Contact angle hysteresis of bovine serum albumin (BSA) solution/metal (Au-Cr) coated glass substrate

Bovine serum albumin (BSA) has an extraordinary property to carry biomolecules. An experimental study on the wettability of BSA is presented in this study. The variations in the surface tension and the equilibrium contact angle with the change in BSA concentration are also reported. The surface tension and the contact angle are measured with pendant and sessile drop techniques, respectively. A nonlinear decrement in the surface tension with the increment in the BSA concentration is observed. An equilibrium contact angle of a BSA solution with particular concentration is determined by studying the hysteresis in the contact angle from dynamic contact angle measurements. The needle-in-drop technique is used to study the hysteresis of the contact angle. It is observed that the obtained surface tension and the equilibrium contact angle vary with the BSA concentration. In this reported study, for the considered combination of the BSA concentration and solid surface, the liquid drop does not recede as the drop volume decreases, which represents nonreceding contact angle condition. The increment in the contact angle with the increment in the BSA concentration is observed. Finally, it is observed that the inclusion of the proteins not only changes the surface tension but also changes the contact angle.     

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.     

Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions

The combination of short-range repulsive and long-range attractive forces in many-body dissipative particle dynamics (MDPD) is examined at a vapor/liquid and liquid/solid interface. Based on the radial distribution of the virial pressure in a drop at equilibrium, a systematic study is carried out to characterize the sensitivity of the surface tension coefficient with respect to the inter-particle interaction parameters. For the first time, the approximately cubic dependence of the surface tension coefficient on the bulk density of the fluid is evidenced. In capillary flow, MDPD solutions are shown to satisfy the condition on the wavelength of an axial disturbance leading to the pinch-off of a cylindrical liquid thread; correctly, no pinch-off occurs below the cutoff wavelength. Moreover, in an example that illustrates the cascade of fluid dynamics behaviors from potential to inertial-viscous to stochastic flow, the dynamics of the jet radius is consistent with the power law predictions of asymptotic analysis. To model interaction with a solid wall, MDPD is augmented by a set of bell-shaped weight functions; hydrophilic and hydrophobic behaviors, including the occurrence of slip in the latter, are reproduced using a modification in the weight function that avoids particle clustering. The dynamics of droplets entering an inverted Y-shaped fracture junction is shown to be correctly captured in simulations parametrized by the Bond number, confirming the flexibility of MDPD in modeling interface-dominated flows.     

Effect of solution viscosity on dynamic surface tension detection

A dynamic surface tension detector (DSTD) was used to examine the molecular diffusion and surface adsorption characteristics of surface-active analytes as a function of solution viscosity. Dynamic surface tension is determined by measuring the differential pressure across the air/liquid interface of repeatedly growing and detaching drops. Continuous surface tension measurement throughout the entire drop growth is achieved for each eluting drop (at a rate of 30 drops/min for 2 μl drops), providing insight into the kinetic behavior of molecular diffusion and orientation processes at the air/liquid interface. Three-dimensional data are obtained through a calibration procedure previously developed, but extended herein for viscous solutions, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Thus, an analyte that lowers the surface tension results in an increase in surface pressure. The calibration procedure derived for the pressure-based DSTD was successfully extended and implemented in this report to experimentally determine standard surface pressures in solutions of varied viscosity. Analysis of analytes in viscous solution was performed at low analyte concentration, where the observed analyte surface activity indicates that the surface concentration is at or near equilibrium when in a water mobile phase (viscosity of 1.0 Cp). Two surface-active analytes, sodium dodecyl sulfate (SDS) and polyethylene glycol (MW 1470 g/mol, PEG 1470), were analyzed in solutions ranging from 0 to 60% (v/v) glycerol in water, corresponding to a viscosity range of 1.0-15.0 Cp. Finally, the diffusion-limited surface activity of SDS and PEG 1470 were observed in viscous solution, whereby an increase in viscosity resulted in a decreased surface pressure early in drop growth. The dynamic surface pressure results reported for SDS and PEG 1470 are found to correlate with solution viscosity and analyte diffusion coefficient via the Stokes-Einstein equation.     

