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Showing papers on "Sessile drop technique published in 2010"


Journal ArticleDOI
TL;DR: Stalder et al. as discussed by the authors proposed a new method based on the Young-Laplace equation for measuring contact angles and surface tension, which can be used to measure axisymmetric sessile drops.

563 citations


Journal ArticleDOI
TL;DR: This paper reviews the experimental progress made in the last few years, the theoretical framework required for modelling and understanding the relevant physico-chemical surface phenomena, and new containerless methods for surface tension measurements.

209 citations


Journal ArticleDOI
28 Oct 2010-Langmuir
TL;DR: The 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.
Abstract: The quality of a liquid-repellent surface is quantified by both the apparent contact angle θ0 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 θ0 related to the surface tension of the liquid and that the orientational growth of nanowires is a favorable factor for robustness.

107 citations


01 Jan 2010
TL;DR: In this article, a review and a direct comparison of the most widely used methods and testing liquids in order to re-evaluate their advantages and disadvantages is presented. And the limits of applicability of the examined methods are discussed.
Abstract: One of the parameters characterizing the surfaces of materials is the surface free energy. The most common way to determine its value is to measure the surface tension by the sessile drop method. In this case a contact angle between the surface and the edge of droplets of liquids is measured. There are various approaches to calculate the surface free energy from the contact angle measurements. We made a review and a direct comparison of the most widely used methods and testing liquids in order to re-evaluate their advantages and disadvantages. In the presented work we discuss the limits of applicability of the examined methods. We confirm that methods using a pair of liquids give results dependent on the liquids chosen. Using a pair of non-polar and polar liquid yielded most reliable results. This is even more clear when two-liquid method is transformed into a multiple-liquid method. The algorithms developed during the work will be implemented into liquid contact angle analysis software.

106 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a theoretical study of the evolution of a drop of pure liquid on a solid substrate, which it wets completely, and find that the drop radius goes to zero like R∝(t0−t)α, where α has value close to 1/2.
Abstract: We present a theoretical study of the evolution of a drop of pure liquid on a solid substrate, which it wets completely. In a situation where evaporation is significant, the drop does not spread, but instead the drop radius goes to zero in finite time. Our description couples the viscous flow problem to a self-consistent thermodynamic description of evaporation from the drop and its precursor film. The evaporation rate is limited by the diffusion of vapor into the surrounding atmosphere. For flat drops, we compute the evaporation rate as a nonlocal integral operator of the drop shape. Together with a lubrication description of the flow, this permits an efficient numerical description of the final stages of the evaporation problem. We find that the drop radius goes to zero like R∝(t0−t)α, where α has value close to 1/2, in agreement with experiment.

95 citations


Journal ArticleDOI
TL;DR: In this paper, a convection-diffusion model was developed to analyze the effect of buoyant convection in the surrounding air on heat and mass transfer phenomena during the evaporation of a pinned water drop deposited on a horizontal substrate of large dimensions.
Abstract: A convection-diffusion model is developed to analyze the effect of buoyant convection in the surrounding air on the heat and mass transfer phenomena during the evaporation of a pinned water drop deposited on a horizontal substrate of large dimensions. The substrate is maintained at constant temperature which can be equal or higher than the temperature of the ambient air. The mathematical model accounts for the motion of the gas phase surrounding the drop due to thermal and solutal buoyancy effects, while only thermal diffusion is considered in the liquid phase. A quasisteady state regime is adopted because of the slow motion of the liquid-gas interface as well as the induced heat and mass transfer phenomena in both phases. The numerical results obtained with the diffusion model or the convection-diffusion model show that heat and mass transfer rates are important toward the contact line. The heat required for evaporation process is taken from the environment, both the liquid and the gas phase, and results in a small cold zone on both sides of the interface. The influence of the buoyancy in air is of greater importance in the lower part of the interface and beyond a distance of a contact radius above the droplet. A weak variation of the evaporation rate is observed on a wider range of contact angle for high wall temperatures. The diffusion model underestimates the overall evaporation rate by 8.5% for a wall temperature equal to an ambient temperature of 25 ° C and by 27.3% for a wall temperature of 70 ° C . Numerical calculations show that the length of the heated wall has very little effect on the evaporation process when it exceeds 25 times the contact radius.

