Contact Line Speed Research Articles

Weak-inertial effects on destabilized receding contact lines

It is known that, beyond a critical speed, the straight contact line of a partially -wetting liquid destabilizes into a corner. One of the earliest theoretical works exploring this phenomenon [Limat and Stone, ] elicited a self-similar conical structure of the interface in the viscous regime. However, noting that inertia is not expected to be negligible at contact line speeds close to and beyond the critical value for many common liquids, we provide the leading-order inertial correction to their solution. In particular, we find the self-similar corrections to the interface shape as well as the flow field, and also determine their scaling with the capillary number. We find that inertia invariably modifies the interface into a cusplike shape with an increased film thickness. Furthermore, when incorporating contact line dynamics into the model, resulting in a narrowing of the corner as the contact line speed increases, we still observe an overall increase in the inertial contribution with speed despite the increased confinement. Published by the American Physical Society 2024

Actuating droplets with electrowetting: Force and dynamics

AbstractElectrowetting on dielectric (EWOD) allows rapid movement of liquid droplets on a smooth surface, with applications ranging from lab‐on‐chip devices to micro‐actuators. The in‐plane force on a droplet is a key indicator of EWOD performance. This force has been extensively modeled but few direct experimental measurements are reported. We study the EWOD force on a droplet using two setups that allow, for the first time, the simultaneous measurement of force and contact angle, while imaging the droplet shape at 6000 frames/s. For several liquids and surfaces, we observe that the force saturates at a voltage of approximately 150 V. Application of voltages of up 2 kV, that is, 10 times higher than is typical, does not significantly increase forces beyond the saturation point. However, we observe that the transient dynamics, localized at the front contact line, do not show saturation with voltage. At the higher voltages, the initial front contact line speed continues to increase, the front contact angle temporarily becomes near zero, creating a thin liquid film, and capillary waves form at the liquid–air interface. When the localized EWOD forces at the contact line exceed the capillary forces, projectile droplets form. Increasing surface tension allows for higher droplet forces, which we demonstrate with mercury.

Time-averaged approach to the dewetting problem at evaporation

Dewetting of liquid films on solid surfaces in the presence of evaporation is a common phenomenon and has been studied by many researchers. The previous numerical approach has revealed that evaporation accelerates the dewetting speed of the triple contact line and established correlations between the dewetting speed and the surface wettability and superheating. However, such a numerical calculation is time- and resource-consuming. We examine dewetting physics and propose a time-averaged approach based on the multiscale theory. The new approach averages the dewetting process over time and consists of only several algebraic equations, making the problem easier to solve. It can produce time-averaged values of essential quantities, such as the dewetting speed and contact angle as a function of superheating, which agrees with the previous numerical results. This simple approach is valuable for many applications, such as modeling pulsating heat pipes and describing the microlayer dynamics under growing vapor bubbles in nucleate boiling.

Asymmetry of wetting and de-wetting on high-friction surfaces originates from the same molecular physics

Motion of three-phase contact lines is one of the most relevant research topics of micro- and nano-fluidics. According to many hydrodynamic and molecular models, the dynamics of contact lines is assumed overdamped and dominated by localized liquid–solid friction, entailing the existence of a mobility relation between contact line speed and microscopic contact angle. We present and discuss a set of non-equilibrium atomistic molecular dynamics simulations of water nanodroplets spreading on or confined between silica-like walls, showing the existence of the aforementioned relation and its invariance under wetting modes (“spontaneous” or “forced”). Upon changing the wettability of the walls, it has been noticed that more hydrophilic substrates are easier to wet rather than de-wet; we show how this asymmetry can be automatically captured by a contact line friction model that accounts for the molecular transport between liquid layers. A simple examination of the order and orientation of near-contact-line water molecules corroborates the physical foundation of the model. Furthermore, we present a way to utilize the framework of multicomponent molecular kinetic theory to analyze molecular contributions to the motion of contact lines. Finally, we propose an approach to discriminate between contact line friction models which overcomes the limitations of experimental resolution. This work constitutes a stepping stone toward demystifying wetting dynamics on high-friction hydrophilic substrates and underlines the relevance of contact line friction in modeling the motion of three-phase contact lines.

