From Contact Line Structures to Wetting Dynamics | Langmuir

Invited Feature Article pubs.acs.org/Langmuir

Cite This: Langmuir XXXX, XXX, XXX−XXX

From Contact Line Structures to Wetting Dynamics Hao Wang*

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The Laboratory of Heat and Mass Transport at Micro-Nano Scale, College of Engineering, Peking University, Beijing 100871, China ABSTRACT: An important reason for the century-long debate concerning wetting dynamics is the lack of decisive information about the contact line. The contact line cannot be treated as a geometric line but is rather a region with complex structures. The contact line regions have been intensively explored in recent years by utilizing advanced nanoscopic experimental and modeling methods. This feature article summarizes the primary observation results and related modeling progress. A framework is then proposed for understanding the wetting dynamics. Basic questions are raised for future research on the partial wetting of nonvolatile as well as volatile liquids.

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INTRODUCTION Wetting occurs when a liquid encounters a solid surface. The physics of wetting involves fluid dynamics and interfacial science, with wetting dynamics critically impacting small-scale liquid systems such as coatings, underground fluids, phasechange heat transfer, nanoassemblies, tribology, and various biological processes.1−7 Wetting involves many factors. Early studies assumed that wetting was determined by the adhesion interactions within the liquid−solid contact area. However, as reviewed by Extrand in 2016,8 there is now ample evidence showing that wetting is controlled by interactions in the contact line region where the liquid front meets the solid surface. The contact line provides the critical boundary conditions for the liquid domain, including the contact angle and the wetting speed. Young in 18059 treated the contact line as a 1D line where the interfacial tensions balanced each other. The drawback of this model is apparent in that the contact line must have multiple speeds when moving, which along with the Newtonian and incompressible fluid assumptions leads to the infinite-stress singularity at the moving contact line. Huh and Scriven raised the paradox in 1971.10−12 Actually, Moffatt in 1964 had noted that when a fluid particle on the liquid surface turned the corner at the contact line, the no-slip boundary condition would enforce its speed to instantaneously increase to the solid surface speed, which would require an infinite acceleration.12,13 Consensus was soon reached regarding the necessity of treating the contact line as a region rather than a line.14 Various hypotheses and theories have been proposed regarding the motion mechanism (molecule replacement, jumping, interface rolling, etc.), the relieving of the hydrodynamic singularity (slip, disjoining pressure, diffusion, phase change, etc.), and the contact angle deviation (hydrodynamic viscous bending, friction, disjoining pressure, etc.).15 Theories. Briefly, Blake and Haynes in 1969 modeled the moving contact line as a process of molecular desorption and adsorption on the substrate to develop the molecular kinetics © XXXX American Chemical Society

theory (MKT). For liquid advancing, the dynamic apparent contact angle, θD, was coupled to the moving speed, U,16 ÅÄÅ ÑÉ Å γ(cos θs − cos θD)λ 2 ÑÑÑ ÑÑ U = 2κ 0λ sinhÅÅÅÅ ÑÑ ÅÅÅ 2kBT ÑÑÖ (1) Ç where the fitting parameters were the microscopic molecular displacement distance, λ, the jump frequency, κ0, and sometimes the static contact angle, θs. The equation can also be regarded as a balance of the surface tension driving force, γ(cos θs − cos θD), and the local friction force.17 There have been many hydrodynamic analyses of contact lines. Dussan and Davis established a well-posed boundaryvalue fluid mechanical problem for a moving contact line14 and contributed to the formalization of the idea of the interface rolling on the solid,10 with analyses of the sensitivity of the overall flow field to the form of the slip boundary condition.18 The model assumed that in the liquid domain closest to the contact line (i.e., the inner region), the hydrodynamic analyses could break down.19 By truncating the inner region, Voinov20 in 1976 obtained the solution for the hydrodynamic viscous bending. The film profile varies to make the capillary pressure balance with the the pressure change due to the viscous flow, such that for an advancing liquid, ij L yz Uμ θD3 − θm 3 = 9Ca lnjjj zzz, Ca = jL z γ k m{

(2)

in which Lm is the scale of the inner region where the microscopic contact angle, θm, is established, μ is the dynamic viscosity and γ is the liquid surface tension. The hydrodynamic viscous bending was assumed to have a concave profile, which made the apparent dynamic angle, θD, larger than the Received: January 30, 2019 Revised: May 30, 2019 Published: May 31, 2019 A

