Axisymmetric Drop Shape Analysis (ADSA): An Outline.

Drop shape techniques for the measurement of interfacial tension are powerful, versatile and flexible. The shape of the drop/bubble depends on the balance between surface tension and external forces, e.g. gravity. This balance is reflected mathematically in the Laplace equation of capillarity. Axisymmetric Drop Shape Analysis (ADSA) is a commonly used drop shape technique. A streamlined version of the development of ADSA over the past several decades is presented to illustrate its validity and range of utility. Several configurations of interest will be considered and presented systematically. Shape and surface tension will be linked to a shape parameter based on proper concepts of differential geometry. The resulting shape parameter will be shown to allow determination of the range of applicability of such a drop shape method.

Laplacian drop shapes and effect of random perturbations on accuracy of surface tension measurement for different drop constellations.

Theoretical drop shapes are calculated for three drop constellations: pendant drops, constrained sessile drops, and unconstrained sessile drops. Based on total Gaussian curvature, shape parameter and critical shape parameter are discussed as a function of different drop sizes and surface tensions. The shape parameter is linked to physical parameters for every drop constellation. The as yet unavailable detailed dimensional analysis for the unconstrained sessile drop is presented. Results show that the unconstrained sessile drop shape depends on a dimensionless volume term and the contact angle. Random perturbations are introduced and the accuracy of surface tension measurement is assessed for precise and perturbed profiles of the three drop constellations. It is concluded that pendant drops are the best method for accurate surface tension measurement, followed by constrained sessile drops. The unconstrained sessile drops come last because they tend to be more spherical at low and moderate contact angles. Of course, unconstrained sessile drops are the only option if contact angles are to be measured.

Total Gaussian curvature, drop shapes and the range of applicability of drop shape techniques.

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.

Accuracy of surface tension measurement from drop shapes: the role of image analysis.

Axisymmetric Drop Shape Analysis (ADSA) has been extensively used for surface tension measurement. In essence, ADSA works by matching a theoretical profile of the drop to the extracted experimental profile, taking surface tension as an adjustable parameter. Of the three main building blocks of ADSA, i.e. edge detection, the numerical integration of the Laplace equation for generating theoretical curves and the optimization procedure, only edge detection (that extracts the drop profile line from the drop image) needs extensive study. For the purpose of this article, the numerical integration of the Laplace equation for generating theoretical curves and the optimization procedure will only require a minor effort. It is the aim of this paper to investigate how far the surface tension accuracy of drop shape techniques can be pushed by fine tuning and optimizing edge detection strategies for a given drop image. Two different aspects of edge detection are pursued here: sub-pixel resolution and pixel resolution. The effect of two sub-pixel resolution strategies, i.e. spline and sigmoid, on the accuracy of surface tension measurement is investigated. It is found that the number of pixel points in the fitting procedure of the sub-pixel resolution techniques is crucial, and its value should be determined based on the contrast of the image, i.e. the gray level difference between the drop and the background. On the pixel resolution side, two suitable and reliable edge detectors, i.e. Canny and SUSAN, are explored, and the effect of user-specified parameters of the edge detector on the accuracy of surface tension measurement is scrutinized. Based on the contrast of the image, an optimum value of the user-specified parameter of the edge detector, SUSAN, is suggested. Overall, an accuracy of 0.01mJ/m(2) is achievable for the surface tension determination by careful fine tuning of edge detection algorithms.

Effect of surfactant concentration, compression ratio and compression rate on the surface activity and dynamic properties of a lung surfactant.

This paper reports dynamic surface tension experiments of a lung surfactant preparation, BLES, for a wide range of concentrations, compression ratios and compression rates. These experiments were performed using Axisymmetric Drop Shape Analysis-Constrained Sessile Drop (ADSA-CSD). The main purpose of the paper is to interpret the results in terms of physical parameters using the recently developed Compression-Relaxation Model (CRM). In the past, only the minimum surface tension was used generally for the characterization of lung surfactant films; however, this minimum value is not a physical parameter and depends on the compression protocol. CRM is based on the assumption that the dynamic surface tension response is governed by surface elasticities, adsorption and desorption of components of the lung surfactant. The ability of CRM to fit the surface tension response closely for a wide variety of parameters (compression ratio, compression rate and surfactant concentration) and produce sensible values for the elastic and kinetic parameters supports the validity of CRM.

Range of validity of drop shape techniques for surface tension measurement.

Drop shape techniques are widely used for surface tension measurement. As the shape becomes close to spherical, the performance of drop shape techniques deteriorates. A quantitative criterion called shape parameter was previously introduced to quantify the meaning of "well-deformed" drops and "close to spherical" drops. In this paper, a modified definition of the shape parameter that does not depend on the radius of curvature at the drop apex is proposed. Such definition is applicable to different constellations of pendant and sessile drops/bubbles. Dimensional analysis is used to describe similarity in constrained sessile drop shapes and to express the problem using appropriate dimensionless groups. The proposed shape parameter is found to depend only on two dimensionless groups: the dimensionless volume (drop volume normalized by the cube of the holder radius) and the Bond number (using the drop holder's radius as the length scale). A critical shape parameter (minimum value of the shape parameter that guarantees a specified accuracy) is shown to depend only on Bond number. A set of experiments were performed with pure liquids to illustrate the change of the critical shape parameter with the Bond number.

A double injection ADSA-CSD methodology for lung surfactant inhibition and reversal studies.