81 citations


Posted Content
TL;DR: In this article, the authors designed surfaces covered with nano-wires obtained by the vapor-liquid-solid (VLS) growth technique, that are able to repel most of the existing non-polar liquids including those of very low surface tension, as well as many polar liquids of moderate to high surface tension.
Abstract: The quality of a liquid-repellent surface is quantified by both the apparent contact angle $\theta_0$ 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 keeping a low-friction condition. We designed surfaces covered with nano-wires obtained by the vapor-liquid-solid (VLS) growth technique, that are able to repel most of the existing non-polar liquids including those of very low surface tension, as well as many polar liquids of moderate to high surface tension. These super-omniphobic surfaces exhibit apparent contact angles ranging from 125 to 160$^{\circ}$ 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 the Young's contact angle $\theta_0$ related to the surface tension of the liquid, and that the orientational growth of NWs is a favorable factor for robustness.

79 citations


Journal ArticleDOI
TL;DR: In this article, a sessile drop method was used to estimate the modified contact angle of pure Mg droplets on pure Ti substrate, taking the morphological changes of the droplet outline due to the evaporation into consideration.

75 citations


Journal ArticleDOI
TL;DR: The crystalline and amorphous forms of CLB exhibited disparate surface milieu, which in turn can have implications on the surface mediated events.

74 citations


Journal ArticleDOI
TL;DR: A high level of surface heterogeneity on the native mannitol crystal surfaces is reported, showing that both IGC and contact angle techniques are able to detect surface chemical variations and detailed surface energetic distribution.

73 citations


Journal ArticleDOI
TL;DR: In this paper, paper samples were rendered superhydrophobic with Alkyl Ketene Dimer using (1) airblasting with cryo ground micro particles, (2) crystallizing from organic solvents and (3) spraying with Rapid Expansion of Supercritical Solutions (RESS) technique.
Abstract: Paper samples were rendered superhydrophobic with Alkyl Ketene Dimer using (1) Airblasting with cryo ground micro particles, (2) crystallizing from organic solvents and (3) spraying with Rapid Expansion of Supercritical Solutions (RESS) technique. The papers were characterized using Scanning Electron Microscopy, contact angle to water measurements and X-ray Photoelectron Spectroscopy (XPS). Advancing contact angles were in the region of 150°–160° and receding contact angles were in the region of 110°–130°. Diagrams showing the drop base diameter vs. the contact angle when water is pumped into, and then withdrawn from, a sessile drop show that a stick slip pattern is present in the advancing phase for a non coated internally sized paper. Papers rendered superhydrophobic with the RESS technique showed a much less pronounced stick slip pattern in the advancing phase but still a stick slip pattern in the receding phase.

Journal ArticleDOI
TL;DR: In this article, a systematic study of the wetting behavior of two Ni-based and one Co-based superalloys, used, in particular, for the fabrication of turbine blades, is presented with reference to different ceramic substrates: sapphire, polycrystalline alumina, zirconia, and mullite.
Abstract: In this work, a systematic study of the wetting behavior of two Ni-based and one Co-based superalloys, used, in particular, for the fabrication of turbine blades, is presented with reference to different ceramic substrates: sapphire, polycrystalline alumina, zirconia, and mullite. Wettability tests have been performed by means of the “sessile drop” method at 1500 °C; the characterization of the interfaces between the molten drop and the substrates has been performed by SEM/EDS analysis in order to check the final characteristics of the solidified interfaces. The results are discussed in terms of chemical interactions in relation to the processing parameters and as a function of the surface and interfacial, morphological and energetic properties of the systems.

