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.     

Modeling of the adsorption kinetics of surfactants at the liquid-fluid interface of a pendant drop

This paper presents a theoretical model for simulating the adsorption kinetics of a surfactant at the liquid-fluid interface of a pendant drop. The diffusion equation is solved numerically by applying the semidiscrete Galerkin finite element method to obtain the time-dependent surfactant concentration distributions inside the pendant drop and inside the syringe needle that is used to form the pendant drop. With the obtained bulk surfactant concentration distributions, the adsorption at the interface is determined by using the conservation law of mass. It should be noted that the theoretical model developed in this study considers the actual geometry of the pendant drop, the depletion process of the surfactant inside the pendant drop, and the mass transfer of the surfactant from the syringe needle to the pendant drop. The present pendant-drop model is applied to study the adsorption kinetics of surfactant C10E8 (octaethylene glycol mono n-decyl ether) at the water-air interface of a pendant drop. The numerical results show that the Ward and Tordai equation, which was derived for adsorption from a semi-infinite surfactant solution to a planar interface, is unsuitable for interpreting the dynamic surface or interfacial tension data measured by using the pendant-drop-shape techniques, especially at low initial surfactant concentrations. The spherical-drop model, which assumes the pendant drop to be a perfectly spherical drop with the same drop volume, can be used to interpret the dynamic surface or interfacial tension data for pendant drops either with high initial surfactant concentrations or with low initial surfactant concentrations in short adsorption durations only. For pendant drops with low initial surfactant concentrations in long adsorption durations, the theoretical model developed in this study is strongly recommended.     

Effects of injection angle on the measurement of surface tension coefficient by drop weight method

The drop weight method for surface tension measurement is based on the weight of drops detached from a nozzle. The original idea was based on a postulate introduced by Tate (On the Magnitude of a Drop of Liquid Formed Under Different Circumstances, Philos. Mag. 27, 176–180, 1864), assuming that the weights of an ideal pendant drop and a detached ideal drop are identical, and that this weight is equal to the surface force that holds a drop attached to the nozzle. To consider the real volume of a drop that detaches from a nozzle, the method required a correction factor. Harkins and Brown suggested such correction factors for vertical injection from a nozzle. In this study, a correction factor for injection at different angles is presented and some of the hydrodynamic effects on surface tension measurement based on the drop weight method are studied. In addition, a model is introduced for the detachment time of drops in directions other than the vertical direction     

Calibration parameters of the pendant drop tensiometer: assessment of accuracy

A method is reported for verifying and controlling the accuracy of the calibration parameters, operating in image acquisition, for drop and bubble shape-analysis tensiometry. An error, impartially affecting the calibration parameters of both Cartesian axes, results in a squared error for the determined surface tension. Moreover, in the case where the calibration factors are affected by different errors, the determined value of surface tension is definitely unreliable, depending on the drop (or bubble) size and showing spurious in-phase or out-of-phase alterations. A procedure is illustrated for correcting the calibration parameters, on the basis of the observed results for a reference liquid. Method and procedure are validated by numerical examples.     

Interfacial tension between polystyrene and a liquid crystal polymer

In this work contact angles formed by drops of polystyrene (PS) on a surface of liquid crystalline polymer (LCP) Vectra A910 were measured as a function of temperature for temperatures ranging from 180 to 230°C. The values were used together with the surface tensions of both polymers to evaluate the interfacial tension between PS and the LCP. In order to validate the method used to evaluate this interfacial tension, the interfacial tension between polypropylene (PP) and PS was evaluated using values of contact angles formed by a drop of PP on PS and the values of surface tension of both polymers in the molten state. The values of interfacial tension between PP and PS corroborated well the values obtained using the pendant drop method. The values of interfacial tension between PS and the LCP were shown to decrease linearly with temperature.     

Adsorption kinetics of NIPAM-based polymers at the air-water interface as studied by pendant drop and bubble tensiometry

The adsorption of N-isopropylacrylamide (NIPAM) based thermoresponsive polymers at the air-water interface was investigated by using drop and bubble shape tensiometry. The molecular weight dependence of polymer adsorption rate was studied by using narrowly distributed polymer fractions (polydispersity < 1.2) that were prepared by solvent:nonsolvent fractionation. The time-dependent surface tension profiles were fitted to the Hua-Rosen equation and the t values obtained were applied for interpretation of the kinetic data. It was found that the rate of polymer adsorption increased as the molecular weight of the polymer decreased. The relationship between polymer surface concentration and surface tension was determined by applying the pendant drop as a Langmuir-type film balance. From this relationship, the kinetics of polymer adsorption determined experimentally was compared with the adsorption rates predicted by a diffusion-controlled adsorption model based on the Ward-Tordai equation. The predicted adsorption rates were in good agreement with what was found experimentally. The dependence of the adsorption rate on the molecular weight of polymers can be satisfactorily described within the diffusion-controlled model.     