Statics of polymer droplets on deformable surfaces

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different surface/drop compatibility and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness, and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupre? wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.     

Linear tension of two-dimensional drops on planar adsorbent faces

The size dependence of the linear tension of round two-dimensional equilibrium drops in the vapor phase on a homogeneous surface of an adsorbent is studied at the pressure of saturated two-dimensional vapor. The calculations are based on the lattice gas model in a quasi-chemical approximation with allowance for the correlation effects of the nearest interacting molecules. Methods for calculating linear tension using the equimolecular reference line are considered. Temperature dependences of the linear tension are studied for metastable and equilibrium drops. It is found that the differences between the thermodynamic properties of two types of drops are slight over a wide range of variation in drop radii.     

The Effects of Resistance to Shift of the Equilibrium State of a Liquid Droplet in Contact with a Solid

The effect of blocking the shift of the contact surface between a liquid drop and a solid body is discussed. The model proposed in (S. D. Iliev, 1997, J. Colloid Interface Sci., 194, 287) is discussed. This equilibrium model considers the resistance to shift by adding an energy to the classical capillary equilibrium model. It is shown that the set of equilibrium shapes of static droplets is effectively modeled. Studying the set of equilibrium axisymmetric drops, located on a horizontal surface, the analysis proves that the contact angle hysteresis is described without introducing a dependence between the resistance-to-shift coefficients and the drop volume and Bond's number. A possibility of realizing a stick-slip motion and division of the equilibrium drops is studied, too. It is shown that the equilibrium model describes also the set of equilibrium nonaxisymmetric static drops. The everyday experience to obtain the various nonaxisymmetric drop shapes by the deforming of contact line with a thin rod is numerically modeled. Copyright 1999 Academic Press.     

CFD evaluation of drop retraction methods for the measurement of interfacial tension of surfactant-laden drops

Drop retraction methods are popular means of measuring the interfacial tension between immiscible polymers. Experiments show that two different drop retraction methods, imbedded fiber retraction (IFR) and deformed drop retraction (DDR), give inconsistent results when a surfactant is present on the surface of the drop. These inconsistencies are deemed to be due to dilution of the surfactant and due to gradients in interfacial concentration of surfactant along the drop surface. This physical picture is quantified for the simple case of a Newtonian drop in a Newtonian matrix, with an insoluble, nondiffusive surfactant at the interface. The drop is deformed in computational fluid dynamics simulations by shearing the matrix, and then allowed to retract. Dilution and interfacial tension gradients effects are found to be especially large at the early stages of retraction, making IFR unsuitable for measuring the interfacial tension of surfactant-laden interfaces. The effects of surfactant dilution and gradients are found to persist even at late stages of retraction, causing the DDR method to underestimate the equilibrium interfacial tension significantly. The largest underestimates occur when the drop viscosity is lower than the matrix viscosity.     

Temperature dependence of the surface tension of indium

Original data on the temperature dependence of the surface tension of indium, obtained using two independent approaches (a large sessile drop and the maximum pressure in a drop) are presented. The focus is on analyzing possible methodological shortcomings of experimental studies in which the surface tension values of a number of pure metals are obtained that are considerably higher than the results from measuring surface tension by traditional means. It is found that cleaning the investigated metal surfaces through bombardment with heavy ions of inert gases can lead to violations of the thermodynamic equilibrium conditions of a surface with its own saturated vapor, and to the ensuing consequences.     

Work of Adhesion of a Sessile Drop to a Clean Surface

According to the Young-Dupré equation, as interpreted by Bangham and Razouk, the work of adhesion of a sessile drop to a smooth solid surface is given by WS(V)L = gammaL (1 + cos θ), where θ is the equilibrium contact angle measured at equilibrium of the system with the saturated vapor of the liquid, and WS(V)L is the work of adhesion of that drop to the solid surface which is in equilibrium with that vapor and may contain an adlayer of the vapor. For calculation of WSL, the work of adhesion of a sessile drop to a clean solid surface, the equation WSL = gammaL (1 + cos θ) + Pie is generally used (although Bangham and Razouk never proposed it). Pie is the negative of the free energy of formation of the adlayer, sometimes called the spreading pressure. In the present work it is shown that the latter equation cannot be accurate. Copyright 1999 Academic Press.     