DOI: 10.1021/acs.langmuir.9b00294 Langmuir XXXX, XXX, XXX−XXX

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Invited Feature Article

Table 1. Sketches of Some Physical Hypotheses for Advancing Contact Lines of Partial-Wetting Systems

microscopic contact angle, θm, as illustrated in Table 1. Then, in 1986, Cox presented a comprehensive analysis of three regions of expansion: the inner region where the hydrodynamic analyses broke down, the intermediate region where the hydrodynamic viscous and capillary effects were significant, and the outer bulk region. At high Ca, the intermediate region experienced significant viscous dissipation with the hydrof (β , ε) =

dynamic viscous bending solution obtained. For an advancing liquid, ji L zy g (θD , ε) − g (θm , ε) = Ca lnjjjj zzzz, where g (θ , ε) = k Lm {

∫0

θ

1 dβ f (β , ε)

(3)

where ε is the dynamic viscosity ratio of the receding gas to the advancing liquid and

2 sin β{ε 2(β 2 − sin 2 β) + 2ε[β(π − β) + sin 2 β ] + [(π − β)2 − sin 2 β ]} ε(β 2 − sin 2 β)[(π − β) + sin β cos β ] + [(π − β)2 − sin 2 β ](β − sin β cos β)

The solution was similar to Voinov’s equation (eq 2). When θD < 135° and the gas viscosity is negligible such that ε ≪1, the g function is approximately θ3/9 such that eq 3 is approximately equal to eq 2. At low Ca, eq 3 gives θD ≈ θm and the intermediate region dissipation is negligible compared to the dissipation in the inner region. Thus, only the inner region affects the dynamic contact angle changes. The MKT might be considered to be a low Ca case of Cox’s analysis since the film profile was assumed not to bend so that θD ≈ θm, as illustrated in Table 1. The microscopic contact angle, θm, was a boundray condition for eqs 2 and 3. Cox’s three-region analysis allowed the dissipation in the inner region; thus, θm could be

dependent on U. However, because of the extreme lack of information about the inner region, θm has been simply assumed to be independent of U in many hydrodynamic considerations.17,19−22 This assumption has now been shown to be invalid, as summarized in the following sections. The MKT can be used to describe the inner region which Petrov used to develop a combined model using the MKT to determine θm for eq 3. Various hypotheses have been proposed for the inner region besides the MKT. One is the tank-tread rolling motion of the liquid surface.10,23 Shikhmurzaev proposed that the surface tension varied when approaching the contact line, as illustrated in Table 1.24 de Gennes25 proposed surface bending due to the long-range intermolecular B


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found to be as much as 60% of the substrate speed near the contact line and persisted as far as 10 μm from the contact line. The slip length was found to be approximately 5 μm when using flood illumination and approximately 500 nm when using total internal reflection fluorescence (TIRF) illumination. Besides the film profile and flow field, interface-sensitive sum frequency generation (SFG) spectroscopy has been used to detect changes in the molecular structures of confined liquids. The results show crystalline-like ordering at the moving contact line,51 which would greatly impact the local viscosity as discussed later in the section on Practical Modeling. Electron microscopy, including environmental scanning electron microscopy,56,57 wet scanning transmission electron microscopy,58−60 transmission electron microscopy,61,62 and environmental transmission electron microscopy,63 has also been widely used in wetting studies. Such studies focused on the overall features of the nanoliquids such as the growth, pinning, and transport of nanodroplets. Many studies have been performed in ultrahigh vacuum. For instance, in situ environmental transmission electron microscopy was used to observe liquids flowing along the outer surface of solid nanowires as a nanoprecursor film.64 Liquid metals at high temperature and under high vacuum have also been studied,65,66 mostly with surface reactions. The vacuum studies provided an important window for understanding wetting with the gas domain eliminated. Air entrainment experiments67,68 have indicated that the gas domain may be important. Atomic force microscopy (AFM) methods have also been used to measure the film profile. The tapping mode (i.e., the intermittent contact mode) has been applied to soft surfaces such as cells and liquids.69−71 The film structures at the contact line have been measured and compared to optical results for the apparent contact angle.72 Pioneering measurements on moving contact lines were carried out on advancing contact lines by Chen et al.40 and on receding contact lines by Deng et al.73 Their resolution was as good as 1 to 3 nm on partially wetting contact lines. Even though the measurements were for only low-speed cases, the results still shed light on the contact line structure. Measurements on volatile liquids were then carried out for equilibrium74 and phase-change states.75,76 Precursor and residual nanofilms beyond the contact line were detected for partially wetting systems. The AFM force curve method was also used such that the tip did not scan across the sample surface but approached perpendicular to and penetrated the liquid film. Different probes with different spring constants were used to give a comprehensive evaluation of the nanofilms.73,75,76 This feature article summarizes contact line structure discoveries in recent nanoscopic explorations, first on nonvolatile and then on volatile liquids. The discussion focuses on partially wetting systems with macroliquid droplets on solids with nanoscale roughness. The liquids were simple, pure Newtonian liquids that did not react with the substrate. The wetting mechanisms and modeling are discussed, with questions for future research posed.