Dewetting acceleration by evaporation

Dewetting of a substrate, i.e. the liquid film retraction under partial wetting conditions, has been studied extensively over the past decades. This theoretical work deals with the dewetting phenomenon in the presence of liquid evaporation into the pure vapour atmosphere driven by substrate superheating with respect to the saturation temperature corresponding to the vapour pressure. The dynamic profile of the vapour–liquid interface is analysed numerically by using the generalised lubrication approximation that can be applied to an interface slope larger than its conventional counterpart. This approximation uses a phenomenological argument to increase the precision of calculations. For small slopes, it reduces to the conventional lubrication approach. Several nanoscale effects are included in the theory to obtain more precise results: the Kelvin effect, the hydrodynamic slip, the Marangoni effect, the vapour recoil and the interfacial thermal resistance. Their relative importance is discussed. The results include the film shape evolution, the apparent contact angle and the contact line speed, all defined by the substrate superheating and its wetting properties. These dependencies agree with existing experimental results. It is found that the dewetting is accelerated by evaporation. The numerical results are compared to those of the multiscale theory that uses two main parameters, the Voinov angle (the apparent angle obtained within the microregion problem) and the Voinov length. The latter is studied for several fluids as a function of superheating, and an approximate expression for it is proposed. A good agreement between the numerics and the multiscale theory shows the validity of the latter. This means that the dewetting speed in the presence of evaporation can be calculated with an analytical expression that requires only the Voinov angle as a numerical input. Such results are important for many applications, for instance, bubble growth in boiling or film dynamics in heat pipes.

Janus micro‐thread to micro‐nanodroplets using dynamic contact line lithography

AbstractDynamic contact line lithography (DCLL) is generally used for the template‐less but well‐ordered deposition of polymer micro/nanostructures from the solution of homopolymer. DCLL from the blend of several polymers in a common suitable solvent can generate rich morphologies including nanostructured Janus micro threads on a surface which might be challenging to fabricate using any other method. A blend of polystyrene (PS) and poly(methyl methacrylate) (PMMA) in toluene with different compositions and concentrations are used for DCLL at a constant contact line speed of 10 μm/s. Variations of compositions and the overall concentration of polymer, engender Janus micro threads to undulated threads and multi‐layered micro/nanodroplets of PS/PMMA. Interestingly, the more soluble PS phase separates first compared to less soluble PMMA near the contact line due to the enhanced local concentration of PS during the convective flow of the solvent toward the contact line. This is also verified by DCLL using PS/PMMA blend in ethyl acetate as well. In that case, more soluble PMMA deposits first near the contact line compared to marginally less soluble PS in the solvent.

Detailed modelling of contact line motion in oscillatory wetting

The experimental results of Xia and Steen for the contact line dynamics of a drop placed on a vertically oscillating surface are analyzed by numerical phase field simulations. The concept of contact line mobility or friction is discussed, and an angle-dependent model is formulated. The results of numerical simulations based on this model are compared to the detailed experimental results of Xia and Steen with good general agreement. The total energy input in terms of work done by the oscillating support, and the dissipation at the contact line, are calculated from the simulated results. It is found that the contact line dissipation is almost entirely responsible for the dissipation that sets the amplitude of the response. It is argued that angle-dependent line friction may be a fruitful interpretation of the relations between contact line speed and dynamic contact angle that are often used in practical computational fluid dynamics.

Regulating Droplet Wetting and Pinning Behaviors on Pathogen-Modified Hydrophobic Surfaces: Strategies and Working Mechanisms.

Hydrophobic surfaces modified by pathogens in agricultural production are one of the main reasons to reduce the utilization of pesticides. Adding surfactants to pesticide solutions is a common method to improve their wetting and spreading properties. In this work, the interaction mechanism between pathogen-modified hydrophobic surfaces and mixtures of surfactants and a pesticide was studied in detail. The interaction mechanism was determined by characterizing the wetting and spreading behaviors of droplets on cucumber powdery mildew leaves at different growth stages. When surfactants were added, droplets on cucumber powdery mildew leaves were in the Wenzel wetting state, the pinning force weakened, the contact line speed accelerated, and the adhesion force increased. We explained the micellar state and aggregation behavior of surfactant molecules in a pesticide solution that was applied to the surface of cucumber powdery mildew leaves. Droplets of solutions containing nonionic surfactants easily formed semibald micelles, binding to the pathogen of powdery mildew, whereas droplets containing cationic surfactants did not do so. Because of the electrostatic interaction between cationic surfactant molecules and powdery mildew pathogens, cationic surfactant molecules did not wet the pathogens very well, so we suggest adding nonionic surfactants rather than cationic surfactants to improve the wetting and spreading of pesticide solutions on cucumber powdery mildew leaves. This study provides new insights into enhancing the wetting and deposition of droplets on pathogen-modified hydrophobic surfaces.

Droplet Impact on Surfaces with Asymmetric Microscopic Features.