01 Jan 2010
TL;DR: Williamsa and Nesselrodea as discussed by the authors proposed a half-angle method to measure the sessile contact angle formed by a droplet of liquid placed on a horizontal surface.
Abstract: The measurement of the contact angle formed by a droplet of liquid placed on a horizontal surface – the so-called sessile drop – has been of interest to scientists and others for at least 200 years, since Young first reported his observations [1]. From this parameter, much valuable information can be calculated, notably surface energy values. These in turn can provide information on surface contamination or the wettability of a surface [2]. For this reason, the measurement of contact angles is of importance in a wide range of scientific and technological fields, including medicine, surface science, surface engineering, and industries producing inks and coatings for plastics and textile goods as described by Adamson [3], Hansen [4], Zisman, and coworkers [5]. The earliest measurements, such as that of Young, used a protractor or a similar graduated scale for measuring the angle. Various other techniques were developed, such as the so-called half-angle method, discussed below. The assumption that the sessile drop was spherical, or formed part of a sphere, underpinned the basis of these methods wherein the contact angle values were computed using the principles of Euclidian geometry. The two most widely-used such methods were: – Constructing a tangent by drawing a line orthogonal to the drop radius that intersects the point of contact with the horizontal surface – the triphase point; – The so-called half-angle method uses a line drawn from the triphase point to the apex of the circle (Fig. 1). This is of course valid only for perfect circles. Over the years, there have been modest advances, notably US Patent 5,268,733 where an image of the drop is projected onto a protractor screen [6]. Rather than being calibrated in degrees, the screen is calibrated at half-scale. The protractor can be moved to the triphase point, and the trace that intersects the apex will give the contact angle. This approach is inherently imprecise since the apex is a flat region covering a range of angles. There have also been several specialized advances customized for production-line environments [7]. Computerised Measurement of Contact Angles By Darren L. Williamsa, Anselm T. Kuhnb, Mark A. Amanna, Madison B. Hausingera, Megan M. Konarika and Elizabeth I. Nesselrodea

Journal ArticleDOI
03 Jun 2010-Langmuir
TL;DR: The results of this study indicate that surface energy is an important physical parameter that should be considered as a basic characterization property of fullerene nanomaterials.
Abstract: The underlying mechanisms of fullerene-fullerene, fullerene-water, and fullerene-soil surface interactions in aqueous systems are not well understood. To advance our understanding of these interfacial interactions, the surface properties of Buckminsterfullerene (C60) and quartz surfaces were investigated. From application of the van Oss-Chaudhury-Good model and the Young-Dupre equation, the Lifshitz-van der Waals, acid-base, and the total surface energies of C60 powder and quartz surfaces were calculated from contact angle measurements using the sessile drop technique. C60 powder measurements indicate low to medium energy surfaces of 41.7 mJ/m2 with a dominant Lifshitz-van der Waals component. In aqueous systems, hydrophobic attraction due to the high cohesion of water is the driving force for C60 aggregation. The high free energy of hydration (DeltaG(pw)(total) = -90.5 mJ/m2) indicates the high affinity of C60 particles for water. Hamaker constants of 4.02 x 10(-21) J (A(pwp)) and 2.59 x 10(-21) J (A(pws)) were derived for C60-C60 and C60-quartz interactions in aqueous systems. The results of this study indicate that surface energy is an important physical parameter that should be considered as a basic characterization property of fullerene nanomaterials.

