Profile, pendant drop

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 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... 

Girault, H.H.J., Schifrin, D.J., and Smith, B.D.V. 1984. The measurement of interfacial tension of pendant drops using video image profile analyzer. J. Colloid Interface Sci. 101 257-266. 

The method can be made independent of the contact angle by measuring the curvature of part of the surface. Ferguson determined the profile of a pendant drop. The formula for the sessile drop given by Worthington is ... 

Figure 5.3 Schematic representation of the profile of a pendant drop.

Measurements of interfacial tensions of polymer melts were reviewed by Wu (55), Koberstein (65), and Demarquette (66). The measurements usually need long equilibrium time because of the high viscosities of polymer melts. The measurements can be divided into two groups static methods in which interfacial tension is calculated based on the equilibrium profile of the drops and dynamic methods that study the evolution of fiber or drop profiles with time. Static methods include pendant drop method, sessile drop method, and rotating drop method. Dynamic methods include breaking thread method, imbedded fiber method, and deformed drop retraction method. 

Song, B., and Springer, J., Determination of interfacial tension from the profile of a pendant drop using computer-aided image processing 1. Theoretical, J. Colloid Interface ScL, 184, 64-76 (1996). 

The profile of a pendant drop (Figure 1) is balanced by hydrodynamic and surface equilibrium. The surface tension is given by ... 

It is also based on drop profile and therefore, similar to pendant drop. Dimensions usually measured are the distance from equator to vertex, R, and the equatorial radius DJ2. Constancy of and DJR are the criteria for equilibrium. The surface tension is given by ... 

Although the use of pendant drops is a robust method and produces interfacial tensions of acceptable accuracy, it is dependent on there being a sufficient difference in density between the two polymers. When the densities become very similar, a true axisymmetric pendant drop may not be obtainable. Figure 2.5 shows an example of a distorted drop of polybutadiene surrounded by poly(2-methyl pentadiene). In some of these cases a sessile drop usually conforms more to the desirable profile than would a pendant one. 

Methods based on the shape of static drops or bubbles include the pendant drop method and the sessile drop or bubble method. The general procedure is to make certain measurements of the dimensions or profile. It is accurate to a few tenths of a percent. 

It is usually called axisymmetric drop shape analysis.The interfacial tension and contact angles are determined from the shape of the axisymmetric menisci of both sessile and pendant drops. The employed strategy is to fit the shape of an experimental drop to the theoretical drop profile according to the Laplace equation, using surface tension as adjustable parameter. Details of the methodology together with a program to implement it can be found elsewhere. ... 

Only methods based on drop profiles are suitable for both surface and interfacial tension measurements. These include the pendant drop method [125-127], the sessile bubble or drop method [128, 129], and the rotating drop or bubble method [130, 131]. These methods are independent of the solid-Uquid contact angle but require accurate knowledge of the density difference across the interface. The demand of accurate density data becomes even greater when the two phases have similar densities. The rotating drop or bubble method is particularly suited for the determination of very low surface and interfacial tensions. 

Girault HH, Schiffrin DJ, Smith BDV (1984) The measmtanent of interfacial tension of pendant drops using a video image profile digitizer. J Colloid Interface Sci 101 257 266... 

C Naggiar [44], radii of curvature (drop profile m od) D Schwarz and Moseley [9], DuNouy ring method E Krishnaswamy and Shashidhar [17], pendant drop method. 

The surface tension of polystyrene in supercritical carbon dioxide is determined experimentally by Axisymmetric Drop Shape Analysis-Profile (ADSA-PX where a high pressure and temperature cell is designed and constructed to facilitate the formation of a pendant drop of polystyrene melt. As pressures and temperatures increase, the surface tension of polystyrene decreases. A linear relationship is found between surface tension and temperature, and between surface tension and pressure. The slope of surface tension change with temperature is dependent on pressure. 

---