Study of the advancing and receding contact angles: liquid sorption as a cause of contact angle hysteresis

Two types of experiments were used to study the behavior of both advancing and receding contact angles, namely the dynamic one-cycle contact angle (DOCA) and the dynamic cycling contact angle (DCCA) experiments. For the preliminary study, DOCA measurements of different liquids on different solids were performed using an automated axisymmetric drop shape analysis-profile (ADSA-P). From these experimental results, four patterns of receding contact angle were observed: (1) time-dependent receding contact angle; (2) constant receding contact angle; (3) 'stick/slip'; (4) no receding contact angle. For the purpose of illustration, results from four different solid surfaces are shown. These solids are: FC-732-coated surface; poly(methyl methacrylate/n-butyl methacrylate) [P(MMA/nBMA)]; poly(lactic acid) (DL-PLA); and poly(lactic/glycolic acid) 50/50 (DL-PLGA 50/50). Since most of the surfaces in our studies exhibit time dependence in the receding contact angle, a more extended study was conducted using only FC-732-coated surfaces to better understand the possible causes of decreasing receding contact angle and contact angle hysteresis. Contact angle measurements of 21 liquids from two homologous series (i.e. n-alkanes and 1-alcohols) and octamethylcyclotetrasiloxane (OCMTS) on FC-732-coated surfaces were performed. It is apparent that the contact angle hysteresis decreases with the chain length of the liquid. It was found that the receding contact angle equals the advancing angle when the alkane molecules are infinitely large. These results strongly suggest that the chain length and size of the liquid molecule could contribute to contact angle hysteresis phenomena. Furthermore, DCCA measurements of six liquids from the two homologous series on FC-732-coated surfaces were performed. With these experimental results, one can construe that the time dependence of contact angle hysteresis on relatively smooth and homogeneous surfaces is mainly caused by liquid retention/sorption. The results also suggested that the contact angle hysteresis will eventually approach a steady state, where the rate of liquid retention-evaporation or sorption process would balance out each other. If the existence of contact angle hysteresis can be attributed to liquid sorption/retention, one should only use the advancing contact angles (measured on a dry surface) in conjunction with Young's equation for surface energetic calculations.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.     

A refractive tilting-plate technique for measurement of dynamic contact angles

The contact angle is a critical parameter in liquid interface dynamics ranging from liquid spreading on a solid surface on earth to liquid motion in partially filled containers in space. A refractive tilting-plate technique employing a scanning laser beam is developed to conduct an experimental study of a moving contact line, with the intention of making accurate measurements of the contact angle. The technique shows promise as an accurate and potentially fully automated means to determine the velocity dependence of the contact angle at the intersection of the interface between two transparent fluids with a transparent solid surface. Ray tracing calculations are included to reinforce the measurement concept. The principal experiments were conducted at speeds ranging from 0.05 to 1.00 mm/s, both advancing and receding, using an immiscible liquid pair (nonane/formamide) in contact with glass. The contact angle was found to depend for practical purposes only on the sign of the velocity and not on its magnitude for the range of velocities studied. Other observations revealed a bimodal behavior of the contact line that depends on which liquid first contacts the glass, with resulting drift in the dynamic contact angle with time.     

Modeling of ultralyophobicity: suspension of liquid drops by a single asperity

With the aim of understanding the underlying physical phenomenon associated with utlralyophobic (or super repellent) surfaces, model studies have been performed on single asperities of different size and shape. A small liquid drop was deposited on top of each model asperity, and liquid was sequentially added. If the advancing contact angle was sufficiently large, it was possible to suspend large drops atop asperities with an apparent contact angle approaching 180 degrees. If more and more liquid was added, eventually the suspended drops collapsed. Roughening the surface of the asperities further bolstered suspension. Using an analysis that accounts for both capillary forces and the influence of gravity, the critical suspension volume was correctly predicted for each liquid/asperity combination.     

