The Pendant Drop Method

The shape adopted by a drop stems from a compromise between the effect of surface tension, which favors a sphere, and gravity (or any other force field), which will cause distortions. For any given situation, analyzing the shape of the drop ought to make it possible to extract the surface tension. Several methods currently used to measure surface (or interfacial) tensions are based on this principle, such as the sessile drop method or the pendant drop method. The latter is the most commonly used.  

FIGURE 2.20. Pendant drop dangling at the end of a tube of inner radius R. 

The tally of the pressure forces in equilibrium at every point of the drop includes a Laplace term and a hydrostatic term. If C is the curvature of the drop s surface, 7 its surface tension, and p its density, the equilibrium condition reads 

The curvature can be expressed in a cylindrical coordinate system (the drop is symmetric around the z-axis).. After defining the quantities rz =  

Equations (2.49) and (2.50) can be solved numerically. The strategy is to treat the surface tension as an adjustable parameter and tweak its value until the results agree with experimental observations. The accuracy that can be achieved is satisfactory (about 1%). Furthermore, the principle dis-c issed here can readily be extended to interfacial tension measurements on the condition that the density of the liquid be replaced by the difference between the densities of the two fluids in equation (2.49). 

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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... 

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). 

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

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)... 

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. 

The pendant drop method (Fig. 4.16) measures the contact angle 6 and drop radius R to determine the surface tension for any liquid surrounded by gas, or the interfacial tension between any two liquids A drop is hung from a syringe tip in air, and the interfacial surface tension J gl is... 

The pendant drop method was applied in order to determine interfacial tension and was carried out by photographing the drop in a high pressure optical cell evaluating the contour... 

The interfacial tension of the binary system a-tocopherol/carbon dioxide was measured using the pendant drop method in the pressure range between 10 and 37 MPa at nine different temperatures 313, 333, 343, 353, 363, 373, 383, 393 and 402 K. The interfacial tension decreases with rising pressure at a constant temperature and increases with increasing temperature at a constant pressure. The interfacial tension was found to be mainly a function of the mutual solubility of the two system components and of the density of pure carbon dioxide. 

Methods used to measure interfacial tension are reviewed by Drelich, Fang, and White [ Measurement of Interfacial Tension in Fluid-Fluid Systems, in Encyclopedia of Surface and Colloid Science (Dekker, 2003), pp. 3152-3156]. Also see Megias-Alguacil, Fischer, and Windhab, Chem. Eng. Sci., 61, pp. 1386-1394 (2006). One class of methods derives intertacial tension values from measurement of the shape, contact angle, or volume of a drop suspended in a second liquid. These metho(Js include the pendant drop method (a drop of heavy liquid hangs from a vertically mounted capillary tube immersed... 

Surface tensions of both the ST copolymers in homopolymers and the PS-PTHF homopolymer blend were measured in argon by the pendant drop method described by Roe (5). 

The pendant drop method, schematically shown in Figure 4.7, was used in many studies of polymeric blends, usually with low molecular weight fractions of given polymer pairs [Wu,... 

Figure 4.7. Schematic representation of the interfacial tension measurements by the pendant drop method d is the maximum drop diameter, and d is the diameter located at the distance d from the drop apex.

Recently, the effect of a reactively formed compatibilizer on Vj2 was smdied using the pendant drop method [Garmabi and Kamal, 1998]. Their results are shown in Figure 4.16. A small quantity of MAH drastically reduced the interfacial tension coefficient, but the amount of formed graft was not determined. 

As a rule, results from the sessile drop" and maximum bubble pressure" as well as from the pendant drop" methods are preferable to results obtained from other methods for metals with very high melting points. 

DSS lowers the surface tension of liquids e.g. water and various electrolyte solutions. The effect of DSS on surface tension may be measured by a variety of methods however, the Pendant Drop Method (12) seems to be most satisfactory for measuring changes in surface tension. The effect of concentration of DSS on surface tension as determined by Pendant Drop Method is shown in Table VII. 

Open circles represent measurements using the pendant drop method. Filled circles in (c) are values determined independently by Gannon and Faber< > using the... 

Morita, A. T., Carastan, D. J., and Demarquette, N. R., Influence of drop volume on surface tension evaluated using the pendant drop method, Colloid Polym. Sci., 280,857-864 (2002). 

Surface and interfacial tensions of the two liquids were measured with a Kruss DSA 100 drop analyser system by the pendant drop method. The liquid was injected... 

The interfacial tensions of water and two ionic liquids in silicone oil are measured by the ECD method and also by the pendant drop method for comparison. As shown in Fig. 7, the measurement results by the two different methods are not significantly different and show consistent value with the literatures. The consistent measurement results by... 

Surface tension was determined via the pendant drop method using a Kruss EasyDrop. The liquid was suspended from an 1832 pm needle with equatorial and neck diameters measured for the largest stable drop. The surface tension was calculated using the relationship ... 

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