This paper presents a continuation of the development of a drop shape method for film studies, ADSA-CSD (Axisymmetric Drop Shape Analysis-Constrained Sessile Drop). ADSA-CSD has certain advantages over conventional methods. The development presented here allows complete exchange of the subphase of a spread or adsorbed film. This feature allows certain studies relevant to lung surfactant research that cannot be readily performed by other means. The key feature of the design is a second capillary into the bulk of the drop to facilitate addition or removal of a secondary liquid. The development will be illustrated through studies concerning lung surfactant inhibition. After forming a sessile drop of a basic lung surfactant preparation, the bulk phase can be removed and exchanged for one containing different inhibitors. Such studies mimic the leakage of plasma and blood proteins into the alveolar spaces altering the surface activity of lung surfactant in a phenomenon called surfactant inhibition. The resistance of the lung surfactant to specific inhibitors can be readily evaluated using the method. The new method is also useful for surfactant reversal studies, i.e. the ability to restore the normal surface activity of an inhibited lung surfactant film by using special additives. Results show a distinctive difference between the inhibition when an inhibitor is mixed with and when it is injected under a preformed surfactant film. None of the inhibitors studied (serum, albumin, fibrinogen, and cholesterol) were able to penetrate a preexisting film formed by the basic preparation (BLES and protasan), while all of them can alter the surface activity of such preparation when mixed with the preparation. Preliminary results show that reversal of serum inhibition can be easily achieved and evaluated using the modified methodology.

Mixed DPPC/DPPG monolayers at very high film compression.

A drop shape technique using a constrained sessile drop constellation (ADSA-CSD) has been introduced as a superior technique for studying spread films specially at high collapse pressures [Saad et al. Langmuir 2008, 24, 10843-10850]. It has been shown that ADSA-CSD has certain advantages including the need only for small quantities of liquid and insoluble surfactants, the ability to measure very low surface tension values, easier deposition procedure, and leak-proof design. Here, this technique was applied to investigate mixed DPPC/DPPG monolayers to characterize the role of such molecules in maintaining stable film properties and surface activity of lung surfactant preparations. Results of compression isotherms were obtained for different DPPC/DPPG mixture ratios: 90/10, 80/20, 70/30, 60/40, and 50/50 in addition to pure DPPC and pure DPPG at room temperature of 24 degrees C. The ultimate collapse pressure of DPPC/DPPG mixtures was found to be 70.5 mJ/m2 (similar to pure DPPC) for the cases of low DPPG content (up to 20%). Increasing the DPPG content in the mixture (up to 40%) caused a slight decrease in the ultimate collapse pressure. However, further increase of DPPG in the mixture (50% or more) caused a sharp decrease in the ultimate collapse pressure to a value of 59.9 mJ/m2 (similar to pure DPPG). The change in film elasticity was also tracked for the range of mixture ratios studied. The physical reasons for such changes and the interaction between DPPC and DPPG molecules are discussed. The results also show a change in the film hysteresis upon successive compression and expansion cycles for different mixture ratios.

Axisymmetric drop shape analysis for estimating the surface tension of cell aggregates by centrifugation.

Biological tissues behave in certain respects like liquids. Consequently, the surface tension concept can be used to explain aspects of the in vitro and in vivo behavior of multicellular aggregates. Unfortunately, conventional methods of surface tension measurement cannot be readily applied to small cell aggregates. This difficulty can be overcome by an experimentally straightforward method consisting of centrifugation followed by axisymmetric drop shape analysis (ADSA). Since the aggregates typically show roughness, standard ADSA cannot be applied and we introduce a novel numerical method called ADSA-IP (ADSA for imperfect profile) for this purpose. To examine the new methodology, embryonic tissues from the gastrula of the frog, Xenopus laevis, deformed in the centrifuge are used. It is confirmed that surface tension measurements are independent of centrifugal force and aggregate size. Surface tension is measured for ectodermal cells in four sample batches, and varies between 1.1 and 7.7 mJ/m2. Surface tension is also measured for aggregates of cells expressing cytoplasmically truncated EP/C-cadherin, and is approximately half as large. In parallel, such aggregates show a reduction in convergent extension-driven elongation after activin treatment, reflecting diminished intercellular cohesion.

Axisymmetric drop shape analysis-constrained sessile drop (ADSA-CSD): a film balance technique for high collapse pressures.

Collapse pressure of insoluble monolayers is a property determined from surface pressure/area isotherms. Such isotherms are commonly measured by a Langmuir film balance or a drop shape technique using a pendant drop constellation (ADSA-PD). Here, a different embodiment of a drop shape analysis, called axisymmetric drop shape analysis-constrained sessile drop (ADSA-CSD) is used as a film balance. It is shown that ADSA-CSD has certain advantages over conventional methods. The ability to measure very low surface tension values (e.g., <2 mJ/m2), an easier deposition procedure than in a pendant drop setup, and leak-proof design make the constrained sessile drop constellation a better choice than the pendant drop constellation in many situations. Results of compression isotherms are obtained on three different monolayers: octadecanol, dipalmitoyl-phosphatidyl-choline (DPPC), and dipalmitoyl-phosphatidyl-glycerol (DPPG). The collapse pressures are found to be reproducible and in agreement with previous methods. For example, the collapse pressure of DPPC is found to be 70.2 mJ/m2. Such values are not achievable with a pendant drop. The collapse pressure of octadecanol is found to be 61.3 mJ/m2, while that of DPPG is 59.0 mJ/m2. The physical reasons for these differences are discussed. The results also show a distinctive difference between the onset of collapse and the ultimate collapse pressure (ultimate strength) of these films. ADSA-CSD allows detailed study of this collapse region.