent values of an apparent elongational viscosity. 

A wide range of experimental techniques has been proposed through the years to measure the interfacial tension. Most popular has been the pendent drop technique but there has been increasing interest in techniques based upon breaking molten polymer threads. Methods of measurement of interfacial tension are summarized in Table 6.1 and values of the interfacial tension for different polymer-melt pairs are summarized in Table 6.2. The larger the polarity difference is, the larger the interfacial tension. Thus the greatest interfacial tension in Table 6,2 is for polyethylene and polyamide 6,... 

Fig. 10 Surface pressure— area isotherms for two different concentrations of hexylamine. The isotherms are recorded with the pendent drop technique by sucking liquid out of the droplet leading to a decrease in surface area of the droplet. The solid lines correspond to fits by (A/Aq) with exponent E as fitting parameter...

One of the variants of the technique involves a pendent drop on a conical tip. The reason for experimenting with this geometry is to reduce drop vibrations, always a source of error if high accuracy is required. Sessile drops and pendent drops on inclined surfaces have been investigated by Nguyen et al. ) and by Lawal and Brown ), respectively. For such systems the drops are no longer axis)rm-metric. 

Table 1.2. Surface tensions of water in mN m , obtained by various investigations using different techniques. Temperatures in degrees Celsius. Abbreviations for methods CR = capillary rise, WP = Wilhelmy plate, DNR = Du Nouy ring, DM = other detachment method or object in the surface. HD = hanging (pendent) drop, SD = sessile drop, MBP = maximum bubble pressure DW = drop weight.

It should be possible to describe the exchange of matter by a diffusion model for surfactant mixtures, as shown by Miller et al (1993b). They also developed another new relaxation technique, based on the pendent drop method (cf. Section 6.3.4), and studied the relaxation behaviour of SDS at the water/air interface. It could be shown that surface active impurities can alter the relaxation behaviour of the adsorption layer tremendously. The same method was also applied to detect impurities in organic solvents (cf Section 5.1.2., Fig. 5.7.). 

Harmonic and transient relaxation experiments for dodecyl dimethyl phosphine oxide solutions were performed with the elastic ring method by Loglio [240]. This methods allows oscillation experiments in the frequency range from about 0.5 to 0.001 Hz and is suitable for comparatively slow relaxing systems. Slow oscillation experiments can be performed much easier now with the pendent drop apparatus [186]. Both techniques are also able to perform transient relaxation experiments. The two types of experiments have a characteristic frequency defined in the same way by Eq. (4.110). 

Interfacial tension studies are conducted with various concentrations of micellar solution components to determine optimal concentration ranges. Measurements are usually made with the spinning drop, pendent drop, or sessile drop techniques. 

Interfacial tension measurement techniques can be divided into two categories equilibrium and transient methods [41]. The pendent-drop method is the most commonly applied method to measure interfadal tension under pressure and involves the measurement of density differences between two fluids and the equilibrium drop profile shape. In the following section, examples of interfacial tension reduction are presented for binary polymer/C02 systems and for polymer blends. 

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