Journal ArticleDOI
TL;DR: In this paper, a set of shape mode equations is derived to describe unsteady motions of a sessile drop actuated by electrowetting, and a modified boundary condition is obtained by combining the contact angle model and the normal stress condition at the surface.
Abstract: A set of shape mode equations is derived to describe unsteady motions of a sessile drop actuated by electrowetting. The unsteady, axially symmetric, and linearized flow field is analyzed by expressing the shape of a drop using the Legendre polynomials. A modified boundary condition is obtained by combining the contact angle model and the normal stress condition at the surface. The electrical force is assumed to be concentrated on one point (i.e., three-phase contact line) rather than distributed on the narrow surface of the order of dielectric layer thickness near the contact line. Then, the delta function is used to represent the wetting tension, which includes the capillary force, electrical force, and contact line friction. In previous work [J. M. Oh et al., Langmuir 24, 8379 (2008)], the capillary forces of the air-substrate and liquid-substrate interfaces were neglected, together with the contact-line friction. The delta function is decomposed into a weighted sum of the Legendre polynomials so that e...

Journal ArticleDOI
TL;DR: In this article, the surface and interfacial properties of a proposed lead-free solder material, the In-31.6Bi-19.6Sn system, were studied on a copper substrate at different reflow temperatures.

Journal ArticleDOI
TL;DR: In this paper, the surface tension and density of three liquid AlTi-based alloys (AlTiV, AlTiNb, and AlTiTa) have been measured using electromagnetic levitation as a tool for containerless processing.
Abstract: The surface tension and density of three liquid AlTi-based alloys (AlTiV, AlTiNb, and AlTiTa) have been measured using electromagnetic levitation as a tool for containerless processing. Surface tension has been determined by the oscillating-drop method, while the density was measured using a shadowgraph technique. Both quantities were determined over a wide temperature range, including the undercooled regime. In addition, sessile-drop and pendant-drop experiments to determine the surface tension were performed in a recently built high-temperature furnace. The measured data were compared to thermodynamic calculations using phenomenological models and the Butler equation. Generally, good agreement was found.

Journal ArticleDOI
TL;DR: A stability limit for the superhydrophobic-to-impregnated transition is given and Laplace's law is probed for the menisci on the micrometre scale.
Abstract: We have studied the microscopic shape, contact angle and Laplace law behavior of the liquid–gas interfaces at a superhydrophobic surface. A superhydrophobic surface is immersed in water, and the radius of liquid gas menicsi that span between adjacent ridges of the surface texture is measured. The surface pattern consists of rectangular grooves, such that the sample is simultaneously an optical grating. The diffraction properties encode the shape of the menisci. The shape of the menisci is determined by measuring the intensity of several diffraction orders as a function of the incident angle, and fitting the data to numerical calculations of the diffraction. The uncertainty of the determined menisci deflections is a few nanometres. Observing the deflection as a function of externally controlled hydrostatic pressure, Laplace's law is probed for the menisci on the micrometre scale. The microscopic contact angle is determined by measuring the radius of the menisci prior to collapse. Close agreement with the macroscopic Young angle is found. A stability limit for the superhydrophobic-to-impregnated transition is given. The measurement is a microscopic analogue of ‘bubble’ and ‘sessile drop’ type methods.

Journal ArticleDOI
TL;DR: In this paper, the effects of Si-graphite interactions on graphite mechanical integrity are also evidenced by varying the temperature, the type of graphite (porosity, grain size) and the vapour phase (inert gas or high vacuum).
Abstract: The capillary properties (wetting, infiltration) of the reactive Si/porous graphite system are studied by the sessile drop technique that enables the spreading and infiltration dynamics to be monitored in situ. The experiments are performed by varying the temperature, the type of graphite (porosity, grain size) and the vapour phase (inert gas or high vacuum). Further experiments are performed in order to quantify the influence of the exothermic reaction between Si and graphite on the temperature field close to the infiltration front. The effects of Si-graphite interactions on graphite mechanical integrity are also evidenced.

Journal ArticleDOI
C. Sperandio1, J. Bardon, Abdelghani Laachachi, H. Aubriet, David S. Ruch 
TL;DR: In this article, the influence of an aluminium surface treatment on the interphase formation and adhesive bond strength was investigated by means of X-ray energy dispersion spectrometer (EDS) in a low vacuum scanning electron microscopy (LVSEM).

