A high-accuracy polynomial fitting approach to determine contact angles

A liquid metal dropper for experiments on the wettability of liquid metals on plasma facing components

A liquid metal dropper has been developed as a part of the Ion-Gas-Neutral Interactions with Surfaces 2 (IGNIS-2) facility at The Pennsylvania State University. The dropper has the capability of directly applying drops to candidate plasma facing materials for nuclear fusion reactors to enable measurements of their liquid metal wetting properties. The results presented here are specific to the use of lithium in the dropper. This paper discusses the design choices of the liquid metal dropper and its chamber, including the heating and temperature control and the dropper's motorized operation. Lithium drops of masses ranging from 0.05 g up to 0.13 g, equivalent to drop diameters between 5.6 mm to 1 cm, have been consistently dispensed by the dropper. A new algorithm is developed and used to automate the analysis of the contact angle between the liquid drops and substrate material for efficient analysis of video data recorded to study the wetting properties of candidate plasma-facing components.

Machine learning enabled orthogonal camera goniometry for accurate and robust contact angle measurements

Characterization of surface wettability plays an integral role in physical, chemical, and biological processes. However, the conventional fitting algorithms are not suitable for accurate estimation of wetting properties, especially on hydrophilic surfaces, due to optical distortions triggered by changes in the focal length of the moving drops. Therefore, here we present an original setup coupled with Convolutional Neural Networks (CNN) for estimation of Contact Angle (CA). The developed algorithm is trained on 3375 ground truth images (at different front-lit illuminations), less sensitive to the edges of the drops, and retains its stability for images that are synthetically blurred with higher Gaussian Blurring (GB) values (GB: 0-22) if compared to existing goniometers (GB: 0-12). Besides, the proposed technique can precisely analyze drops of various colors and chemistries on different surfaces. Finally, our automated orthogonal camera goniometer has a significantly lower average standard deviation (6.7° vs. 14.6°) and coefficient of variation (14.9 vs. 29.2%) than the existing techniques and enables wettability assessment of non-spherical drops on heterogeneous surfaces.

Deep Learning to Analyze Sliding Drops

State-of-the-art contact angle measurements usually involve image analysis of sessile drops. The drops are symmetric and images can be taken at high resolution. The analysis of videos of drops sliding down a tilted plate is hampered due to the low resolution of the cutout area where the drop is visible. The challenge is to analyze all video images automatically, while the drops are not symmetric anymore and contact angles change while sliding down the tilted plate. To increase the accuracy of contact angles, we present a 4-segment super-resolution optimized-fitting (4S-SROF) method. We developed a deep learning-based super-resolution model with an upscale ratio of 3; i.e., the trained model is able to enlarge drop images 9 times accurately (PSNR = 36.39). In addition, a systematic experiment using synthetic images was conducted to determine the best parameters for polynomial fitting of contact angles. Our method improved the accuracy by 21% for contact angles lower than 90° and by 33% for contact angles higher than 90°.

Assessment of the Antibiofilm Performance of Chitosan-Based Surfaces in Marine Environments

Marine biofouling is a natural process often associated with biofilm formation on submerged surfaces, creating a massive economic and ecological burden. Although several antifouling paints have been used to prevent biofouling, growing ecological concerns emphasize the need to develop new and environmentally friendly antifouling approaches such as bio-based coatings. Chitosan (CS) is a natural polymer that has been widely used due to its outstanding biological properties, including non-toxicity and antimicrobial activity. This work aims to produce and characterize poly (lactic acid) (PLA)-CS surfaces with CS of different molecular weight (Mw) at different concentrations for application in marine paints. Loligo opalescens pens, a waste from the fishery industry, were used as a CS source. The antimicrobial activity of the CS and CS-functionalized surfaces was assessed against Cobetia marina, a model proteobacterium for marine biofouling. Results demonstrate that CS targets the bacterial cell membrane, and PLA-CS surfaces were able to reduce the number of culturable cells up to 68% compared to control, with this activity dependent on CS Mw. The antifouling performance was corroborated by Optical Coherence Tomography since PLA-CS surfaces reduced the biofilm thickness by up to 36%, as well as the percentage and size of biofilm empty spaces. Overall, CS coatings showed to be a promising approach to reducing biofouling in marine environments mimicked in this work, contributing to the valorization of fishing waste and encouraging further research on this topic.