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.     

Influence of gas sorption on the surface tension of liquid crystalline substances. A relaxation test on a liquid-crystalline side-chain polyacrylate

Computer-aided pendant drop profile analysis is used to investigate the relaxation of gas sorption at the surface of the liquid-crystalline side-chain polyacrylate PAC-6 after transient surface area changes – square-pulse disturbance. This test demonstrates, for the first time, the possibility of qualitative estimation of the surface molecular order. The results confirm the existence of a pretransitional order and indicate the enrichment of the liquid-crystalline side chains at the polymer surface. The influence of drop size on the accuracy of the surface tension determination by using the pendant drop method is also discussed.     

Study on the initial evaporation rates of distilled sulphur mustard (HD) in concrete using wind tunnel and TD-GC/MSD: effect of drop size and temperature

In this paper, we demonstrate a robust, analytical method for the study of the initial evaporation rates of distilled sulphur mustard (HD) in concrete at various drop sizes and temperatures. We used a 5-cm wind tunnel and thermal desorption (TD) in connection with gas chromatograph and mass spectrometry detection (GC/MSD). Drops of neat HD, ranging in sizes of 1, 3, 6 and 9 µL, were applied to small concrete coupons. The temperatures were either 18°C, 25°C, 35°C or 50°C. The drop of HD rapidly spread in concrete upon its release. The initial evaporation rates of the drop of HD were analysed by TD in conjunction with GC/MSD. The results showed that the initial evaporation rates increased while HD spread over the surface of concrete, then decreased as the contamination was over. We also found that the initial evaporation rates of the drop of HD in concrete are linearly proportional to drop size and temperature. In particular, drop size or spreading factor has a more pronounced effect on the initial evaporation rates of the drop of HD in concrete than temperature.     

Interfacial tensions from drop retraction versus pendant drop data and polydispersity effects

Interfacial tensions sigma were measured by means of both methods for the following polymer pair: polyisobutylene (PIB 3) plus poly(dimethylsiloxane) (PDMS 152) and poly(dimethyl-co-methylphenylsiloxane) (CoP26*) plus PDMS 48. The numbers after the abbreviation state the molar masses in kilograms; the homopolymers exhibit polydispersities on the order of 2. The reliability of the method of drop retraction is backed up by systematic measurements, which demonstrate that it is possible to study the time evolution of sigma. Because of the free choice of the phases (drop or matrix) and the possibility to vary the overall composition of the system in a wide range, drop retraction yields more information than the pendant drop method. For the present systems both types of experiments yield identical results for the droplets of higher density. Experiments with the inverse blends and at higher volume fractions of the disperse phase demonstrate that the polydispersity of the components plays an important role. In the case of the system PIB 3/PDMS 152 the steady-state interfacial tension at 25 degrees C is 2.25 mN m(-1) if the drop consists of PDMS, but only 1.3 mN m(-1) if it consists of PIB. Furthermore, the time-independent sigma values are attained much more rapidly in the latter case.     

Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

Dynamic surface tensions of Athabasca bitumen vacuum residue including the effect of dissolved air

The pendant drop technique was used to measure the equilibrium and dynamic surface tensions of Athabasca bitumen vacuum residue (500 degrees C+) (AVR) between 150 and 280 degrees C. A significant (16%) slow (over hours) decrease from initial to equilibrium values was found. In addition, the effect of dissolved air on surface tension was studied at 150 degrees C by comparing dynamic surface tensions of air- or nitrogen-saturated AVR in contact with air or nitrogen. It was found that the presence of dissolved air significantly decreases the dynamic change in surface tension (from 16 to 5%). In order to perform the surface tension studies, the density of AVR was required. Archimedes method was used to measure the density of AVR from 98 to 335.8 degrees C.     

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.     

A finite element based algorithm for determining interfacial tension (gamma) from pendant drop profiles

This paper introduces a robust algorithm to determine the interfacial tension (gamma) from pendant drop profiles using the Galerkin finite element method (gamma-PD-FEM) to solve the axisymmetric form of the Young-Laplace (YL) equation. In this algorithm, the theoretical profiles are generated by solving the spherical coordinate form of the YL equation. gamma-PD-FEM also solves for the parameter estimates by minimizing the difference between the theoretical and experimental surface functions, f(theta). This technique is compared to the widely used method of converting the YL equation to the three arc length-based (ALB) first-order ODEs developed by Bashforth and Adams (BA) in 1883, or as denoted in this paper, the gamma-PD-BA method. The drop apex is the initial condition for the gamma-PD-BA algorithm and the integration is terminated at a specified location along the drop profile. In contrast to techniques based on the BA approach, computation of the theoretical drop profile in gamma-PD-FEM is obtained from a second-order ordinary differential equation and requires boundary conditions at the drop apex and at the contact line of the drop to the nozzle. By incorporating both boundary conditions into the problem formulation, the algorithm can also determine if the drop shape is at static equilibrium. Results to be presented include an outline of the computer algorithm, and comparison of gamma values obtained from the gamma-PD-FEM and the traditional gamma-PD-BA method using simulated and experimental drop profile data sets.     