forces. Additional studies have addressed the intermolecular forces at the contact line using disjoining pressure theory and microscopic simulations.13,26−31 For volatile liquids, the contact line physics is even more complicated. There have been many experimental studies of menisci and film evaporation with the modeling being very challenging whenever it involves the contact line. Most theoretical studies have been limited to the static and complete-wetting cases where the liquid film was rather flat and thick. Many have tried to model steady contact lines on isothermal surfaces using continuum mathematical models based on the lubrication approximation and the dispersion component of the disjoining pressure.4,32,33 Limited theoretical studies focused on partial-wetting systems, and the results vary considerably.34−38 The Marangoni effect is also an issue for volatile systems. Qu et al.39 suggested that the existence of both evaporation and Marangoni flow prevented simple scaling of the system. A few theoretical discussions have been presented, but only for complete wetting.5 Experiments. The biggest challenge in contact line research is that “It is difficult to model a phenomenon for which there has been very little direct experimental measurements.”14 The inner region is no more than tens of nanometers high, while the optical resolution of most instruments is usually no better than 100 nm due to the light wavelength limitation. Thus, models can be evaluated against experimental data only for the apparent dynamic contact angle, which is far from efficient.15,17,42 Many studies have sought to develop better tools for nanoscale exploration of the contact line region. Improved optical methods have been developed, such as ellipsometry, that can measure the thickness of the adsorbed film of various vapors over various substrates.43 Ellipsometry has been used with interferometry to detect the precursor film in front of a spreading droplet in the complete wetting regime.44,45 A reflecting light microscope with an electrooptically phase-shifting laser feedback interferometer was used to show that the precursor length decreased with increasing U.45 Reflectometry was used to measure a complete-wetting thin film profile.46 A Shack−Hartmann sensor was used for higher-speed measurements over larger areas.47 However, most optical measurements have been on rather flat, thin films. Measurements on partially wetting films are more difficult because of the sharp profile change at the contact line. Reflection interference contrast microscopy with a lateral resolution of about 200 nm is applicable to small contact angle films.48 The interferometry image analysis technique was improved for contact angle measurements of condensing droplets in a vapor chamber.49,50 A thickness resolution of 10 nm was achieved using an optical interferometry method.51 The flow field near the contact line has also been measured. Particle image velocimetry (PIV) was used to make simultaneous measurements of the interface shape and the velocity field near a moving interface with the velocity vectors calculated from several hundred micrometers to as close as 30 μm from the contact line.52 Then, a micro PIV system was used to show an interesting recirculation zone within 20 μm of the contact line and less than 5 μm from the wall.53 A subregion measurement method was developed from an evanescent-wave-based multilayer nanoparticle image velocimetry technique.54 Recently, two particle-tracking velocimetry techniques55 were used for both receding and advancing contact lines for capillary numbers on the order of 10−5 and Reynolds numbers on the order of 10−3. The slip velocity was

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CONTACT LINE STRUCTURES Nonvolatile Liquids. Quite a few AFM studies of static liquid droplets with contact diameters from tens of micrometers to several millimeters have confirmed that the film profile at the contact line is the same as that of the intrinsic interface (i.e., it follows the bulk curvature up to the measurement resolution limit of 1 to 3 nm).40,72 Because the

C


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Figure 1. Typical film structures for nonvolatile partially wetting liquids detected after low-speed receding contact lines (a) adapted with permission from ref 73, copyright 2016 American Chemical Society and advancing contact lines (b) adapted with permission from ref 40, copyright 2014 American Chemical Society. In these experiments, Ca < 10−6 and Re < 10−7. The residual nanofilm in (a) had a greater chance to appear with better wettability.

droplets were large and thus the bulk interface curvatures were small, the film profile appeared to be straight without significant curvature in a submicrometer viewing window. Measurements on natural sand rocks showed that the local angles differed along the contact line because of surface heterogeneities, but for each location, the film profile near the contact line was still nearly straight.77 A few studies have used the disjoining pressure concept to propose that surface force bending should occur at the contact line as shown in Table 1.25,74 However, the predicted scale of the bending was very close to the measurement limit.74 Therefore, the measurements do not prove or disprove the existence of the surface force bending. The film profile was found to be straight down to the contact line in a submicrometer viewing window for a receding contact line with a low Ca. A typical result is shown in Figure 1a, adopted from Deng et al.73 The microscopic angle was about equal to the apparent contact angle, falling within Cox’s two-region analysis predictions which neglected hydrodynamic viscous bending in the intermediate region. The angle significantly decreased with receding U, indicating the role of local friction at the contact line. Meanwhile, there may be residual nanofilms with thicknesses of usually less than 10 to 20 nm remaining after the contact line depending on the wettability. Various tested systems73,78 always had a residual nanofilm when the equilibrium contact angle was less than 20°, with no film for contact angles larger than 50° and some films for contact angles of between 20 and 50°. In 2002, similar films were observed by Qu et al.39 in dipping coating experiments, but only for volatile liquids. They were referred to as precursor films but may be more accurately referred to as residual nanofilms because the films remained after the receding contact line and did not appear with advancing or static contact lines for nonvolatile liquids. The residual nanofilm modified the solid surface properties. There was no direct evidence, but the contact line could be sliding on this nanofilm to recede, which relaxes the shear stress at the receding contact line because the finite nanofilm thickness indicates a finite velocity gradient across the film thickness. Thus, a receding contact line may not be the simple reverse action of an advancing contact line and thus may not be described by the same set of equations.