Sessile Drop Method: Critical Analysis and Optimization for Measuring the Contact Angle of an Ion-Exchange Membrane Surface

The contact angle between a membrane surface and a waterdrop lying on its surface provides important information about the hydrophilicity/hydrophobicity of the membrane. This method is well-developed for solid non-swelling materials. However, ion-exchange membranes (IEMs) are gel-like solids that swell in liquids. When an IEM is exposed to air, its degree of swelling changes rapidly, making it difficult to measure the contact angle. In this paper, we examine the known experience of measuring contact angles and suggest a simple equipment that allows the membrane to remain swollen during measurements. An optimized protocol makes it possible to obtain reliable and reproducible results. Measuring parameters such as drop size, water dosing speed and others are optimized. Contact angle measurements are shown for a large number of commercial membranes. These data are supplemented with values from other surface characteristics from optical and profilometric measurements.

A Modified Contact Angle Measurement Process to Suppress Oil Drop Spreading and Improve Precision

Static contact angle measurement is a widely applied method for wettability assessment. Despite its convenience, it suffers from errors induced by contact angle hysteresis, material heterogeneity, and other factors. This paper discusses the oil drop spreading phenomenon that was frequently observed during contact angle measurements. Experimental tests showed that this phenomenon is closely related to surfactants in the surrounding phase, the remaining oil on the rock surface, and oil inside the surrounding phase. A modified contact angle measurement process was proposed. In the modified method, deionized water was used as the surrounding phase, and a rock surface cleaning step was added. Subsequent measurements showed a very low chance of oil drop spreading and improved precision. A further comparison study showed that, when the surrounding phase was deionized water, the measured contact angle values tended to be closer to intermediate-wet conditions compared to the values measured in clean surfactant solutions. This difference became more significant when the surface was strongly water-wet or strongly oil-wet. As a result, the developed process has two prerequisites: that the in-situ contact angle values inside surfactant solutions are not required, and that the wettability alteration induced by the surfactant solution is irreversible.

Contact angle measurements: From existing methods to an open-source tool

Contact angle measurement is an effective way to investigate solid surface properties. The introduction of low-cost digital cameras, as well as software and libraries for image analysis, has made contact angle measurement potentially accessible to every laboratory. In this review, we provide a comparison of the main methods developed to evaluate contact angle from digital images, including the so-called Young-Laplace method, the circle and polynomial fittings, as well as the mask method. All methods have been implemented and compared analyzing virtual and real drop images in an open-source software, Dropen, developed as an app in MATLAB environment. The code enables single image analysis evaluation, for the robust automatic identification of the contact points and contact angle evaluation, with the goal of minimizing user inputs, automatizing the process and facilitating measurements for all users, from less experienced to advanced wetting experts. Dropen and its code are made available at BOA, the Bicocca Open Access public repository, for use and further development.

Development of Chitosan-Based Surfaces to Prevent Single- and Dual-Species Biofilms of Staphylococcus aureus and Pseudomonas aeruginosa

Implantable medical devices (IMDs) are susceptible to microbial adhesion and biofilm formation, which lead to several clinical complications, including the occurrence of implant-associated infections. Polylactic acid (PLA) and its composites are currently used for the construction of IMDs. In addition, chitosan (CS) is a natural polymer that has been widely used in the medical field due to its antimicrobial and antibiofilm properties, which can be dependent on molecular weight (Mw). The present study aims to evaluate the performance of CS-based surfaces of different Mw to inhibit bacterial biofilm formation. For this purpose, CS-based surfaces were produced by dip-coating and the presence of CS and its derivatives onto PLA films, as well surface homogeneity were confirmed by contact angle measurements, Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). The antimicrobial activity of the functionalized surfaces was evaluated against single- and dual-species biofilms of Staphylococcus aureus and Pseudomonas aeruginosa. Chitosan-based surfaces were able to inhibit the development of single- and dual-species biofilms by reducing the number of total, viable, culturable, and viable but nonculturable cells up to 79%, 90%, 81%, and 96%, respectively, being their activity dependent on chitosan Mw. The effect of CS-based surfaces on the inhibition of biofilm formation was corroborated by biofilm structure analysis using confocal laser scanning microscopy (CLSM), which revealed a decrease in the biovolume and thickness of the biofilm formed on CS-based surfaces compared to PLA. Overall, these results support the potential of low Mw CS for coating polymeric devices such as IMDs where the two bacteria tested are common colonizers and reduce their biofilm formation.

