Contact line motion in confined liquid-gas systems: Slip versus phase transition

In two-phase flows, the interface intervening between the two fluid phases intersects the solid wall at the contact line. A classical problem in continuum fluid mechanics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a nonintegrable stress singularity. Recently, various diffuse-interface models have been proposed to explain the contact line motion using mechanisms missing from the sharp-interface treatments in fluid mechanics. In one-component two-phase (liquid-gas) systems, the contact line can move through the mass transport across the interface while in two-component (binary) fluids, the contact line can move through diffusive transport across the interface. While these mechanisms alone suffice to remove the stress singularity, the role of fluid slip at solid surface needs to be taken into account as well. In this paper, we apply the diffuse-interface modeling to the study of contact line motion in one-component liquid-gas systems, with the fluid slip fully taken into account. The dynamic van der Waals theory has been presented for one-component fluids, capable of describing the two-phase hydrodynamics involving the liquid-gas transition [A. Onuki, Phys. Rev. E 75, 036304 (2007)]. This theory assumes the local equilibrium condition at the solid surface for density and also the no-slip boundary condition for velocity. We use its hydrodynamic equations to describe the continuum hydrodynamics in the bulk region and derive the more general boundary conditions by introducing additional dissipative processes at the fluid-solid interface. The positive definiteness of entropy production rate is the guiding principle of our derivation. Numerical simulations based on a finite-difference algorithm have been carried out to investigate the dynamic effects of the newly derived boundary conditions, showing that the contact line can move through both phase transition and slip, with their relative contributions determined by a competition between the two coexisting mechanisms in terms of entropy production. At temperatures very close to the critical temperature, the phase transition is the dominant mechanism, for the liquid-gas interface is wide and the density ratio is close to 1. At low temperatures, the slip effect shows up as the slip length is gradually increased. The observed competition can be interpreted by the Onsager principle of minimum entropy production.     

Dynamic wetting of Boger fluids

The impact of fluid elasticity on the dynamic wetting of polymer solutions is important because many polymer solutions in technological use exhibit non-Newtonian behaviors in the high shear environment of the wedge-like flow near a moving contact line. Our former study [G.K. Seevaratnam, Y. Suo, E. Ramé, L.M. Walker, Phys. Fluids 19 (2007) Art. No. 012103] showed that shear thinning induced by a semi-flexible high molecular weight polymer reduces the viscous bending near a moving contact line as compared to a Newtonian fluid having the same zero-shear viscosity. This results in a dramatic reduction of the dependence of the effective dynamic contact angle on contact line speed. In this paper, we discuss dynamic wetting of Boger fluids which exhibit elasticity-dominated rheology with minimal shear thinning. These fluids are prepared by dissolving a dilute concentration of high molecular weight polymer in a "solvent" of the oligomer of the polymer. We demonstrate that elasticity in these fluids increases curvature near the contact line but that the enhancement arises mostly from the weakly non-Newtonian behavior already present in the oligomeric solvent. We present evidence of instabilities on the liquid/vapor interface near the moving contact line.     

Early stage spreading: Mechanisms of rapid contact line advance

Inertial spreading occurs at the onset of a droplet wetting a solid; for low viscosity, highly wetting liquids, very high contact line velocities have been observed during this regime. Initial wetting kinetics are so rapid that careful experimental exploration of this phenomenon has only occurred over the past ~ 10 years. Herein, we review recent experimental and computational investigations into inertial spreading. We highlight results and discussion from literature that bear out an initially surprising conclusion: even nanometer scale drops exhibit a regime of early stage wetting kinetics that are well described as inertia dominated. Given this, some focus is placed on reviewing results from atomic scale simulations of inertial wetting and how they can be used to battle the lack of understanding regarding fundamental mechanisms of rapid contact line advancement. To bolster this discussion, new results are also presented from molecular dynamics simulations exploring inertial wetting in metallic systems. It is demonstrated that atomic scale simulations can reveal nanoscale size effects on inertial wetting and that, after accounting for these nanoscale effects, inertial regime spreading data for nanodrops are fully explained by otherwise continuum fluid mechanics theory. Data obtained are thus used to explore the role of order in liquid films near solid surfaces in controlling contact line advancement. In exploring the structure of an ordered liquid layer adjacent to the solid surface that undergoes significant slip during inertial spreading, it is demonstrated that a tensile strain gradient manifests in the layer as the film edge is approached.     

