Pendant-drop method

An alternative to obtaining 0 directly involves defining some more convenient shape-dependent function, and an early but still very practical method is the following. We define a shape-dependent quantity as S = dsldg, as indicated in Fig. 11-16, de is the equatorial diameter and ds is the diameter measured at a distance de up from the bottom of the drop. The hard-to-measure size parameter h in Eq. 11-17 is combined with 0 by defining the quantity H = -0(defb). Thus 

The relationship between the shape-dependent quantity H and the experimentally measurable quantity S originally was determined empirically [66], but a set of quite accurate XjH versus S values were later obtained by Niederhauser and Bartell [67] (see also Refs. 34 and 68) and by Stauffer [69], 

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]. 

A modem alternative procedure involves computer matching of the entire drop profile to a best fitting theoretical curve in this way the entire profile is used, rather than just d and de, so that precision is increased. Also, drops whose ds is not measurable (how does this happen ) can be used. References 61 and 71-74 provide examples of this type of approach. 

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], 

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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. 

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. 

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

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). 

Shape of the liquid drop (Pendant drop method) The liquid drop forms as it flows through a tubing (Figure 2.11). At a stage just before it breaks off, the shape of the pendant drop has been used to estimate y. The drop shape is photographed and, from the diameter of the shape, y can be accurately determined. 

The pendant drop method is very useful under specific conditions ... 

The shape of a drop forming slowly at a submerged orifice is the basis for the hanging-drop (pendant-drop) method for determining inter-... 

The capillary rise method, althongh simple, is in practice, not as useful as the pendant drop method because of several experimental problems, snch as the need to determine the contact angle, non-sphericity of the meniscns and nneven bore of the capillary. 

The interfacial tension was measured by the pendant drop method. Detailed description of the apparatus and the method was given previously (3 ). ... 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Eowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usually differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

Blasco, L., Duracher, L., Forestier, J. P., Vian, L., and Marti-Mestres, G. (2006). Skin constituents as cosmetic ingredients. Part I A study of bio-mimetic monoglycerides behavior at the squalene-water interface by the pendant drop method in a static mode. J. Dispers. Sci. Technol. 27, 799-810. 

The energy associated with the interfaces between phases plays an important part in certain aspects of the migration of petroleum in underground reservoirs. For this reason there has long been interest in the interfacial tension between the phases of petroleum. The work of Swartz (71) was one of the early efforts to determine the effect of changes in pressure and composition upon the interfacial tension between the liquid and gas phases of petroleum. The methods of determining the interfacial tension between phases have been improved and the pendant drop method (16, 25) appears to be one of the more useful approaches to such measurements, particularly at elevated pressures. 

Several additional points might be noted about the use of the Bashforth-Adams tables to evaluate 7. If interpolation is necessary to arrive at the proper (3 value, then interpolation will also be necessary to determine (x/bl. . This results in some loss of accuracy. With pendant drops or sessile bubbles (i.e., negative /3 values), it is difficult to measure the maximum radius since the curvature is least along the equator of such drops (see Figure 6.15b). The Bashforth-Adams tables have been rearranged to facilitate their use for pendant drops. The interested reader will find tables adapted for pendant drops in the material by Padday (1969). The pendant drop method utilizes an equilibrium drop attached to a support and should not be confused with the drop weight method, which involves drop detachment. 

The pendant drop method has been used to measure the interfacial tension at the surface between mercury and cyclohexane solutions of stearic acid at 30 and 50°C. 

Weaver, F. Epoxy Adhesive Surface Energies Via The Pendant Drop Method, Air Force Materials Laboratory Report, AFWAL-TR-82-4179 (1982)... 

To apply the sitting or pendant drop method to measure the surface tension of a liquid the drop must be large enough so that gravitation plays a significant role. Why ... 

The pendant drop method and the sessile drop methods for surface tension appear quite different, but are similar in principle. In each case a drop is formed which either sits on a plane surface (sessile, see Figure 3.10) or hangs as a pendant drop... 

Surface Tension Measurement. The surface tension of the surfactant solution was determined by means of the Dynamic Contact Angle Tester FIBRO DAT 1100 (FIBRO Systems, Sweden) using the pendant drop method. It was also an output of the ADSA captive bubble contact angle measurements with surfactant solutions. 

Pendant drop method of measuring surface tension Drop of liquid hangs from pipette the z axis is vertical, the x axis is horizontal, and R is the (maximum) radius of the drop. To obtain / , many values of the radii S S— 0 to R) are measured at heights z (z = 0 to R) above the apex of the drop 4> is the tangent angle at the radius S. 

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