Temperature dependence of the contact angle of water: A review of research progress, theoretical understanding, and implications for boiling heat transfer

Contact angle, a quantitative measure of macroscopic surface wettability, plays an important role in understanding liquid-vapor heterogeneous phase change phenomena, e.g., boiling heat transfer. The contact angles of water at elevated temperatures are of particular interest for understanding of wettability-regulated boiling heat transfer in steam-based power generation. From a more theoretical perspective, the temperature dependence of contact angle of water is also essential to estimation of several key surface thermodynamic properties, such as the solid surface tension, the surface entropy, and the heats of immersion and adsorption. Here, a comprehensive review of historical efforts in measuring the contact angles of water over a wide temperature range on a variety of solids, not limited to metallic surfaces, is presented. As suggested by the literature data, the temperature dependence of contact angle of water may be classified into three regimes: (a) low temperatures below the saturation point (i.e., 100 °C at atmospheric pressure), (b) medium temperatures up to ~170 °C, and (c) high temperatures up to 300 °C at pressurized conditions. A slightly-decreasing or nearly-invariant trend of the contact angles of water on both non-metallic and metallic surfaces was reported for the low-temperature regime. In contrast, a steeper linear decline in water contact angle was demonstrated at temperatures above 100 °C. The few experimental data available on several metallic surfaces showed that the contact angle of water either again becomes nearly temperature-independent or further decreases with temperature above 210 °C. A theoretical understanding of the temperature dependence is given based on surface thermodynamic analysis, although the exact molecular mechanisms underlying these experimental observations remain unclear. Consequently, the theoretical model for predicting the variation of the contact angle of water with temperature is not well-developed. As the critical point of water (374 °C and 22.1 MPa) is approached, the surface tension, and hence the contact angle, should become vanishingly small. However, this theoretical expectation has not yet been verified due to the lack of experimental data at such high temperatures/pressures. Finally, future research directions are identified, including a systematic exploration of the contact angle at near-critical temperatures, the effects of surface oxidation, corrosion, and deposition on contact angle during operation of boilers and reactors, and the particular effect of irradiation on contact angle in nuclear reactor applications.

Robust Contact Angle Determination for Needle-in-Drop Type Measurements

One of the main approaches for contact angle determination using sessile drops with a missing apex (e.g., because of the presence of the needle tip) is the polynomial drop-profile fitting method. The major disadvantage of this fitting procedure is that the derived contact angle is highly sensitive to the polynomial order and the number of pixels involved in the actual fit. In the present work, an easily implementable method is introduced to effectively tackle these drawbacks. Instead of fitting the drop-profile itself, the polynomial fitting is applied to the difference between the drop profile and the circumcircle, independently for both sides of the drop. The derivative value of this difference at the contact point is used to correct the slope obtained analytically from the circumcircle. It is shown that this approach allows the robust determination of the contact angle with high (≤0.6°) accuracy in a straightforward manner, and the results are not affected by the actual contact angle, drop volume, or the resolution of the captured image. Validation of this new approach is also given in the contact angle range of 20°-150° by comparing the results to the values calculated by the Young-Laplace fit.

Uncertainties in contact angle goniometry

The most widely used method to quantify the wetting properties of surfaces is by measuring contact angles. Even though contact angle goniometry is a powerful technique for characterizing wetting properties, it is not accurate for very hydrophobic surfaces. As the technique relies on image processing, it has inherent errors due to optical limitations, especially near the three-phase contact line. This leads to uncertainties in the positioning of the baseline, which can cause large errors in the measured contact angles. In this paper, we systematically evaluate these errors both theoretically and experimentally, focusing on the importance of image resolution. For ∼9 microliter droplet, displacement of the baseline by a single pixel leads to errors of approximately ±0.5° to ±1° for contact angles up to 150°, and errors increase rapidly in the superhydrophobic regime, up to ±8°. The error in the contact angle can be slightly reduced by increasing the image resolution, but cannot be eliminated entirely.