Wetting: Inverse Dynamic Problem and Equations for Microscopic Parameters

Movement of a liquid meniscus in a low-diameter capillary while it is being filled or emptied is considered. The liquid is nonvolatile. Assuming low Reynolds number and low capillary number, the liquid-gas interface shape is studied. Angles of inclination of this boundary to the solid near the contact line are small. Consideration is given to the inverse problem in wetting dynamics: to establish an analytic expression for the universal constant that influences the dynamics of a three-phase contact line. Inverse relations for microscopic parameters in terms of macroscopic measured values obtained in experiments with a meniscus moving through a capillary are derived. The inverse relations are substantiated independently. To do so, numerical experiments for a van der Waals liquid have been carried out, using the de Gennes model of partial wetting. General formulas for microparameters agree well with numerical experiments. The article provides the similarity criterion which influences the wetting in the case of a van der Waals liquid meniscus. The inverse dynamic problem for both an advancing and a receding meniscus is solved. A relation for the critical speed of meniscus recession is proposed. Two contact angles for a meniscus are discussed. Behavior of dynamic contact angles in the vicinity of the critical speed is studied. One of the angles is shown to vanish at less than the critical speed, and the other one, exactly at the critical speed. In the case of an advancing meniscus the equations for microparameters are valid for both partial and complete wetting. The proposed inverse expression for complete wetting allows determination of the maximum precursor film thickness and its dependence on the motion speed (also determination of the Hamaker constant in the case of a van der Waals liquid). Copyright 2000 Academic Press.     

Modeling of the moving deformed triple contact line: influence of the fluid inertia

For partial wetting, motion of the triple liquid-gas-solid contact line is influenced by heterogeneities of the solid surface. This influence can be strong in the case of inertial (e.g., oscillation) flows where the line can be pinned or move intermittently. A model that takes into account both surface defects and fluid inertia is proposed. The viscous dissipation in the bulk of the fluid is assumed to be negligible as compared to the dissipation in the vicinity of the contact line. The equations of motion and the boundary condition at the contact line are derived from Hamilton's principle. The rapid capillary rise along a vertical inhomogeneous wall is treated as an example.     

Wetting phenomena on polymeric surfaces

Classic theory predicts a unique value of equilibrium contact angle, θ_o, for a given solid/liquid/fluid system. However, wetting phenomena are often very complicated in practice, with contact angle hysteresis being a major source of problems in interpretation. Contact angle variability is related to several factors, but we consider two which are particularly relevant to polymeric substrates - effects of orientation of molecular chains near the surface and local solid strain at the wetting front. A model is proposed to explain “stick-slip” motion of the triple line.     

Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces

The moving contact line problem of liquid-vapor interfaces was studied using a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 2004, 69, 032602]. We have examined the static and dynamic interfacial behaviors by means of the bubble and capillary wave tests and found that both the Laplace equation of capillarity and the dispersion relation were satisfied. Dynamic contact angles followed the general trend of contact line velocity observed experimentally and can be described by Blake's theory. The velocity fields near the interface were also obtained and are in good agreement with fluid mechanics and molecular dynamics studies. Our simulations demonstrated that incorporating interfacial effects into the lattice Boltzmann model can be a valuable and powerful alternative in interfacial studies.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic-to-nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau-de Gennes model for rod-like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic-isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic-nematic interface and the substrate-nematic-isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Contact line shape on ultrahydrophobic post surfaces

In this work, we investigate the configuration of the contact line of a water drop lying on an ultrahydrophobic post surface using the numerical algorithm Surface Evolver. For the special situation of Cassie wetting, we propose a modified definition of the contact line as the line in space where the meniscus starts to curve upward out of the plane of the composite surface. In our simulations, it is found that the contact line is very strongly distorted, indicating a strong tendency of the drop to "ball up" in those areas where it is not in contact with the solid surface. The distortion of the contact line corresponds to a pronounced deformation of the liquid-air interface around the base of the drop. We discuss the consequences of this distortion for the definition and practical measurement of the contact angle on ultrahydrophobic surfaces.     