It is well known in the coating industry that a receding contact line that exceeds a critical speed has a contact angle that is close to zero and deposits a several-micrometer-thick macroscopic film on the solid due to viscous drag.79−81 This macroscopic film differs from a residual nanofilm. The residual nanofilm occurs only on a well-wetted surface while the macroscopic films occur on all kinds of surfaces. Also, the residual nanofilm appears at very low speeds when the contact angle is close to the static angle, while the macroscopic film needs a high Ca. Recall that Qu et al.’s measurements of dipcoated films formed by withdrawing the substrate from the liquid reservoir39 left a micrometer-thick macroscopic residual film when the speed made the apparent contact angle about 1°. A precursor nanofilm appeared at the contact line at the tip of the macroscopic film when the liquid was the least viscous (nominal kinematic viscosity 0.65 cSt) and most volatile. Therefore, a two-tiered film structure appeared with the macrofilm coexisting with the residual nanofilm at high Ca. A sketch of the two-tiered structure is shown in the graphical abstract. Some residual nanofilms can have a uniform thickness which increases with increasing receding U, for example, PEG on silicon wafers.73,78 Teletzke et al.82 theoretically predicted the residual nanofilm thickness and qualitatively predicted that at slow speeds the film would be dominated by the disjoining pressure only, thus its thickness, on the nanoscale, was independent of U. However, at high speeds, the film would be much thicker as a result of viscous forces, which was consistent with experimental results with PEG on a silicon wafer. However, the residual nanofilm can also be nonuniform and rupture into patterns. Liu et al. investigated the criteria for the formation of a residual film and it remaining stable on the substrate.78 The Hamaker constant was identified as an important parameter. The literature has extensive discussions about the dewetting film stability, with most studies concerning initially uniform polymer films.83,84 There can be different hole-opening modes on the film such as spinodal dewetting, heterogeneous nucleation, and thermal (homogeneous) nucleation. After hole opening, the process could be hole growth, combinations to form ribbons, or the decay of ribbons into droplets. Fluctuations may also occur, and the rim may become unstable and form fingers. In 2002, Becker et al.85 developed a thin-film equation and modeled the full spatial− D


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Figure 2. Evaporating contact line of partially wetting liquids: (a) Schematic diagram, adapted with permission from ref 76. Copyright 2018 Elsevier. (b) The evaporating nanofilm beyond the contact line explained the abnormally high heat flux of nanopore evaporation, which was reduced to below the theoretical limit once the outer surface became hydrophobic. Adapted with permission from ref 96. Copyright 2019 American Chemical Society.

temporal evolution of a polymer film rupture that was in quantitative agreement with experiments using a wellcontrolled flat film as the initial condition. The effective interface potential for the system consisted of a short-range component besides the long-range dispersion component represented by the Hamaker constant. The results showed that a change in the initial film thickness of only 1 nm could cause a significant difference in the evolution dynamics, which might explain the diversity of the film patterns. Note that Becker et al.’s initial condition was a well-controlled flat film. The residual nanofilms of macrodroplets observed by Deng et al.73 are much more complicated. Advancing contact lines, in contrast to static or receding contact lines, have convex nanobending rather than a straight profile at the contact line.40 As illustrated in Figure 1b, the convex nanobending has a shoe-tip-like bending region with a thickness of around 20 nm.40 The bending profile and the microscopic contact angle at the root of the profile vary with U. The nanobending is convex, which is similar to the prediction of de Gennes et al.25 based on the long-range intermolecular forces as illustrated in Table 1. However, the scale is much larger than predicted, which gives a bending thickness of only σθ−1, where σ is the molecular size. Moreover, the observed nanobending increases with higher U and vanishes for a static contact line, which differs from their prediction that the bending would not vanish because the surface force always existed. Kuchin and Starov29,30 also studied the film profile using surface forces. The disjoining pressure isotherm included electrostatic, intermolecular, and structural components. Similar convex bending was observed for the contact line with a microscopic advancing motion and a residual film as in Figure 1a as observed for a contact line with a microscopic receding motion. However, the scale of the predicted bending was again much smaller than the observations because the long-range intermolecular interactions are significant only within about 5 nm of the surface. The convex nanobending was recently successfully reproduced in Liu et al.’s ultra-large-scale molecular dynamics simulation as shown in Figure 1b.86 Blake et al.87,88 and Lukyanov et al.89 had not observed the nanobending in their simulations. As Lukyanov et al. speculated, the simulation domains might not be big enough. The nanobending itself had a height of about 20 nm. Thus, to capture the nanobending, the model must have a larger domain because the bending appears in contrast to the bulk liquid profile. Liu et al.’s ultralarge-scale molecular dynamics simulation had a 50 nm liquid domain. Gravity had no critical influence on the nanobending