Contact line stick-slip motion and meniscus evolution on micrometer-size wavy fibres

HYPOTHESIS

The architecture of complex-shaped fibres affects the motion of the contact line and the evolution of its associated menisci when a fibre is immersed into a liquid. Understanding and predicting the motion of the contact line is critical in the design of complex-shaped fibres for many engineering applications as well as for surface science. While wetting on classic circular cylinders has been well studied, singularities during the wetting process of complex-shaped fibres are not yet well understood.

EXPERIMENTS

The dynamic wetting behaviour of axisymmetric sinus-shaped fibres immersed vertically in a liquid volume was investigated. Fibres were 3D-printed down to micrometre dimensions, and the Wilhelmy method was used in parallel with meniscus shape analysis. Moreover, a quasi-static theoretical model predicting the contact line movement and free energy of the system evolution on these fibres is also proposed.

FINDINGS

The observation of liquid advancing and receding fronts highlighted a stick-slip motion of the meniscus depending on both the fibre surface curvature and its intrinsic wettability. The model predicts that the behaviour of the seemingly pinned and then jumping contact line, with associated changes in apparent contact angles, can be explained by the interplay between a constant local contact angle and the movement of the bulk liquid, leading to the storage of energy which is suddenly released when the contact line passes a given point of fibre curvature. Besides, acceleration/deceleration events that take place before and after the jumps are experimentally observed in good agreement with the model.

Spontaneous Displacement of High Viscosity Micrometer Size Oil Droplets from a Curved Solid in Aqueous Solutions

Spontaneous displacement of high viscosity (∼10³ Pa·s) micrometer size oil droplets from a curved solid in aqueous solutions was investigated. For high viscosity oils, the dynamic droplet shape was found to deviate significantly from a spherical cap shape due to the considerable viscous force in the oil phase. The displacement dynamics of high viscosity droplets were analyzed using molecular kinetic and hydrodynamic models. The molecular kinetic model was found to describe the dynamic displacement well for the droplets of small departure from the spherical cap shape, while the hydrodynamic model is more applicable to the droplets of higher three-phase contact line displacement velocities and hence larger deviation of the droplets from the spherical cap shape.

Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [ Sauer , E. ; Gross , J. Ind. Eng. Chem. Res. 56 , 2017 , 4119 - 4135 ] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77°.

Contact angle measurement with a smartphone

In this study, a smartphone-based contact angle measurement instrument was developed. Compared with the traditional measurement instruments, this instrument has the advantage of simplicity, compact size, and portability. An automatic contact point detection algorithm was developed to allow the instrument to correctly detect the drop contact points. Two different contact angle calculation methods, Young-Laplace and polynomial fitting methods, were implemented in this instrument. The performance of this instrument was tested first with ideal synthetic drop profiles. It was shown that the accuracy of the new system with ideal synthetic drop profiles can reach 0.01% with both Young-Laplace and polynomial fitting methods. Conducting experiments to measure both static and dynamic (advancing and receding) contact angles with the developed instrument, we found that the smartphone-based instrument can provide accurate and practical measurement results as the traditional commercial instruments. The successful demonstration of use of a smartphone (mobile phone) to conduct contact angle measurement is a significant advancement in the field as it breaks the dominate mold of use of a computer and a bench bound setup for such systems since their appearance in 1980s.

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.