The influence of asymmetry in drop shape on an interfacial tension measurement

A requirement of the drop method for interfacial tension measurement is that the drop must have an axi-symmetry. The drop shape was measured as a function of the angle of the rod from which the drop was hanging. The deviation of the interfacial tension caused by asymmetry was calculated using the selected plane method in the pendant drop technique. A sharp maximum was seen in the interfacial tension vs angle curve when the rod was at the vertical point. The maximum value was concluded as being the true value of the interfacial tension. Both decreases in the pressure difference and in the curvature of the drop associated with an increase in the rod-angle are a counterpart with each other to satisfy the Bashforth and Adams equation. The underestimation of the interfacial tension seems to be caused by the apparent inconsistency between the decreases in the curvature and pressure difference terms. The rigorous mechanical setup demonstrated here is necessary to attain the true axi-symmetric condition, and thus obtain a reliable value for the interfacial tension.     

Finite-size effects in dissipative particle dynamics simulations

We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.     

Dynamic surface tension analysis of dodecyl sulfate association complexes

First, a novel calibration method is used to expand the current understanding of spherical drop growth and elongation that occurs during on-line measurements of surface pressure using the dynamic surface tension detector (DSTD). Using a novel surface tension calibration method, the drop radius is calculated as a function of time from experimental drop pressure data and compared to the theoretical drop radius calculated from volumetric flow rate. From this comparison, the drop volume at which the drop shape starts to deviate ( approximately 4 mul) from a spherical shape is readily observed and deviates more significantly by approximately 6 mul drop volume (5% deviation in the ideal spherical drop radius) for the capillary sensing tip employed in the DSTD. From this assessment of drop shape, an experimental method for precise drop detachment referred to as pneumatic drop detachment is employed at a drop volume of 2 mul (two second drops at 60 mul/min) in order to provide rapid dynamic surface tension measurements via the novel on-line calibration methodology. Second, the DSTD is used to observe and study kinetic information for surface-active molecules and association complexes adsorbing to an air-liquid drop interface. Dynamic surface tension measurements are made for sodium dodecyl sulfate (SDS) in the absence and presence of either tetra butyl ammonium (TBA) or chromium (III). Sensitive, indirect detection of chromium and other multiply charged metals at low concentrations is also investigated. The DSTD is utilized in examining the dynamic nature of SDS: cation association at the air-liquid interface of a growing drop. Either TBA or Cr(III) were found to substantially enhance the surface tension lowering of dodecyl sulfate (DS), but the surface tension lowering is accompanied by a considerable kinetic dependence. Essentially, the surface tension lowering of these DS: cation complexes is found to be a fairly slow process in the context of the two second DSTD measurement. The limit of detection for both SDS and chromium (III) is in the 300-400 part-per-billion (by mass) range.     

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.     

Characterisation of alkyl amines at the water/air surface with the drop and bubble profile analysis tensiometry

Pendant drop and buoyant bubble methods have been used to study the surface characteristics of alkyl amines at the water/air surface. The investigated alkyl amines, triethylamine and octylamine, showed unusual changes in the surface tension as a function of time: an initially steep drop and a subsequent steady increase in the surface tension until a value close to the one of the pure water/air system was observed. This phenomenon is explained by the evaporation of the alkyl amines, for which several sets of experiments have been conducted with the pendant drop and buoyant bubble methods. Using an appropriate experimental protocol, the equilibrium adsorption behaviour of the two amines can be quantitatively measured.     

Entropy generation in nonlinear mixed convective flow of nanofluid in porous space influenced by Arrhenius activation energy and thermal radiation

This paper focuses on an experimental study of the surface tension of nanofluids based on ethylene glycol with various types of nitride nanoparticles. Samples were prepared using a two-step method with mass content between 1 and 5% of particles. Nanofluids contain three types of nitride nanoparticles: aluminum nitride, silicon nitride and titanium nitride with various particle average sizes. Surface tension of nanofluids was investigated at a constant temperature of 298.15 K with two different techniques: du Noüy ring method and pendant drop method. It is presented that experimental values obtained with both methods are in good agreement with each other. Also, results obtained during this study show that the addition of this type of nanoparticles does not have a significant impact on the surface tension of base fluid for the concentrations and diameters of nitride nanoparticles considered.