Liquid coating of moving fiber at the nanoscale

Using large scale molecular dynamics, we study the contact line motion of a liquid meniscus crossed by a moving nanofiber. Varying the amplitude of the liquid/solid interactions, we analyze the shape of the meniscus versus time for a range of velocities. The associated contact angles are estimated by fitting the profiles using the James equation. The corresponding flux lines describing the displacement of the liquid molecules inside the meniscus have also been measured. The analysis of the dynamic contact angle is in agreement with the molecular-kinetic theory and confirms the existence of an optimal speed for wetting.     

VOF simulations of the contact angle dynamics during the drop spreading: Standard models and a new wetting force model

Introduction

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas–liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

Methodology

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an “adhesion-like” force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid–air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

Results

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θ_adv = 10° – 70°) and hydrophobic (θ_adv = 105° – 120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

Conclusion

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We < ˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic‐to‐nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau–de Gennes model for rod‐like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic‐isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic–nematic interface and the substrate–nematic–isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Molecular simulation of fluid-solid interfaces at nanoscale

The equilibrium states of vapor and liquid coexistent phases in contact with a solid surface are studied at the nanoscale by molecular dynamics simulations for a temperature close to the fluid triple point. The characteristics of the solid-fluid interfaces are determined when the interaction strength between the fluid and the solid varies in order to go from a situation of complete drying to that of complete wetting. From the vapor-liquid density profiles of liquid drops lying on the substrate surface or menisci of liquid films confined in slit pores, the contact angles made by the vapor-liquid interface with the solid are computed. The angle values are similar for the drops and the films. They are also in good qualitative agreement with the estimates obtained through the Young's relation from the surface tensions associated with the vapor-solid, liquid-solid, and vapor-liquid interfaces. However, at this scale, the uncertainties inherent to the angle computation and, to a lesser extent, to size effects seem to preclude that the quantitative agreement between the angle estimates obtained from the interface geometry and calculated from the Young's relation can be better than few degrees.     

Motion of liquid drops on surfaces induced by asymmetric vibration: role of contact angle hysteresis

Hysteresis of wetting, like the Coulombic friction at solid/solid interface, impedes the motion of a liquid drop on a surface when subjected to an external field. Here, we present a counterintuitive example, where some amount of hysteresis enables a drop to move on a surface when it is subjected to a periodic but asymmetric vibration. Experiments show that a surface either with a negligible or high hysteresis is not conducive to any drop motion. Some finite hysteresis of contact angle is needed to break the periodic symmetry of the forcing function for the drift to occur. These experimental results are consistent with simulations, in which a drop is approximated as a linear harmonic oscillator. The experiment also sheds light on the effect of the drop size on flow reversal, where drops of different sizes move in opposite directions due to the difference in the phase of the oscillation of their center of mass.     

Influence of fluid flow on the deposition of soluble surfactants through receding contact lines of volatile solvents

Soluble surfactants are often deposited from volatile solvents through moving contact lines. In this study, we demonstrate that altering the flow field near such a contact line fundamentally changes the deposited surfactant structure. At slow contact line speeds, the substrate emerges dry. A densely packed, tilted monolayer of surfactant is deposited along the solid-vapor interface from the rolling fluid motion at the contact line. At faster speeds, the substrate emerges with an evaporating thin film entrained on its surface. Surfactant is confined in the film in a constantly increasing concentration environment. Monodisperse crystalline islands nucleate and grow on the surface with sizes and shapes controlled by varying the deposition conditions. These results contrast with disordered deposits that result from evaporation at a pinned contact line. Our results suggest that dip-coating with control of dipping speed and evaporation rate may provide better control of deposition through contact lines of evaporating solvents.     

