A Simple and Accurate Method for Determining Low IFT from Pendant Drop Measurements
Authors: Guo B. , Schechter D.S. 
Published: December 2007

Abstract
Determination of interfacial tension (IFT) is of importance for understanding oil recovery mechanisms. Pendant drop measurement for IFT determination is an important practical technique since it permits continuous study of interfacial phenomena without mechanical interference that occurs when other techniques are used. In application of the pendant drop technique, several methods, such as shape factor method and regression method, have been developed by previous investigators for extracting IFT information from the shape of pendant drops. It is generally recognized that some of these methods are accurate but time consuming due to a great deal of numerical computations; while others are simplified and easy to use but unfortunately inaccurate in the low IFT region. It is highly desirable to develop a simple and accurate calculation method to determine low IFT from pendant drop measurements.
As IFT gets lower, pendant drops tend to be small and flat. In this case the existing methods are difficult to apply because the upper portion of the pendant drop is strongly affected by the presence of the tip and its wetting behavior. We developed a new method for IFT determination on the basis of force balance on the lower half of the pendant drop. A simple equation relating the IFT, fluid densities, and drop geometry was formulated. With known profile data of the lower half of the pendant drop, IFT can be calculated quickly from the simple equation. Like some existing methods, this new method requires high quality drop-profile data near the apex of the drop to determine the total curvature of the drop surface at the apex. Unfortunately, this high quality data is usually not available due to the nature of image digitizing. We solved this problem by digitizing rotated drop images, fitting a smoothing spline to the drop profile data, and differentiating this smoothed spline in curvature calculations.
The result of IFT determined using this new method was compared with that given by other methods for water, normal decane, decyl alcohol, 2,2,4 trimethyl pentane, normal heptane, hexadecane and toluene under ambient conditions. This comparison shows a consistency among the methods in the high IFT region (IFT &gt;10 mN/m). Using our pendant drop generating apparatus and image processing system, we tested the new method under various conditions for water, normal decane, ethane, and carbon dioxide (CO2). We found the new method more accurate than the shape factor method in the low IFT region (IFT &lt;1 mN/m). This is because the new method allows calculation of IFT from very small droplets as long as the droplets have equators developed.

Introduction
Determination of IFT is of importance in various lines of chemistry, chemical engineering and petroleum engineering. Many techniques of IFT measurement are currently used at different conditions. Detachment techniques, such as Du Nouy ring and Wilhelmy slide, rely on the condition of perfect wetting of the withdrawing surface. Capillary rise, maximum bubble pressure, and drop weight techniques require calibration with liquids of known IFT. They also involve a three phase contact which introduces systematic error. The spinning drop technique is not easy to use for high temperature and pressure applications. Although Laser-Light-Scattering has been used successfully in IFT measurement, it involves systematic error with a high pressure cell where it is not practical for a diffraction grating to be located very close to the liquid surface. The traditional pendant/sessile drop technique, which is not affected by a three phase boundary, has been revived by the advances in digital video and image analysis.
The principle of the pendant drop technique relies on measurement of the coordinates of an axisymmetric shaped drop and its match to the solution of the Laplace equation. All the information on the value of the IFT is contained in the shape assumed by the drop. Our literature survey indicates that six calculation methods have been developed to extract IFT information from the drop shape in the past six decades: P. 59