Removal of Natural Organic Matter by Forward Osmosis Membrane: Flux Behaviour and Foulant Characterization

Fouling of cellulose triacetate(CTA) forward osmosis(FO) membranes by natural organic matter(NOM) was studied by means of a cross-flow flat-sheet forward osmosis membrane system. The NOM solution was employed as the feed solution(FS), and a sodium chloride solution(3 mol/L) was used for the draw solution(DS). The process was conducted at various temperatures and cross-flow velocities. The flux decline was investigated with 3 h forward osmosis operation. The substances absorbed on the membranes were cleaned by ultrasonic oscillation of the fouled membranes and were characterized by methodologies including fluorescence excitation-emission matrices (EEMs) and liquid chromatography with an organic carbon detector(LC-OCD), and the variations of membrane properties were also investigated by Fourier transform infrared spectrometer(FTIR) and a contact angle meter. It was noted that the rejection efficiency of NOM is remarkable and that ultrasonic oscillation is an effective method to extract the NOM fouled on the CTA membranes after FO process. A higher cross-flow velocity and lower temperature benefit the anti-fouling capacity of the membrane significantly. Although humic substances accounted for the majo- rity of the NOM, aromatic proteins and amino acids were the main fouling components on the membranes, with symbolic FTIR peaks at 2355, 1408 and 873 cm^-1. The present surface foulant made the membranes becoming more hydrophilic, as demonstrated by a significant decrease in contact angle(ranging from 20% to 46%) under all the operation conditions.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

Recent progress in the determination of solid surface tensions from contact angles

Advancing contact angles of different liquids measured on the same solid surface fall very close to a smooth curve when plotted as a function of liquid surface tension, i.e., gamma(lv)costheta versus gamma(lv). Changing the solid surface, and hence gamma(sv), shifts the curve in a regular manner. These patterns suggest that gamma(lv)costheta depends only on gamma(lv) and gamma(sv). Thus, an "equation of state for the interfacial tensions" was developed to facilitate the determination of solid surface tensions from contact angles in conjunction with Young's equation. However, a close examination of the smooth curves showed that contact angles typically show a scatter of 1-3 degrees around the curves. The existence of the deviations introduces an element of uncertainty in the determination of solid surface tensions. Establishing that (i) contact angles are exclusively a material property of the coating polymer and do not depend on experimental procedures and that (ii) contact angle measurements with a sophisticated methodology, axisymmetric drop shape analysis (ADSA), are highly reproducible guarantees that the deviations are not experimental errors and must have physical causes. The contact angles of a large number of liquids on the films of four different fluoropolymers were studied to identify the causes of the deviations. Specific molecular interactions at solid-vapor and/or solid-liquid interfaces account for the minor contact angle deviations. Such interactions take place in different ways. Adsorption of vapor of the test liquid onto the solid surface is apparently the only process that influences the solid-vapor interfacial tension (gamma(sv)). The molecular interactions taking place at the solid-liquid interface are more diverse and complicated. Parallel alignment of liquid molecules at the solid surface, reorganization of liquid molecules at the solid-liquid interface, change in the configuration of polymer chains due to contact with certain probe liquids, and intermolecular interactions between solid and liquid molecules cause the solid-liquid interfacial (gamma(sl)) tension to be different from that predicted by the equation of state, i.e., gamma(sl) is not a precise function of gamma(lv) and gamma(sv). In other words, the experimental contact angles deviate from the "ideal" contact angle pattern. Specific criteria are proposed to identify probe liquids which eliminate specific molecular interactions. Octamethylcyclotetrasiloxane (OMCTS) and decamethylcyclopentasiloxane (DMCPS) are shown to meet those criteria, and therefore are the most suitable liquids to characterize surface tensions of low energy fluoropolymer films with an accuracy of +/-0.2 mJ/m2.     

Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state. The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles, respectively. It is interesting to observe that the advancing/receding contact angles (and contact angle hysteresis) are a function of viewing angle. In addition, the receding (or advancing) contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable (equilibrium) contact angle. The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed.     

Oscillatory phenomena at polyvinylpyridine/silica interfaces

Oscillations of the aggregate sizes of SiO₂ particles covered by an adsorbed layer of poly(vinylpyridine) (PVP) at pH 3 with a periodicity of about 15 h were observed using a particle counting technique. The same oscillation was found for the contact angle values of water on the surface of Si wafers (with top silica layer) covered by adsorbed PVP as a function of exposure time in a PVP water solution.     