results with the 50 nm droplet, but if gravity was greatly increased by around 103-fold, such that the Bond number was close to those in the experiments,40 then the nanobending was even more obvious.86 The important finding of the simulations was that no convex nanobending would occur if the solid had an absolutely smooth surface, no matter how the equilibrium contact angle varied. In contrast, on an atomically smooth surface, the local friction at the contact line has a stronger effect on the local region than on the bulk, which produces convex nanobending.86 The simulations also showed that the scale of the nanobending was enlarged by the roughness, consistent with AFM measurments.86 Therefore, the convex nanobending is induced by the local friction at the contact line. The convex nanobending is an important mesoscopic structure because it links the molecular and macroscopic domains. The nanobending effectively truncates the film, prevents a very thin liquid wedge at the contact line, and facilitates interface rolling and slipping, which all reduce the local friction. Chen et al. proposed a four-region description, including a molecular sublayer, a convex nanobending layer, an intermediate region with hydrodynamic viscous bending, and the bulk region.40 Then, Wang and Chen41 treated the combination of the molecular sublayer and the convex nanobending region as the inner region in Cox’s three-region analysis. A detailed discussion of the modeling is given later in the section on Practical Modeling. Volatile Liquids. Starting from the equilibrium state without net phase-change flux, AFM measurements have shown the nanoscopic morphology of volatile contact lines.74−76 The profiles were straight down to the substrate in a submicrometer viewing window, just like for static nonvolatile liquids. The distinct feature was the ubiquitous presence of nanofilms beyond the contact line. Three methods have been utilized to confirm these nanofilms. The first was to scan the morphology of the substrate using the AFM tapping mode. The second was to measure the force curve in contact mode with soft probes and analyze the retracting curve. The third was to use hard probes and analyze the approaching curves.76 Evaporating and receding contact lines were then measured in a chamber with heating applied either through the gas domain75 or from the substrate.76 Low heating rates were applied with measured receding speeds of less than 50 nm/s, Ca < 10−6, and Re < 10−7. The intrinsic meniscus profile again continued straight down to the contact line in the submicrometer viewing window, and the microscopic angle E


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varied with U as in nonvolatile systems. These films had nanofilms beyond the contact line. As illustrated in Figure 2, the nanofilm can be divided into evaporating and nonevaporating regions, with the evaporating region being thicker than the nonevaporating region.

significant compared to the intrinsic surface of the macroliquids but could be comparable or even larger for nanoliquids. In recent years, “ultrahigh” evaporation fluxes of the menisci in nanochannels have gained increasing attention.94,95 The heat fluxes were calculated on the basis of the intrinsic meniscus area, and the results broke the limits predicted by the classical Hertz−Knudsen−Schrage equation by at least 1 order of magnitude.94,95 The precursor nanofilm can be used to explain this anomaly because the nanofilm area beyond the contact line which covers the surface area outside the nanochannel could be much larger than the intrinsic meniscus area whose characteristic lengths were only tens of nanometers in the experiments.94,95 This hypothesis was well echoed by most recent experiments by Li et al.,96 who varied the surface wettability outside the nanochannel. When the outside surface was hydrophilic, the heat flux calculated on the basis of the menisci area exceeded the theoretical limit as in previous reports. However, when the outer surface was hydrophobic, which prevented the precursor nanofilms from forming, the calculated heat flux dropped sharply to only 66% of the theoretical limit. Therefore, they concluded that the ultrahigh evaporation from nanochannels with hydrophilic outer surfaces mainly stemmed from evaporating thin films outside of the nanochannel. Mehrizi and Wang presented an evaporation model for partially wetting liquids.76 As illustrated in Figure 2, for millimeter and submillimeter macroscopic liquid droplets, the intrinsic interface can be assumed to be much larger than the nanofilm beyond the contact line; therefore, the model needs to consider only the intrinsic interface and could neglect the contribution of the nanofilm beyond the contact line. The intrinsic interface can be divided into the microscale part that could be easily measured by optical methods or modeled by assuming the interface to be a spherical cap if only the capillary pressure dominates and the nanoscale part that could be modeled by extrapolation of the microscale result based on the observation that the nanoscopic intrinsic film profile is nearly straight in a submicrometer viewing window.76 The extrapolated profile will finally reach a singularity or a meshing problem when it reaches the contact line. Truncation is then necessary at the contact line, as illustrated in Figure 2. Many simulations in the literature have used this method for macroliquids with their calculated heat transfer and Marangoni flow fields being quite consistent with experimental results,97−99 even for complete-wetting systems.100,101 Many did not truncate the film at the contact line but simply depended on the local meshing size, while others set the truncation thickness. For example, the truncation thickness was set as 1 μm in the study by Wang et al. on millimeter-sized menisci.100 The film beyond the truncation was also discussed by incorporating a submodel near the truncation point with the results showing that this could be neglected. Special attention has to be paid to the mesh so that the numerical error does not induce fake slow diffusion when refining the mesh near the truncation point with higher-order algorithms and stricter convergence criteria being necessary.101 If the liquid is rapidly receding, then the residual nanofilm could be large, but at the same time, the macrofilm with microthicknesses could also be large such that it could still be fine to neglect the residual nanofilm. A recent study measuring and modeling macrofilms under a moving bubble with micrometer resolution made excellent predictions of the flow boiling heat transfer.102

