Journal of Colloid and Interface Science 330 (2009) 501–504 Contents lists available at ScienceDirect Journal of Colloid and Interface Science www.elsevier.com/locate/jcis Short Communication The importance of aspect ratio in proﬁle analysis tensiometry Stoyan I. Karakashev, Anh V. Nguyen ∗ Division of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia article info abstract Article history: Received 20 July 2008 Accepted 2 November 2008 Available online 20 November 2008 Keywords: Proﬁle analysis tensiometry Surface tension Surface rheology The latest developments in proﬁle analysis tensiometry (PAT) for determining surface tension and interfacial viscoelastic parameters involve the determination of a digital interface proﬁle and its best ﬁt with the Young–Laplace equation. In this short communication, we show that the results for surface tension and other interfacial parameters determined by PAT are extremely sensitive to the (aspect) ratio of length to width of a pixel. Fine calibration (to ﬁve decimal digits) for the aspect ratio required to obtain physically consistent results is not always achieved with conventional numerical procedures due to nanometer resolution limit of optical imaging devices but can be manually adjusted using the known surface tension of pure water and/or surfactant solutions at reference temperature.  2008 Elsevier Inc. All rights reserved. 1. Introduction Proﬁle analysis tensiometry (PAT) is a well-known method for determining surface and interfacial tension from the shape of a sessile drop, pendant drop or captive bubble [1]. It involves the experimental determination of interface proﬁles and comparison of the proﬁles with the Young–Laplace equation which describes the balance between surface tension and gravitational forces on the ﬂuid phases and the interface. The popularity of this method is due to a number of advantages over other methods such as the Wilhelmy plate method, the Du Noüy ring method, the method of Brown–Harkins and the maximum bubble pressure method [1]. The early experimental setups (up to the 1980s) used cameras for taking photographs of the bubbles or drops needed for determining the interface proﬁles. During the last 20 years, the experimental setups have become more sophisticated with the use of digital cameras and computers for the determination of interface proﬁles from the digital images [2,3], and the determination of surface tension by the best ﬁt of the experimental proﬁles with the nu- merical solution of the Young–Laplace equation [4–8]. A recent development includes oscillating the drop or bubble volume at low frequency [9] for determining the surface viscoelastic parameters of surfactant adsorption layers [10–14] and cyclic dynamic surface tension [15]. However, there are still a number of hidden pitfalls associated with proﬁle analysis tensiometry. For example, there is evidence in the literature [16–19] showing that the surface tension obtained by the tensiometer depends on the volume of the bubble or drop. The larger the volume, the weaker is the dependence. It * Corresponding author. E-mail address: anh.nguyen@eng.uq.edu.au (A.V. Nguyen). has been explained that this artifact volume dependence of surface tension is due to both the insuﬃcient precision in determining the bubble proﬁle [16] and optical anisotropy [18] caused by the liquid phase. The rectangular pixel digital format of bubble images was used to calibrate the optical anisotropy [2,19]. The standard cali- bration consists of acquiring the image of a solid sphere with a known diameter or a calibration grid and comparing the two di- mensions of the images to determine the degree of anisotropy for calibration [2,19]. The width and the length of one pixel are cal- culated with “one picometer” precision by a numerical ﬁtting of circumference to the image of the sphere proﬁle [19]. However, a small change in the length or the width of one pixel by, for ex- ample, one nanometer can cause a signiﬁcant change in distorted bubble images. Evidently, one nanometer resolution is beyond the limit of any optical imaging devices and the aspect ratio calibration crucial for proﬁle analysis tensiometry can be imprecise due to the optical limit of the shape detection which also depends upon the illumination, the focus, the image resolution and the shape detec- tion procedure. All of these factors make the whole procedure of calibration for optical anisotropy diﬃcult and uncertain. The uncertainty caused by optical anisotropy is not very cru- cial if only the surface tension at a constant volume is measured due to fact that the tensiometer can be calibrated against a ref- erence liquid sample (e.g., pure water) of known surface tension. The aim of this communication is ﬁrstly to show that the uncer- tainty of the routine calibration procedures becomes crucial in the cyclic dynamic measurements, in which the bubble or drop vol- ume varies with time. Secondly, in this communication we suggest a new yet simple method for calibrating the aspect ratio by ﬁne manual adjustment of the ratio until the reference surface tension constant over a range of bubble volume is obtained. 0021-9797/$ – see front matter  2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.11.034