Theoretical evaluation of nano- or microparticulate contact angle at fluid/fluid interfaces: analysis of the excluded area behavior upon compression

A novel method for the determination of the particle contact angle at the liquid/gas or liquid/liquid interface based on the excluded area concept revealed, in spite of its simplicity, some serious difficulties connected with the exact quantitative particle deposition at the interface and with changes in the particulate contact angle upon binary monolayer compression. The comprehensive theoretical consideration of the contact angle behavior made for such a system allowed considerable improvements: firstly, the prediction of direction of the particles' displacement at surface pressure increase is now possible and hence an unambiguous identification of particle hydrophobicity can be done. Secondly, the analytical relation describing the dependence of the particulate contact angle on the surface tension (surface pressure) was derived, allowing the prediction of whether or not particles of a given hydrophobicity will be expelled from the monolayer at certain surface pressure and of the area relinquished by the displaced particles. Thirdly, the transformation of this relation upon taking into consideration the initial conditions led to a linear dependence between excluded area and normalized surface tension allowing the determination of the particle contact angle and the exact number of deposited particles simultaneously and independently of each other. Finally, the application of the improved approach to the previously collected experimental data yielded reasonable values for both particle contact angle and number of deposited particles.     

Quantitative testing of robustness on superomniphobic surfaces by drop impact

The quality of a liquid-repellent surface is quantified by both the apparent contact angle θ(0) that a sessile drop adopts on it and the value of the liquid pressure threshold the surface can withstand without being impaled by the liquid, hence maintaining a low-friction condition. We designed surfaces covered with nanowires obtained by the vapor-liquid-solid (VLS) growth technique that are able to repel most of the existing nonpolar liquids including those with very low surface tension as well as many polar liquids with moderate to high surface tension. These superomniphobic surfaces exhibit apparent contact angles ranging from 125 to 160° depending on the liquid. We tested the robustness of the surfaces against impalement by carrying out drop impact experiments. Our results show how this robustness depends on Young's contact angle θ(0) related to the surface tension of the liquid and that the orientational growth of nanowires is a favorable factor for robustness.     

Low‐rate dynamic contact angles on poly(methyl methacrylate/ethyl methacrylate, 30/70) and the determination of solid surface tensions

Low‐rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/ethyl methacrylate, 30/70) P(MMA/EMA, 30/70) copolymer were measured by an automated axisymmetric drop shape analysis‐profile (ADSA‐P). It was found that five liquids yield nonconstant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining seven liquids, it is found that the liquid–vapor surface tension times cosine of the contact angle changes smoothly with the liquid–vapor surface tension (i.e., γ_l|Kv cos θ depends only on γ_l|Kv for a given solid surface or solid surface tension). This contact angle pattern is in harmony with those from other methacrylate polymer surfaces previously studied.^45,50 The solid–vapor surface tension calculated from the equation‐of‐state approach for solid–liquid interfacial tensions¹⁴ is found to be 35.1 mJ/m², with a 95% confidence limit of ± 0.3 mJ/m², from the experimental contact angles of the seven liquids. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2039–2051, 1999     

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.     

Droplet morphologies on particles with macroscopic surface roughness

The equilibrium configuration of liquid droplets on the surface of macroscopically rough solid particles was determined by numerical simulations using the volume-of-fluid (VOF) method. The fractional surface coverage of the particle as a function of the droplet size, equilibrium contact angle, and the particle surface roughness amplitude and correlation length has been systematically investigated. Droplet size and contact angle were found to generally have a stronger effect on surface coverage than particle surface roughness. Because of droplet coalescence, a relatively large variation in surface coverage was observed for any given total liquid volume, particularly for larger values of the equilibrium contact angle.     