Contact angle hysteresis of microbead suspensions

Microbead suspensions are often used in microfluidic devices for transporting biomolecules. An experimental investigation on the wettability of microbead suspension is presented in this study. The variation in the surface tension and the equilibrium contact angle with the change in the volume fraction of the microbead is presented here. The surface tension of the microbead suspension is measured with the pendant drop technique, whereas the dynamic contact angle measurements, i.e., advancing and receding contact angles, are measured with the sessile drop technique. An equilibrium contact angle of a suspension with particular volume fraction is determined by computing an average over the measured advancing and receding contact angles. It is observed that the surface tension and the equilibrium contact angle determined from advancing and receding contact angles vary with the magnitude of the microbeads volume fraction in the suspension. A decrease in the surface tension with an increase in the volume fraction of the microbead suspension is observed. The advancement and the recession in contact line for dynamic contact angle measurements are achieved with the motorized dosing mechanism. For microbead suspensions, the advancement of the contact line is faster as compared to the recession of the contact line for the same flow rate. The presence of microbeads assists in the advancement and the recession of the contact line of the suspension. A decrease in the equilibrium contact angles with an increase in the microbead suspension volume fraction is observed. Inclusion of microbeads in the suspension increases the wetting capability for the considered combination of the microbead suspension and substrate. Finally, empirical correlations for the surface tension and the contact angle of the suspension as a function of microbead volume fraction are proposed. Such correlations can readily be used to develop mechanistic models for the capillary transport of microbead suspensions related to LOC applications.     

Wetting and spreading of nanofluids on solid surfaces driven by the structural disjoining pressure: statics analysis and experiments

The wetting and spreading of nanofluids composed of liquid suspensions of nanoparticles have significant technological applications. Recent studies have revealed that, compared to the spreading of base liquids without nanoparticles, the spreading of wetting nanofluids on solid surfaces is enhanced by the structural disjoining pressure. Here, we present our experimental observations and the results of the statics analysis based on the augmented Laplace equation (which takes into account the contribution of the structural disjoining pressure) on the effects of the nanoparticle concentration, nanoparticle size, contact angle, and drop size (i.e., the capillary and hydrostatic pressure); we examined the effects on the displacement of the drop-meniscus profile and spontaneous spreading of a nanofluid as a film on a solid surface. Our analyses indicate that a suitable combination of the nanoparticle concentration, nanoparticle size, contact angle, and capillary pressure can result not only in the displacement of the three-phase contact line but also in the spontaneous spreading of the nanofluid as a film on a solid surface. We show here, for the first time, that the complete wetting and spontaneous spreading of the nanofluid as a film driven by the structural disjoining pressure gradient (arising due to the nanoparticle ordering in the confined wedge film) is possible by decreasing the nanoparticle size and the interfacial tension, even at a nonzero equilibrium contact angle. Experiments were conducted on the spreading of a nanofluid composed of 5, 10, 12.5, and 20 vol % silica suspensions of 20 nm (geometric diameter) particles. A drop of canola oil was placed underneath the glass surface surrounded by the nanofluid, and the spreading of the nanofluid was monitored using an advanced optical technique. The effect of an electrolyte, such as sodium chloride, on the nanofluid spreading phenomena was also explored. On the basis of the experimental results, we can conclude that a nanofluid with an effective particle size (including the electrical double layer) of about 40 nm, a low equilibrium contact angle (<3°), and a high effective volume concentration (>30 vol %) is desirable for the dynamic spreading of a nanofluid system with an interfacial tension of 0.5 mN/m. Our experimental observations also validate the major predications of our theoretical analysis.     