Journal ArticleDOI
TL;DR: In this paper, the interfacial tension between molten slags and solid Fe was investigated to understand the effect of the ionic structure of molten slag, by using solid Fe instead of molten steel.
Abstract: Interfacial tension is an important property that plays an essential role in understanding wetting behavior between refractories–molten slag–steel in the steelmaking process. Most work on interfacial tensions of molten slag system have been done to clarify the effect of surface active elements in molten metal and slag composition, but there has been little work done with respect to the slags ionic structure. In this study, the interfacial tension between molten slag and solid Fe was investigated to understand the effect of the ionic structure of molten slag on interfacial tension by using solid Fe instead of molten steel. Interfacial tension measurements in CaO–SiO2–FeO and CaO–SiO2–MnO slags were carried out at 1,773 K on interstitial free (IF)-steel substrates using the sessile drop method. The composition of the slag was varied with amphoteric oxides of either FeO or MnO at unit basicity (C/S = 1.0). Results indicated a decrease in the interfacial tension with increased amphoteric oxide additions. The ionic species of molten slags were analyzed by FT-IR and the various types of oxygen ions (O2−, O−, O0) in the slag was determined by X-ray photoelectron spectroscopy. The silicate bonding degree and the slags ionic behavior were semi-quantitatively analyzed with respect to the slag’s ionic structure model. By dissociating the slags networking structure with increased free oxygen ions, the interfacial tension decreased. Considering the ionic theory of molten slags, results indicate that the interfacial properties are directly affected by the ionic structure of the slag. This work hopes to clarify the relationship between the interfacial tension and the distribution of various oxygen ions.

Journal ArticleDOI
01 Oct 2010-Langmuir
TL;DR: Empirical correlations for the surface tension and the contact angle of the suspension as a function of microbead volume fraction are proposed and can readily be used to develop mechanistic models for the capillary transport of microBead suspensions related to LOC applications.
Abstract: 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.

Journal ArticleDOI
01 Jun 2010-Langmuir
TL;DR: It is shown that an exponential distribution of the displacement fluctuation arises due to the nonlinear hysteresis term in the Langevin equation, and this result indicates that the fluctuation of displacement may be used as a tool to study the surface property of a low energy substrate.
Abstract: Relaxation of the three phase contact line of a sessile drop of water on a low energy surface is studied by subjecting it to a white noise vibration. While a spring force acts on the contact line w...

Journal ArticleDOI
Longlong Yang1, Ping Shen1, Qiaoli Lin1, Feng Qiu1, Qi-Chuan Jiang1 
TL;DR: In this article, the isotherm wetting of porous graphite substrates by the molten Cu-Ti alloys with 1, 3, 4 and 5 at.% Ti was investigated at 1373 K in a flowing Ar atmosphere using a modified sessile drop method.

Journal ArticleDOI
TL;DR: In this article, the Si3N4 porous coating constitutes a barrier to wetting and infiltration due to the presence of a nonwettable SiO2 layer on nitride particles.

Journal ArticleDOI
TL;DR: In this article, a simple model is proposed to describe temporal dynamics both the shape of the drop and the volume fraction of the colloidal particles inside the drop, and the concentration dependence of the viscosity is taken into account.
Abstract: Using lubrication theory, drying processes of sessile colloidal droplets on a solid substrate are studied. A simple model is proposed to describe temporal dynamics both the shape of the drop and the volume fraction of the colloidal particles inside the drop. The concentration dependence of the viscosity is taken into account. It is shown that the final shapes of the drops depend on both the initial volume fraction of the colloidal particles and the capillary number. The results of our simulations are in a reasonable agreement with the published experimental data. The computations for the drops of aqueous solution of human serum albumin (HSA) are presented.