Ultra-low voltage electrowetting using graphite surfaces

The control of wetting behaviour underpins a variety of important applications from lubrication to microdroplet manipulation. Electrowetting is a powerful method to achieve external wetting control, by exploiting the potential-dependence of the liquid contact angle with respect to a solid substrate. Addition of a dielectric film to the surface of the substrate, which insulates the electrode from the liquid thereby suppressing electrolysis, has led to technological advances such as variable focal-length liquid lenses, electronic paper and the actuation of droplets in lab-on-a-chip devices. The presence of the dielectric, however, necessitates the use of large bias voltages (frequently in the 10-100 V range). Here we describe a simple, dielectric-free approach to electrowetting using the basal plane of graphite as the conducting substrate: unprecedented changes in contact angle for ultra-low voltages are seen below the electrolysis threshold (50° with 1 V for a droplet in air, and 100° with 1.5 V for a droplet immersed in hexadecane), which are shown to be reproducible, stable over 100 s of cycles and free of hysteresis. Our results dispel conventional wisdom that reversible, hysteresis-free electrowetting can only be achieved on solid substrates with the use of a dielectric. This work paves the way for the development of a new generation of efficient electrowetting devices using advanced materials such as graphene and monolayer MoS₂.

A highly accurate dynamic contact angle algorithm for drops on inclined surface based on ellipse-fitting

To improve the accuracy in the calculation of dynamic contact angle for drops on the inclined surface, a significant number of numerical drop profiles on the inclined surface with different inclination angles, drop volumes, and contact angles are generated based on the finite difference method, a least-squares ellipse-fitting algorithm is used to calculate the dynamic contact angle. The influences of the above three factors are systematically investigated. The results reveal that the dynamic contact angle errors, including the errors of the left and right contact angles, evaluated by the ellipse-fitting algorithm tend to increase with inclination angle/drop volume/contact angle. If the drop volume and the solid substrate are fixed, the errors of the left and right contact angles increase with inclination angle. After performing a tremendous amount of computation, the critical dimensionless drop volumes corresponding to the critical contact angle error are obtained. Based on the values of the critical volumes, a highly accurate dynamic contact angle algorithm is proposed and fully validated. Within nearly the whole hydrophobicity range, it can decrease the dynamic contact angle error in the inclined plane method to less than a certain value even for different types of liquids.

An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis

In this study, an error analysis is performed to study real water drop images and the corresponding numerically generated water drop profiles for three widely used static contact angle algorithms: the circle- and ellipse-fitting algorithms and the axisymmetric drop shape analysis-profile (ADSA-P) algorithm. The results demonstrate the accuracy of the numerically generated drop profiles based on the Laplace equation. A significant number of water drop profiles with different volumes, contact angles, and noise levels are generated, and the influences of the three factors on the accuracies of the three algorithms are systematically investigated. The results reveal that the above-mentioned three algorithms are complementary. In fact, the circle- and ellipse-fitting algorithms show low errors and are highly resistant to noise for water drops with small/medium volumes and contact angles, while for water drop with large volumes and contact angles just the ADSA-P algorithm can meet accuracy requirement. However, this algorithm introduces significant errors in the case of small volumes and contact angles because of its high sensitivity to noise. The critical water drop volumes of the circle- and ellipse-fitting algorithms corresponding to a certain contact angle error are obtained through a significant amount of computation. To improve the precision of the static contact angle measurement, a more accurate algorithm based on a combination of the three algorithms is proposed. Following a systematic investigation, the algorithm selection rule is described in detail, while maintaining the advantages of the three algorithms and overcoming their deficiencies. In general, static contact angles over the entire hydrophobicity range can be accurately evaluated using the proposed algorithm. The ease of erroneous judgment in static contact angle measurements is avoided. The proposed algorithm is validated by a static contact angle evaluation of real and numerically generated water drop images with different hydrophobicity values and volumes.

Methods and preliminary measurement results of liquid Li wettability

A test of lithium wettability was performed in high vacuum (< 3 × 10(-4) Pa). High magnification images of Li droplets on stainless steel substrates were produced and processed using the MATLAB(®) program to obtain clear image edge points. In contrast to the more standard "θ/2" or polynomial fitting methods, ellipse fitting of the complete Li droplet shape resulted in reliable contact angle measurements over a wide range of contact angles. Using the ellipse fitting method, it was observed that the contact angle of a liquid Li droplet on a stainless steel substrate gradually decreased with increasing substrate temperature. The critical wetting temperature of liquid Li on stainless steel was observed to be about 290 °C.

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.