Figure 3. Evaporation heat transfer modeling for partially wetting liquids.

For advancing contact lines, the nanofilm beyond the contact line was shorter but still existed even when the substrate was heated in open air. Thus, these nanofilms were precursors in front of the advancing contact line. For example, in tests using formamide droplets, the nanofilms beyond the contact line were between 100 and 200 nm long, shorter than the evaporating nanofilms detected in the receding case which reached several micrometers long.76 These precursor evaporating nanofilms were especially interesting because the precursor film rarely occurs for nonvolatile partially wetting liquids.40 Therefore, the evaporating precursor nanofilm indicates that the phase change must play a role in the contact line dynamics. Wayner90 proposed that volatile molecules might evaporate from the contact line and jump to just in front of the contact line, thus facilitating the contact line advance. Similarly, Mehrizi and Wang76 speculated that the local vapor atmosphere moisturized the dry substrate beyond the contact line and thus altered the substrate wettability to induce the precursor film. Simulations have shown that the precursor film consists of condensed molecules from the vapor and those directly supplied from the bulk by some feeding mechanism.91 The literature has many studies of precursor films in different systems, including the complete wetting of nonvolatile liquids, surfactant systems with autophobing,92 few cases of partial wetting of nonvolatile liquids, and, in the extreme case, solid−solid contacts. There is no doubt that precursor films play an important role in dynamic wetting by acting like a lubricatnt for the contact line. However, as pointed out by Popescu et al. in 2012,93 basic questions still await answers, in particular, what are the necessary and sufficient conditions for a precursor film to occur and what is the link between the mesoscopically thick film and the ultathin films? According to Mehrizi and Wang’s observations,76 liquid−vapor phase change may not be the necessary condition but could be sufficient. The adsorption on the substrate must play important roles in the residual and precursor nanofilms as discussed in the section on Adsorption. Greater volatility and wettability enhance the adsorption and facilitate the formation of the precursor film. For heat transfer, the residual or precursor nanofilm beyond the contact line could contribute additional evaporating area besides the intrinsic liquid surface. This area may not be F


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In contrast, for tiny liquids such as nanodroplets and nanomenisci in nanochannels or pores, the nanofilm beyond the contact line can contribute significantly to the total heat transfer because its evaporating area can be comparable to the intrinsic interfacial area. Accurate predictions of nanofilm shapes and heat transfer rates as well as their connection to the intrinsic meniscus are still a formidable problem. Most recently, Setchi et al.36 applied boundary conditions in the microscale region to predict the film profile back through the nanoscale region. They tried out five different forms of the dispersion components and five different forms of the structural components to show that only the dispersion component, short-range Born repulsion component, and one specific form of the structural component working together gave a reasonable film profile from the microscale to nanoscale regions including the evaporating nanofilm beyond the contact line. The modeling was very complicated.

Figure 4. Snapshots of droplets at equilibrium (top row) and with hysteresis (bottom row) on various surfaces, adapted with permission from ref 86. Surface A was absolutely smooth with no hysteresis, with the droplet simply sliding on surface A as a result of the lateral force without any change in the contact angle. Surface B was an atomically smooth surface with distinct atomic force potentials.