Studies of dynamic surface tension of polyoxyethylene alkylphenols at the air–water interface

This paper presents the study of dynamic surface tension of polyoxyethylene alkylphenol surfactants (Igepals) at the air–solution interface. The experimental investigation of the surface tension dynamics are carried out using a pendant drop method for two of the representative alkylphenols (Igepal-630 and Igepal-720) nonionic surfactants. The general trend of the dynamic surface tension for the two surfactants appears to be similar. However, the absolute surface activities are different. Between the two poloxyethylene alkylphenol surfactants, it was found that Igepal-C0-630 has a higher surface activity and a lower critical micelle concentration (CMC) value. This agreed well with their reported hydrophile–lipophile balance (HLB). The equilibrium adsorption parameters for these surfactant systems have been estimation using two different methods and are in good agreement. The theoretical model developed for the surface tension dynamics based on the Statistical Rate Theory (SRT) in our earlier (J. Colloid Interface Sci., 286, 2005, 14–27) work satisfactorily predicted the experimental results for the present systems.     

Limiting conditions for applying the spherical section assumption in contact angle estimation

The shape of liquid drops on solid surfaces deviates from the spherical as tension decreases and gravity effects start affecting the drop shape. This paper attempts to define this deviation and estimates the dimensionless Eotvos number limits above which the deviation becomes "significant." The use of these limiting values can facilitate estimation of contact angle in the following manner. It is well known that the equilibrium contact angle made by a liquid drop on a solid surface can be estimated from measurements of two drop parameters. These parameters can be any two chosen from the drop volume, height, and wetted radius. In case the effect of gravity on the drop shape is negligible, simple algebraic relations derived from the spherical section assumption exist, from which the contact angle can be estimated. In systems where the "spherical section" assumption is invalid, the Laplace equation for the drop shape has been solved numerically with any two of the above parameters as the constraints, to obtain the contact angle. In this paper, Eotvos numbers at which the deviation of the drop profile from the spherical is significant enough to result in contact angle deviation of 1 degrees are estimated. The limiting values of Eotvos number, expressed as a function of the original contact angle made by the spherical profile, are obtained by solving the Laplace equation for the drop shape with the drop volume and wetted radius constraints for decreasing values of Interfacial tension. These limiting values are also estimated for different drop sizes and for cases where the drop phase is heavier (sessile) and lighter (buoyant) than the surrounding fluid. The independence of the Eotvos number estimates from the sign of the density difference as well as the drop size is shown. These Eotvos number limits can be used to check if the spherical section assumption, with the resulting simple algebraic relations, can be used for contact angle estimation and other shape-related analysis for a system.     

Measurement of the kinetic rate constants for the adsorption of superspreading trisiloxanes to an air/aqueous interface and the relevance of these measurements to the mechanism of superspreading

