Pendant drops

A set of pendant drop profiles is shown in Fig. 11-17 as an illustration of the range of shapes that may be observed. It has been pointed out that for practical reasons, the size of the tip from which the drop is suspended should be such that rja is about 0.5 or less [66]. 

The automated pendant drop technique has been used as a film balance to study the surface tension of insoluble monolayers [75] (see Chapter IV). A motor-driven syringe allows changes in drop volume to study surface tension as a function of surface areas as in conventional film balance measurements. This approach is useful for materials available in limited quantities and it can be extended to study monolayers at liquid-liquid interfaces [76],... 

The usual experimental situation is that of a sessile drop and, as with the pendant drop, it is necessary to determine a shape parameter and some absolute length. Thus /3 may be determined by profile fitting, and Ze measured, where Ze is the distance from the plane at = 90 to the apex. If the drop rests with... 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

Surface tension of the nonpolarized ITIES was investigated by using the drop-weight [2,3,29], maximum bubble pressure [30] and pendant drop [4] methods. The latter method... 

Recently, Samec et al. [38] have investigated the same system by the video-image pendant drop method. Surface tension data from the two studies are compared in Fig. 2, where the potential scale from the study [36] was shifted so that the positions of the electrocapillary maxima coincide. The systematic difference in the surface tension data of ca. 3%, cf. the dotted line in Fig. 2, was ascribed to the inaccurate determination of the drop volume, which was calculated from the shape of the drop image and used further in the evaluation of the surface tension [38]. A point of interest is the inner-layer potential difference A (pj, which can be evaluated relative to the zero-charge potential difference A cpp c by using Eq. 

Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water-1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water-nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of —0.225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41]. 

In a closely related study, Marecek et al. [46] used the pendant drop video-image method to investigate the adsorption and surface reactions of calix[4]arene ligands at the ideally polarized water-1,2-dichloroethane interface. The difference between the surface tensions in acidic and alkaline media was ascribed to a difference in the charge on the... 

Recently, the size and shape of a liquid droplet at the molten tip of an arc electrode have been studied,12151 and an iterative method for the shape of static drops has been proposed. 216 Shapes, stabilities and oscillations of pendant droplets in an electric field have also been addressed in some investigations. 217 218 The pendant drop process has found applications in determining surface tensions of molten substances. 152 However, the liquid dripping process is not an effective means for those practical applications that necessitate high liquid flow rates and fine droplets (typically 1-300 pm). For such fine droplets, gravitational forces become negligible in the droplet formation mechanism. 

Interfacial Tension of Aqueous Surfactant Solutions by the Pendant Drop Method... 

The low interfacial tensions between two liquids have been measured for different systems by using the pendant drop method. In the case of the quaternary system Ci2ll25S 3 tNa+H20+n-Butanol+Toluene, the interfacial data as measured by pendant drop method are compared with reported literature data, using other methods (with varying NaCl concentration). In order to understand the role of co-surfactant, ternary systems were also investigated. The pendant drop method was also used for measuring the interfacial tension between surfactant-H20/n-alcohol (with number of carbon atoms in alcohol varying from 4-10). The interfacial tension variation was dependent on both the surfactant and alcohol. 

If we consider the pendant drop as shown in Figure 1, we can write from the Laplace equation (20) for the point P in terms of the pressure differences across the interface at a reference point B ... 

BIRDl AND STENBY Interfacial Tension by the Pendant Drop Method 331... 

All chemicals used were of very high purity grade (>99 %). The quaternary systems were mixed and allowed to reach equilibrium over a week at constant temperature, with occasional stirring. The oil phase (top phase) was placed in the measuring cell of the pendant drop apparatus. The bottom (aqueous) phase was filled in the syringe for the measurement. 

Figure 4. Variation of y of the systems. A, aqueous phase surfactant + H O oil phase toluene with pendant drop method (24 °C). Concentration of detergent = 20 g/L. NaDOC (4) NaDOC + 8% n-butanol(A) NaDDS ( ) NaDDS + 8% n-butanol (O). B, aqueous phase surfactant + H2O oil phase n-heptane by pendant drop method 25 °c). Key same as for 4A.

These studies, carried out by measuring interfacial tensions, Yq , between aqueous and oil phases, by using the pendant drop method, show that this method is very useful for ternary and quaternary systems. In one system (A), NaDDS + H2O + n-butanol + Toluene... 

The pendant drop method was satisfactory for low Yqw values,. e. 0.02 mN/m. Typical data are given in Table III. In the systems where ultra-low yij values have been reported by other methods (like spinning drop), the pendant drop needs further investigations before it can be applied, since this would require syringes with much smaller diameters (J. e. 10 mm). As regards the theoretical analyses, we cannot find any concern why pendant drop should have any limitations for such studies. (Same is valid for spinning drop method). 

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