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MECHANISMS AND MODELING Local Friction. According to Young’s equation, there should be only one unique contact angle for a specific system, but this is contradicted by both the contact angle hysteresis for a static contact line and the contact angle variations for moving contact lines. Regarding the hysteresis, liquids always show various static contact angles on solids. They will not advance if the contact angle is smaller than a critical value called the advancing static contact angle and will not recede if the contact angle is larger than a critical value called the receding static contact angle. The difference between the advancing and receding contact angles has been defined as the contact angle hysteresis.28,103 Surface heterogeneities such as the surface roughness, the disjoining pressure in the thin film, and liquid− solid adhesion have all been considered as origins of these phenomena. The solid roughness has long been considered to be an important factor in the hysteresis. Many experiments have shown that the hysteresis increases with the roughness. However, there is no clear evidence showing that the hysteresis originates from the roughness. Some studies have attributed the hysteresis to the disjoining pressure in the thin liquid film near the contact line.104 On absolutely smooth, homogeneous solid surfaces, the hysteresis can be calculated from the disjoining/conjoining pressure isotherms.105,106 Many studies have also debated the effective roughness scale for hysteresis. A few theoretical studies have assumed that surfaces with a rootmean-square (RMS) roughness of 90°) the gas domain becomes a gas wedge, which provides slippage due to the gas entrainment.67,68,112 Equations 3−5 together predict the apparent contact angle, θD. According to the model, the monotonous and nonmonotonous variations can be unified to a competition between the drop in the local friction and the rise of the hydrodynamic viscous bending. The fitting accuracy was unprecedented as shown in Figure 5b. The experimental data was from Blake111 where a tape was dipped into a reservoir. The fitting parameters, A, ζ0, and α, were all clearly correlated with the system properties. The primary frictional coefficient, ζ0, had a simple relationship with the bulk viscosity such that ζ0 had the same units as viscosity with a value that was hundreds to thousands of times that of the bulk viscosity. The higher viscous-like effect has been seen in recent measurements that have identified strong crystalline-like ordering at the moving contact line.51 The water viscosity can abruptly increase to that of molasses in a nanosized region.113 Thus, ζ0 could be an index for the local liquid viscosity at the contact line where the nanoconfinement occurs. The scale ratio, A, was found to be very stable with a mean value of 9.8 and a standard deviation of as small as 0.98 for the 11 sets of experiments in this study. The value of A also indicated that the convex frictional nanobending and the hydrodynamic viscous bending could overlap in space. Adsorption. As mentioned, nanoscopic observations have detected various nanofilms beyond the contact line in partially wetting systems. For nonvolatile liquids, a residual nanofilm may occur after the receding contact line.73,78 Volatile liquids had residual and precursor nanofilms regardless of whether the contact line was receding, advancing, or static.

i ζU yzz γ(cos θas − cos θme) = ζU , therefore θme = ac cosjjjjcos θas − z γ z{ k (4)

where θas is the advancing static contact angle. The local friction was proposed to be calculated by multiplying the mesoscopic friction coefficient, ζ, by the contact line advancing speed, U. The frictional coefficient was proposed to be H


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friction, the nonmonotonous variations of the dynamic contact angle with speed, and the abnormal heat fluxes during nanopore evaporation. A general understanding of the contact line is given in Figure 6. The basic competing factors include the cohesion within the

As discussed, nonvolatile residual nanofilms differ from macroscopic deposited films.79−81 The nanofilm should be related to the adsorption of the liquid sublayer on the solid. Studies have shown that the liquid structure in the liquid sublayer can differ from that in the liquid bulk as a result of the strong liquid−solid intermolecular forces.114−117 With a receding contact line, the weakest part that is easiest to disrupt may not be the liquid−solid interface but rather the interface between the liquid sublayer and the liquid bulk, which would result in the adsorbed sublayer adhering to the solid rather than following the receding liquid. This adsorption is strengthened by the liquid−solid adhesion (i.e., the wettability). Liu et al.78 always found a residual nanofilm when the equilibrium contact angle was less than 20°. Molecular dynamic simulations of receding droplets showed the same trend.78 For volatile liquids, these nanofilms indicate vapor adsorption on the substrate. Nanofilms were seen even when the contact line was advancing on a heated substrate in air, where the conditions did not favor adsorption. Adsorption is defined as the accumulation of a substance at an interface. Besides the liquid and vapor adsorption to the solid, noncondensable gas molecules will also adsorb onto the interfaces as a result of attractive intermolecular forces such as the omnipresent van der Waals forces. For advancing contact lines, the gas molecules may adsorb onto the liquid interface, roll with the interface, and then adsorb onto the solid surface to form a gas nanofilm. Both effects would bring gas molecules to the advancing contact line and induce slippage. Some recent experiments have indicated such slippage and signs of residual gas.55 Other studies have confirmed that reduced air pressures affect the dynamic wetting.67,68 Various adsorption isotherms (i.e., Langmuir, BET, FHH, AD, etc.) have been proposed since 1918. A Langmuir isotherm assumes one gas molecule adsorbed on one adsorption site. The BET isotherm follows the Langmuir isotherm and assumes that adsorption occurs layer on layer. In 2007,118 Ward and Wu and proposed the ζ isotherm based on statistical thermodynamics by assuming molecular clusters at adsorption sites. The isotherm avoids the problem of infinite adsorption in previous isotherms when the vapor pressure approaches the saturation pressure.119 Combined with Gibbsian thermodynamics, the isotherm can establish the expression for the solid−vapor surface tension. Adsorption has recently been modeled at the local atomic structure level using the concept of interface complexes which are an equilibrium 2D state of an interface.120 Wetting systems have many complex factors such as the shear stress parallel to the interface and the connection and mass transport between the adsorbed film and the bulk. The shear stress can increase the residual film thickness or induce instabilities. The disjoining pressure could provide a theoretical approach to understanding the connection and the fluid supply,36 but the relationships are very complicated and the parameters are hard to determine. In addition, the effects of the surface roughness are also difficult to represent.