A robust polynomial fitting approach for contact angle measurements

Polynomial fitting to drop profile offers an alternative to well-established drop shape techniques for contact angle measurements from sessile drops without a need for liquid physical properties. Here, we evaluate the accuracy of contact angles resulting from fitting polynomials of various orders to drop profiles in a Cartesian coordinate system, over a wide range of contact angles. We develop a differentiator mask to automatically find a range of required number of pixels from a drop profile over which a stable contact angle is obtained. The polynomial order that results in the longest stable regime and returns the lowest standard error and the highest correlation coefficient is selected to determine drop contact angles. We find that, unlike previous reports, a single polynomial order cannot be used to accurately estimate a wide range of contact angles and that a larger order polynomial is needed for drops with larger contact angles. Our method returns contact angles with an accuracy of <0.4° for solid-liquid systems with θ < ~60°. This compares well with the axisymmetric drop shape analysis-profile (ADSA-P) methodology results. Above about 60°, we observe significant deviations from ADSA-P results, most likely because a polynomial cannot trace the profile of drops with close-to-vertical and vertical segments. To overcome this limitation, we implement a new polynomial fitting scheme by transforming drop profiles into polar coordinate system. This eliminates the well-known problem with high curvature drops and enables estimating contact angles in a wide range with a fourth-order polynomial. We show that this approach returns dynamic contact angles with less than 0.7° error as compared to ADSA-P, for the solid-liquid systems tested. This new approach is a powerful alternative to drop shape techniques for estimating contact angles of drops regardless of drop symmetry and without a need for liquid properties.

Pendant bubble method for an accurate characterization of superhydrophobic surfaces

The commonly used sessile drop method for measuring contact angles and surface tension suffers from errors on superhydrophobic surfaces. This occurs from unavoidable experimental error in determining the vertical location of the liquid-solid-vapor interface due to a camera's finite pixel resolution, thereby necessitating the development and application of subpixel algorithms. We demonstrate here the advantage of a pendant bubble in decreasing the resulting error prior to the application of additional algorithms. For sessile drops to attain an equivalent accuracy, the pixel count would have to be increased by 2 orders of magnitude.

Methodology for calculating the volume of condensate droplets on topographically modified, microgrooved surfaces

Liquid droplets on micropatterned surfaces consisting of parallel grooves tens of micrometers in width and depth are considered, and a method for calculating the droplet volume on these surfaces is presented. This model, which utilizes the elongated and parallel-sided nature of droplets condensed on these microgrooved surfaces, requires inputs from two droplet images at ϕ = 0° and ϕ = 90°--namely, the droplet major axis, minor axis, height, and two contact angles. In this method, a circular cross-sectional area is extruded the length of the droplet where the chord of the extruded circle is fixed by the width of the droplet. The maximum apparent contact angle is assumed to occur along the side of the droplet because of the surface energy barrier to wetting imposed by the grooves--a behavior that was observed experimentally. When applied to water droplets condensed onto a microgrooved aluminum surface, this method was shown to calculate the actual droplet volume to within 10% for 88% of the droplets analyzed. This method is useful for estimating the volume of retained droplets on topographically modified, anisotropic surfaces where both heat and mass transfer occur and the surface microchannels are aligned parallel to gravity to assist in condensate drainage.

Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.

In situ characterization of microdroplet interfacial properties in digital microfluidic systems

Real-time characterization of digital microfluidic lab-on-a-chip devices is important for biological and chemical applications in which the properties of the microdroplet are time variant. In this paper, a method for in situ characterization of microdroplet interfacial properties is introduced. The proposed characterization method relies on two submodules, namely the contact angle and capacitance sampling submodules, in a digital microfluidic system. In the contact angle measurement submodule, the microdroplet profile is acquired and an accurate contact angle is determined. In the capacitance sampling submodule, the capacitance of the system is measured by means of an activation voltage signal. For verification purposes, the results obtained from the proposed method are compared to the Lippmann-Young equation. The results are in excellent agreement with previously reported values. Finally, the proposed submodules are used to characterize the interfacial properties of a microdroplet containing an aqueous solution of bovine serum albumin (BSA) in which adsorption is a predominant effect. The results show the temporal behaviour of both microdroplet interfacial properties and dielectric characteristics.