Dynamical force and imaging characterization of superhydrophobic surfaces

We devised a dangling cantilever optical lever setup with imaging that permits dynamical studies of superhydrophobic surfaces without the effects of gravitational acceleration for better insight into the mechanics. The setup enabled us to ascertain liquid loss and ascribe it to the interaction of liquid that just touched the superhydrophobic surface as it translated at various constant lateral speeds. At lower speeds (20-60 μm/s), the interactions were characterized by a strong initial liquid pin (at up to 0.6 nN force) and depin followed by a series of smaller force pin and depins before sufficient liquid loss led to total liquid detachment from the surface. At higher translation speeds (80-100 μm/s), the interactions were characterized by liquid pinning and depinning processes at a sustained force (around 0.7 nN) in which liquid loss was low enough to engender a much later liquid detachment (beyond 100 s). A linear reduction of the receding contact angle with time, but not with the advancing contact angle, was found up to the point of first liquid depinning. This suggested a stronger role played by the receding contact line in establishing liquid adherence to the superhydrophobic surface. The detachment process from the surface was also characterized by a liquid bridge driven to rupture by way of liquid being conveyed away from the bridge.     

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.     

Influence of the work of adhesion on the dynamic wetting of chemically heterogeneous surfaces

The velocity dependence of the dynamic contact angle for a glycerol-water mixture wetting two different chemically heterogeneous surfaces (mixed thiols on gold and partially methylated titania, 16 samples in all) was studied. The molecular kinetic theory (MKT) of wetting was used to interpret the dynamic contact angle data. The equilibrium displacement frequency ( K 0) was predominantly determined by the viscous contribution from the bulk liquid, with a minor contribution from the surface. The mean distance between surface sites (lambda) decreased with increasing work of adhesion. The contact line friction coefficient zeta 0 was found to vary exponentially with the work of adhesion, enabling the unit flow volume of the liquid to be obtained.     

Thermoresponsive poly(N-isopropylacrylamide) copolymers: contact angles and surface energies of polymer films

Surface properties of poly(N-isopropylacrylamide) (PNIPAM) copolymer films were studied by contact angle measurements and optical and atomic force microscopy. We prepared a series of copolymers of N-isopropylacrylamide with N-tert-butylacrylamide (NtBA) in order of increasing hydrophobicity. The measurements of the advancing contact angle of water at 37 degrees C were hampered by the observation of a distinct stick/slip pattern on all polymers in the series with the exception of poly(NtBA) (PNtBA). We attributed this behavior to the film deformation by the vertical component of liquid surface tension leading to the pinning of the moving contact line. This was confirmed by the observation of a ridge formed at the pinned contact line by optical microscopy. However, meaningful contact (without the stick/slip pattern and with a time-independent advancing contact angle) angles for this thermoresponsive polymer series could be obtained with carefully selected organic liquids. We used the Li and Neumann equation of state to calculate the surface energy and contact angles of water for all polymers in the series of copolymers and van Oss, Chaudhury, and Good (vOCG) acid-base theory for PNtBA. The surface energies of the thermoresponsive polymers were in the range of 38.9 mJ/m2 (PNIPAM) to 31 mJ/m2 (PNtBA) from the equation of state approach. The surface energy of PNtBA calculated using vOCG theory was 29.0 mJ/m2. The calculated contact angle for PNIPAM (74.5 +/- 0.2 degrees ) is compared with previously reported contact angles obtained for PNIPAM-modified surfaces.     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

Comparison of contact angle hysteresis of different probe liquids on the same solid surface

Advancing and receding contact angles of water, formamide and diiodomethane were measured on 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on three different solid supports—glass, mica and poly(methyl methacrylate). Up to five statistical monolayers were deposited on the surfaces by spreading DPPC solution. It was found that even on five statistical DPPC monolayers, the hysteresis of a given liquid depends on the kind of solid support. Also on the same solid support the contact angle hysteresis is different for each probe liquid used. The AFM images show that the heights of roughness of the DPPC films cannot be the primary cause of the observed hysteresis because the heights are too small to cause the observed hystereses. It is believed that the hysteresis is due to the liquid film present right behind the three-phase solid surface/liquid drop/gas (vapour) contact line and the presence of Derjaguin pressure. The value of contact angle hysteresis depends on both the solid surface and liquid properties as well as on intermolecular interactions between them.