Figure 6. Understanding of the contact line dynamics.

liquid, the adhesion between the liquid and solid, and the energy barriers along the solid surface. The balance of the cohesion and adhesion forces creates a unique contact angle, while the energy barriers lead to differing static friction and dynamic friction forces, which in turn lead to contact angle hysteresis and dynamic contact angles. The convex nanobending and the residual nanofilms are mesoscopic structures that reduce the local friction. The adsorption is a complicated two-way coupling factor determined by the cohesion, adhesion, and surface barrier effects that then change the adhesion and the energy barrier in return. The nanofilms beyond the contact line result from the adsorption complicated by the local shear stress variations and the liquid supply mechanism. Many additional efforts are needed to create a comprehensive understanding of the contact line physics. To summarize, four groups of questions await answers: (i) The atomic-scale roughness has been shown to affect the contact line dynamics, and there is mimicking between the nanoscopic and macroscopic worlds. Further studies are needed to effectively describe the surface multiscale energy barriers and collect experimental data to verify these models. (ii) There may be an abrupt change in the viscosity when liquid molecules come into the contact line region. Are there changes in other properties? What are the relationships between the mesoscopic properties and the mesoscopic structures such as the convex nanobending and the nanofilms, and how do the properties affect the hydrodynamic analyses? (iii) Adsorption occurs on all surfaces. How do we determine whether absorption is significant enough to affect the wetting dynamics? When does the liquid volatility strongly impact the contact line dynamics? Is there a clear boundary between the contact line dynamics for volatile and nonvolatile liquids? (iv) How does the nanofilm connect to the macroscopic film and receive liquid from the macroscopic film? Is the current disjoining pressure theory an effective approach for modeling nanofilms? The surface energy barriers are a critical mechanism affecting the wetting dynamics, but

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CONCLUSIONS AND OUTLOOK The complexities of wetting dynamics are rooted in the multiscale and multiphase natures of the phenomena. State-ofthe-art microscopy and simulation methods have enabled nanoscale studies of the contact line region that have shed light on complexities such as the speed dependency of the microscopic contact angle, the local static and dynamic I


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there are still no explicit studies on roughness in the disjoining pressure considerations.

REFERENCES

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Because the contact line is the junction among the solid, gas, and liquid interfaces, these questions involve many basic, formidable aspects of interfacial science. Breakthroughs will require close collaboration among experimentalists and theorists from various disciplines. Besides the basic theoretical aspects, there are many other aspects of the complex, multiphysics wetting systems that need to be investigated. The moving contact line physics of non-Newtonian and nanofluids has been considered in recent years.121−123 The interactions among the Marangoni effect, the phase change, and the particle or solute concentrations then further complicate the contact line dynamics for solutions.101 Others topics include but are not limited to the effects of liquid metals, electrowetting, and magnetic wetting, which are all complicated and intriguing with many applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or [email protected]. ORCID

Hao Wang: 0000-0003-2882-3802 Notes

The author declares no competing financial interest. Biography

Hao Wang is an associate professor with tenure in the College of Engineering at Peking University. He entered Tsinghua University in 1996 and obtained his Ph.D. in 2004, followed by 3 years of postdoctoral work at Purdue University. Dr. Wang has been the director of the Laboratory of Heat and Mass Transport at MicroNano Scale at Peking University since 2007. He is an experienced researcher in the areas of phase change and interfacial phenomena. His group is developing a comprehensive understanding of contact line dynamics.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (no. 51622601). The author acknowledges stimulating discussions with Prof. Terence D. Blake at the University of Mons-Hainaut, Prof. Elizabeth B. Dussan at the Massachusetts Institute of Technology, Prof. Xiaodong Wang at North China Electric Power University, Prof. Yi Sui at Queen Mary University of London, and Prof. Yulii Shikhmurzaev at the University of Birmingham. The author also acknowledges the reviewers’ great efforts. J


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