Methodology for high accuracy contact angle measurement

A new version of axisymmetric drop shape analysis (ADSA) called ADSA-NA (ADSA-no apex) was developed for measuring interfacial properties for drop configurations without an apex. ADSA-NA facilitates contact angle measurements on drops with a capillary protruding into the drop. Thus a much simpler experimental setup, not involving formation of a complete drop from below through a hole in the test surface, may be used. The contact angles of long-chained alkanes on a commercial fluoropolymer, Teflon AF 1600, were measured using the new method. A new numerical scheme was incorporated into the image processing to improve the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. The images acquired in the experiments were also analyzed by a different drop shape technique called theoretical image fitting analysis-axisymmetric interfaces (TIFA-AI). The results were compared with literature values obtained by means of the standard ADSA for sessile drops with the apex. Comparison of the results from ADSA-NA with those from TIFA-AI and ADSA reveals that, with different numerical strategies and experimental setups, contact angles can be measured with an accuracy of less than 0.2 degrees. Contact angles and surface tensions measured from drops with no apex, i.e., by means of ADSA-NA and TIFA-AI, were considerably less scattered than those from complete drops with apex. ADSA-NA was also used to explore sources of improvement in contact angle resolution. It was found that using an accurate value of surface tension as an input enhances the accuracy of contact angle measurements.

General methodology for evaluating the adhesion force of drops and bubbles on solid surfaces

The shortcomings of the current formulation for calculating the adhesion force for drops and bubbles with noncircular contact lines are discussed. A general formulation to evaluate the adhesion force due to surface forces is presented. Also, a novel methodology, that is, IBAFA, image based adhesion force analysis, was developed to allow implementation of the general formulation. IBAFA is based on the use of multiple profile images of a drop. The images are analyzed (1) to accurately reconstruct the contact line shape, which is analytically represented by a Fourier cosine series, and (2) to measure contact angles at multiple locations along the contact line and determine the contact angle distribution based on a linear piecewise interpolation routine. The contact line shape reconstruction procedure was validated with both actual experiments and simulated experiments. The procedure for the evaluation of the adhesion force was tested using simulated experiments with synthetic drops of known shapes. A comparison with current methods showed that simplifying assumptions (e.g., elliptical contact line or linear contact angle distribution) used in these methods result in errors up to 76% in the estimated adhesion force. However, the drop adhesion force evaluated using IBAFA results in small errors on the order of 1%.

Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates

Drop shape techniques, such as axisymmetric drop shape analysis, are widely used to measure surface properties, as they are accurate and reliable. Nevertheless, they are not applicable in experimental studies dealing with fluid configurations that do not present an apex. A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates. The theoretical shape of the interface is generated numerically as a function of surface tension and some geometrical parameters at the starting point of the interface, e.g., contact angle and radius of the interface. Then, the numerical shape is fitted to the experimental profile, taking the interfacial properties as adjustable parameters. The best fit identifies the true values of surface tension and contact angle. Comparison between the experimental and the theoretical profiles is performed using the theoretical image fitting analysis (TIFA) strategy. The new method, TIFA-axisymmetric interfaces (TIFA-AI), is applicable to any axisymmetric experimental configuration (with or without apex). The versatility and accuracy of TIFA-AI is shown by considering various configurations: liquid bridges, sessile and pendant drops, and liquid lenses.

Importance of Surface Tension Characterization for Food, Pharmaceutical and Packaging Products: A Review

This article reviews the various theoretical approaches that have been developed for determination of the surface tension of solids, and the applications to food industrial products. The surface tension of a solid is a characteristic of surface properties and interfacial interactions such as adsorption, wetting or adhesion. The knowledge of surface tension is thus of great interest for every domain involved in understanding these mechanisms, which recover a lot of industrial investigations. Indeed, it is the case for the packaging industry, the food materials science, the biomedical applications and the pharmaceutical products, cleaning, adhesive technology, painting, coating and more generally all fields in relation with wettability of their systems. There is however no direct method for measurements of surface tension of solids, except the contact angle measurements combined with an appropriate theoretical approach are indirect methods for estimation of surface tension of solids. Moreover, since the publication by Young (1805) who developed the basis of the theory of contact angle some two hundred years ago, measurements and interpretations are still discussed in scientific literature, pointing out the need to better understand the fundamental mechanisms of solid-liquid interfacial interactions. Applications of surface tension characterization in the field of food materials science are detailed, especially for packaging and coating applications, which recover different actual orientations in order to improve process and quality.