Wetting by simple room-temperature polymer melts: deviations from Newtonian behavior

The hydrodynamics near moving contact lines of two room-temperature polymer melts, polyisobutylene (PIB) and polystyrene (PS), are different from those of a third polymer melt, polydimethylsiloxane (PDMS). While all three fluids exhibit Newtonian behavior in rotational rheological measurements, a model of the hydrodynamics near moving contact lines which assumes Newtonian behavior of the fluid accurately describes the interface shape of a variety of PDMS fluids but fails to describe the interface deformation by viscous forces in PIB and PS. The magnitude of the deviations from the model and the distance along the liquid-vapor interface over which they are seen increase with increasing capillary number. We conclude that the wetting behaviors of PIB and PS are influenced by weak elasticity in these low molecular weight melts and that dynamic wetting is more sensitive to this elasticity than standard rheometric techniques.     

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.     

Contact line motion and dynamic wetting of nanofluid solutions

The effect that nanoparticles play in the spreading of nanofluids dynamically wetting and dewetting solid substrates is investigated experimentally, using 'drop shape' analysis technique to analyse aluminium-ethanol contact lines advancing and receding over hydrophobic Teflon-AF coated substrates. Results obtained from the advancing/receding contact line analysis show that the nanoparticles in the vicinity of the three-phase contact line enhance the dynamic wetting behaviour of aluminium-ethanol nanofluids for concentrations up to approximately 1% concentration by weight. Two mechanisms were identified as a potential reason for the observed enhancement in spreading of nanofluids: structural disjoining pressure and friction reduction due to nanoparticle adsorption on the solid surface. The observed 'lubricating effect' that the nanoparticles seem to be inducing is similar to the 'superspreading' effect for surfactant solutions spreading on hydrophobic surfaces, up to a concentration (weight) of approximately 1%, could be a result of the predicted enhanced wetting behaviour. Indeed, Trokhymchuk et al. [Langmuir, 2001, 17, 4940] observed a solid-like ordering of nanoparticles in the vicinity of the three-phase contact line, leading to an increased pressure in the fluid 'wedge'. This increased pressure leads to a pressure gradient which causes the nanofluids to exhibit enhanced wetting characteristics. Another possible cause for the observed increase in advancing/receding contact line velocity could be deposition of nanoparticles on the solid surface in the vicinity of the three-phase contact line resulting in the nanofluid effectively advancing over aluminium rather than Teflon-AF, or the contact line 'rolling' over nanoparticles at the three-phase contact line due to sphericity of nanoparticles. For either of these to be the case, the nanoparticle effect at the three-phase contact line would have to be enhanced for the lower concentration in the same way that it would have to be for the increased pressure in the fluid 'wedge'.     

Numerical simulations of capillary-driven flows in nonuniform cross-sectional capillaries

In this study the wetting behavior of converging-diverging and diverging-converging capillaries is investigated numerically using an in-house written, finite-element code. An interface tracking procedure based on the predicted change in the total liquid volume, to update the interface location, and Cox's formulation, to determine the dynamic contact angle and the interface shape, is proposed and used. Flow simulations revealed that both converging-diverging and diverging-converging capillaries exhibit significantly slower wetting behavior than straight capillaries and that any deviation in the capillary diameter necessarily tends to slow the overall wetting speed. This behavior was attributed to local regions of very low capillary pressure and high viscous retardation force when the capillary diameter at the interface was significantly larger than the capillary diameter over the upstream fluid. Though the local wetting velocities were different, when equivalent capillaries were compared it was found that both converging-diverging and diverging-converging capillaries had the same total fill time independent of the number of irregular regions, suggesting that the simple model is sufficient for predicting the overall effect. The influence of surface tension and contact angle on the total wetting time was found to be similar for both straight and irregularly shaped capillaries.     

Does macroscopic flow geometry influence wetting dynamic?

The macroscopic flow geometry has long been assumed to have little impact on dynamic wetting behavior of liquids on solid surfaces. This study experimentally studied both spontaneous spreading and forced wetting of several kinds of Newtonian and non-Newtonian fluids to study the effect of the macroscopic flow geometry on dynamic wetting. The relationship between the dynamic contact angle, θ(D), and the velocity of the moving contact line, U, indicates that the macroscopic flow geometry does not influence the advancing dynamic wetting behavior of Newtonian fluids, but does influence the advancing dynamic wetting behavior of non-Newtonian fluids, which had not been discovered before.