Journal ArticleDOI
TL;DR: In this article, a comparative discussion on the results obtained for the surface tension of Ti-Al-Nb and TiAl-Ta alloys, together with corresponding theoretical values calculated by thermodynamic models are presented.
Abstract: Within the Integrated Project IMPRESS, funded by the EU, a concerted action was taken to determine the thermophysical properties of a γ-TiAl-based alloys, suitable for casting of large turbine blades for aero-engines and stationary gas turbines. The challenge was to develop a castable alloy, free of grain refiners and susceptible to heat treatment. Owing to the high reactivity of this class of alloys, many difficulties were encountered to process the liquid phase in a crucible. This prevented also the measurements of specific heat, viscosity and electrical conductivity in the liquid phase. However, surface tension and density could be measured using container-less techniques. For the surface tension determination, both the oscillating droplet method by the electromagnetic levitation as well as a combined method using two methodologies in one test (i.e. the pendant drop and sessile drop) by an advanced experimental complex that has been designed for investigations of high temperature capillarity phenomena were applied. All the quantities have been obtained as a function of temperature, in some cases also in the undercooled liquid. In this article, we report a comparative discussion on the results obtained for the surface tension of Ti–Al–Nb and Ti–Al–Ta alloys, together with the corresponding theoretical values calculated by thermodynamic models.

Journal ArticleDOI
TL;DR: In this paper, the sessile drop technique has been used to measure the temperature dependence of the contact angle, θ, of the liquid metals Ag and Cu in contact with polycrystalline yttrium oxide (yttria, Y2O3) at the temperature range 1,333-1,773 K in Ar/4%H2 atmosphere.
Abstract: The sessile drop technique has been used to measure the temperature dependence of the contact angle, θ, of the liquid metals Ag and Cu in contact with polycrystalline yttrium oxide (yttria, Y2O3) at the temperature range 1,333–1,773 K in Ar/4%H2 atmosphere. Combination of the experimental results with literature data taken for nonwetted and nonreactive oxide/liquid metal systems permit the calculation of the surface energy of Y2O3 as γsv (J/m2) = 2.278–0.391 × 10−3 T. For the same atmospheric conditions, thermal etching experiments on the grain boundaries intersecting the surface of the polycrystalline ceramic allow to determine the groove angles, ψ, with respect to temperature and time as well as the grain-boundary energy of Y2O3 as γss (J/m2) = 1.785–0.306 × 10−3 T. Grain-boundary grooving studies on polished surfaces of Y2O3 annealed in Ar/4%H2 atmosphere between 1,553 K and 1,873 K have shown that surface diffusion is the dominant mechanism for the mass transport. The surface diffusion coefficient can be expressed according to the equation Ds (m2/s) = 1.22 × 10−3 exp(−343554/RT).

Journal ArticleDOI
TL;DR: The surface modification of PMMA with a CO2 laser in order to vary the wettability characteristics was investigated by generating a number of patterns of various topography on the surface using the CO2-laser.

Journal ArticleDOI
15 Mar 2010
TL;DR: A theory, based on the presence of an adsorbed film in the vicinity of the triple contact line, provides a molecular interpretation of intrinsic hysteresis during the measurement of static contact angles.
Abstract: A theory, based on the presence of an adsorbed film in the vicinity of the triple contact line, provides a molecular interpretation of intrinsic hysteresis during the measurement of static contact angles. Static contact angles are measured by placing a sessile drop on top of a flat solid surface. If the solid surface has not been previously in contact with a vapor phase saturated with the molecules of the liquid phase, the solid surface is free of adsorbed liquid molecules. In the absence of an adsorbed film, molecular forces configure an advancing contact angle larger than the static contact angle. After some time, due to an evaporation/adsorption process, the interface of the drop coexists with an adsorbed film of liquid molecules as part of the equilibrium configuration, denoted as the static contact angle. This equilibrium configuration is metastable because the droplet has a larger vapor pressure than the surrounding flat film. As the drop evaporates, the vapor/liquid interface contracts and the apparent contact line moves towards the center of the drop. During this process, the film left behind is thicker than the adsorbed film and molecular attraction results in a receding contact angle, smaller than the equilibrium contact angle.