Experiments on the motion of drops on a horizontal solid surface due to a wettability gradient

Results from experiments performed on the motion of drops of tetraethylene glycol in a wettability gradient present on a silicon surface are reported and compared with predictions from a recently developed theoretical model. The gradient in wettability was formed by exposing strips cut from a silicon wafer to dodecyltrichlorosilane vapors. Video images of the drops captured during the experiments were subsequently analyzed for drop size and velocity as functions of position along the gradient. In separate experiments on the same strips, the static contact angle formed by small drops was measured and used to obtain the local wettability gradient to which a drop is subjected. The velocity of the drops was found to be a strong function of position along the gradient. A quasi-steady theoretical model that balances the local hydrodynamic resistance with the local driving force generally describes the observations; possible reasons for the remaining discrepancies are discussed. It is shown that a model in which the driving force is reduced to accommodate the hysteresis effect inferred from the data is able to remove most of the discrepancy between the observed and predicted velocities.

Dynamics of the rise around a fiber: experimental evidence of the existence of several time scales

We study experimentally the dynamics of the spontaneous rise of a meniscus made of polydimethylsiloxane of various viscosities on the outside of a micrometric fiber made of monofilament in polyethyleneterephthalate. Optical methods are used to measure simultaneously the height of the liquid interface and the associated contact angle versus time. Versus the liquid viscosity, we observe asymptotically, for the dynamic contact angle, either a t(-1/2) behavior in agreement with the hydrodynamic description or a t(-1) behavior predicted by the molecular-kinetic theory, in its linear form, thus confirming the existence of at least two major time scales in the rise phenomenon.

A robust algorithm for the simultaneous parameter estimation of interfacial tension and contact angle from sessile drop profiles

The pendant and sessile drop profile analysis using the finite element method (PSDA-FEM) is an algorithm which allows simultaneous determination of the interfacial tension (gamma) and contact angle (theta(c)) from sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second-order spherical coordinate form of the Young-Laplace equation. Thus, the boundary conditions at the drop apex and contact position of the drop with the substrate are required to solve for the drop profile coordinates. The boundary condition at the position where the drop contacts the substrate may be specified as a fixed contact line or fixed contact angle. This paper will focus on the fixed contact angle boundary condition for sessile drops on a substrate and how this boundary condition is used in the PSDA-FEM curve-fitting algorithm. The PSDA-FEM algorithm has been tested using simulated drop shapes with and without the addition of random error to the drop profile coordinates. The random error is varied to simulate the effect of camera resolution on the estimates of gamma and theta(c) values obtained from the curve-fitting algorithm. The error in the experimental values for gamma from sessile drops of water on acrylic and Mazola corn oil on acrylic falls within the predicted range of errors obtained for gamma values from simulated sessile drop profiles with randomized errors that are comparable in magnitude to the resolution of the experimental setup.

Effect of electric fields on contact angle and surface tension of drops

Contact angles of sessile drops were experimentally investigated in the electric field. The experimental setup was designed such that the electric field was applied to all three interfaces. The advanced Automated Polynomial Fitting (APF) methodology was employed to measure contact angles with high accuracy. The significance of the observations and trends was examined by conducting statistical tests of hypothesis. It was found that contact angles of polar liquids such as alcohols increase in the electric field. However, no significant trend was observed for nonpolar liquids such as alkanes. The change in the contact angle was found to be stronger for liquids with longer molecules. It was shown that the polarity of the electric field is not an underlying factor in the observed trends. Using the equation of state for interfacial tensions, the observed shift in contact angles was translated into a corresponding change in surface tension of the liquids. The results suggest that the surface tension of alcohols increases by one to two percent (depending on the size of molecules) when an electric field of the order of magnitude of 10(6) V/m is applied.