Super-spreading trisiloxane surfactants are a class of amphiphiles which consist of nonpolar trisiloxane headgroups ((CH3)3-Si-O)2-Si(CH3)(CH2)3-) and polar parts composed of between four and eight ethylene oxides (ethoxylates, -OCH2CH2-). Millimeter-sized aqueous drops of trisiloxane solutions at concentrations well above the critical aggregate concentration spread rapidly on very hydrophobic surfaces, completely wetting out at equilibrium. The wetting out can be understood as a consequence of the ability of the trisiloxanes at the advancing perimeter of the drop to adsorb at the air/aqueous and aqueous/hydrophobic solid interfaces and to reduce considerably the tensions of these interfaces, creating a positive spreading coefficient. The rapid spreading can be due to maintaining a positive spreading coefficient at the perimeter as the drop spreads. However, the air/aqueous and solid/aqueous interfaces at the perimeter are depleted of surfactant by interfacial expansion as the drop spreads. The spreading coefficient can remain positive if the rate of surfactant adsorption onto the solid and fluid surfaces from the spreading aqueous film at the perimeter exceeds the diluting effect due to the area expansion. This task is made more difficult by the fact that the reservoir of surfactant in the film is continually depleted by adsorption to the expanding interfaces. If the adsorption cannot keep pace with the area expansion at the perimeter, and the surface concentrations become reduced at the contact line, a negative spreading coefficient which retards the drop movement can develop. In this case, however, a Marangoni mechanism can account for the rapid spreading if the surface concentrations at the drop apex are assumed to remain high compared to the perimeter so that the drop is pulled out by the higher tension at the perimeter than at the apex. To maintain a high apex concentration, surfactant adsorption must exceed the rate of interfacial dilation at the apex due to the outward flow. This is conceivable because, unlike that at the contact line, the surfactant reservoir in the liquid at the drop center is not continually depleted by adsorption onto an expanding solid surface. In an effort to understand the rapid spreading, we measure the kinetic rate constants for adsorption of unaggregated trisiloxane surfactant from the sublayer to the air/aqueous surface. The kinetic rate of adsorption, computed assuming the bulk concentration of monomer to be uniform and undepleted, represents the fastest that surfactant monomer can adsorb onto the air/aqueous surface in the absence of direct adsorption of aggregates. The kinetic constants are obtained by measuring the dynamic tension relaxation as trisiloxanes adsorb onto a clean pendant bubble interface. We find that the rate of kinetic adsorption is only of the same order as the area expansion rates observed in superspreading, and therefore the unaggregated flux cannot maintain very high surface concentrations at the air/aqueous interface, either at the apex or at the perimeter. Hence in order to maintain either a positive spreading coefficient or a Marangoni gradient, the surfactant adsorptive flux needs to be augmented, and the direct adsorption of aggregates (which in the case of the trisiloxanes are bilayers and vesicles) is suggested as one possibility.     

Spreading of a fluid phase on a spherical surface

The adsorption between a liquid drop and a micro-particle in an air or an air bubble and a micro-particle in water is dominated by liquid-solid or air-solid interfacial tension and wetting area of the liquid or air on the particle surface. The wetting area is determined by the spreading of the liquid drop or the bubble on the micro-particle. To explore this spreading, a wetting model of a fluid phase on a spherical particle was built. According to the theoretical results, the contact angle is constant when a fluid phase spreads on a spherical solid surface; the micro-particle can not submerge under a fluid when only interfacial tensions are involved and the wetting is not a complete wetting. The corresponding experiments were performed to confirm the theoretical results.     

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.     

The line tension and the generalized Young equation: the choice of dividing surface

Using Gibbs method of dividing surfaces, the condition of equilibrium of a sessile drop on a flat non-deformable solid substrate is investigated. The dependence of the line tension on the curvature radius of the dividing three-phase contact line is found. It has been derived a relationship between the partial derivative of the line tension with respect to the curvature radius of the three-phase contact line (which stands in the generalized Young equation) and the total derivative of the line tension with respect to the same radius along the equilibrium states. Various approximated formulas of the generalized Young equation used in the literature are analyzed.     

Equilibrium of multi-phase systems in gravitational fields

Four necessary conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field were derived by Ward and Sasges (1998) in a unified setting, by using an entropy maximization approach, and under the assumption that the liquid-vapor surface tension does not depend on elevation. These are thermal equilibrium, the Laplace and Young equations, and a condition on the chemical potentials of the components present in the system. Gibbs (1876) had obtained the Young equation in a derivation separate from the derivation of the other three conditions and by using an energy minimization approach. However, Gibbs had derived a more general form of the Laplace equation than Ward and Sasges's. Gibbs's equation contained a term expressing the contribution of the variation of surface tension with elevation. This equation has since been neglected by most of the scientific community. In the present paper, the same approach as Ward and Sasges's is used to derive, in an unified setting, the conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field but under the assumption that the liquid-vapor surface tension may depend on elevation. The four well-known conditions for equilibrium are obtained, with Gibbs's generalized Laplace equation instead of the classical Laplace equation. The derivations in this paper were carried out for two different system geometries, namely, for a sessile drop and for a conical capillary tube, and similar conditions for equilibrium were obtained.