The impact of liquid drops on a rigid surface is central in cleaning, cooling, and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness, and texture on the solid surface influence the initial stages of the impact dynamics. Here, we experimentally study drops impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. We found that the difference between impact velocity and the capillary speed on a solid surface is a key factor of spreading asymmetry, where the capillary speed is determined by the friction at a moving three-phase contact line. The line-friction capillary number Caf = μfV0/σ (where μf,V0, and σ are the line friction, impact velocity, and surface tension, respectively) is defined as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We show that when Caf ≪ 1, the droplet impact is asymmetric; the contact line speed in the direction against the inclination of the ridges is set by line friction, whereas in the direction with inclination, the contact line is pinned at acute corners of the ridges. When Caf ≫ 1, the geometric details of nonsmooth surfaces play little role.

Microscale tracking of unconstrained moving multiphase contact lines via a capacitance sensor array

The ability to track the spatial location of a moving multiphase contact line in time significantly enhances understanding into the fundamental physics behind biological processes, condensation- and evaporation-based heat transfer, and a host of other important phenomena. In this work, we present a capacitance-based microdevice capable of tracking a moving phase interface at the microscale for an unconstrained liquid droplet. The microdevice is comprised of an array of planar interdigitated electrodes beneath a thin insulating polymer layer. Monitoring changes in capacitance with time facilitates sensing of the multiphase contact line location and speed as it passes over each capacitance sensor in turn. This capacitive sensing scheme is designed to be highly sensitive and noninvasive to the droplet under study. Results show the speed and location of moving multiphase contact lines for advancing and receding water droplets are indeed able to be detected through the change in capacitance signals in the sensor array. It is also shown that the array can be used to measure the advancing and receding contact angles of unconstrained droplets.

Study of early time dynamics of drop spreading in different surrounding pressure

The initial spreading phenomena of oil droplets on a partially wettable surface under various surrounding pressures was conducted through an experimental investigation outlined in this study. The gauge pressure of the surrounding medium was varied stepwise in the range from atmospheric pressure to 30 MPa. Upon contact with the surface, spreading alters the total energy of the system. The timescale for this process is very fast and the spreading involves the motion of the three-phase contact line established at the junction of the droplet, the substrate and the surrounding medium. In this study, the early time dynamics of different grades of oil drops spreading on PTFE substrates were examined utilizing high-speed imaging and drop shape analysis. Results show that the temporal evolution of the spreading radius closely resembles a power law where the empirically obtained exponent, α, was calculated for different surrounding pressures. Observations of instantaneous drop spreading reveal that spreading occurs through three distinct regimes: an initial spreading regime, a short transition regime and a viscous regime. In the inertial regime of the early time dynamics, spreading radius scales as r~tα where the spreading exponent, α, decreases with the increase of pressure. In addition, pressure influences the onset of the transition regime, the contact line speed, and the contact angle during the initial wetting process.

Moving contact lines and dynamic contact angles: a \u2018litmus test\u2019 for mathematical models, accomplishments and new challenges

After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.

Wettability and capillary effects: Dynamics of pinch-off in unconstricted straight capillary tubes.

We study the interfacial evolution of immiscible two-phase flow within a capillary tube in the partial wetting regime using direct numerical simulation. We investigate the flow patterns resulting from the displacement of a more viscous fluid by a less viscous one under a wide range of wettability conditions. We find that beyond a wettability dependent critical capillary number, a uniform displacement by a less viscous fluid can transition into a growing finger that eventually breaks up into discrete blobs by a series of pinch-off events for both wetting and nonwetting contact angles. This study validates previous experimental observations of pinch-off for wetting contact angles and extends those to nonwetting contact angles. We find that the blob length increases with the capillary number. We observe that the time between consecutive pinch-off events decreases with the capillary number and is greater for more wetting conditions in the displaced phase. We further show that the blob separation distance as a function of the difference between the inlet velocity and the contact line speed collapses into two monotonically decreasing curves for wetting and nonwetting contact angles. For the phase separation in the form of pinch-off, this work provides a quantitative study of the emerging length and timescales and their dependence on the wettability conditions, capillary effects, and viscous forces.

Cox–Voinov theory with slip

Abstract

Non-axisymmetric elastohydrodynamic solid-liquid-solid dewetting: Experiments and numerical modelling

.We have studied the dewetting dynamics of partially wetting liquid films confined between a soft elastic hemisphere and an elastomer layer by means of systematic experiments. We focused on the experimentally most relevant case of non-axisymmetric dewetting, which initiated at the locations of minimum film thickness near the perimeter of the contact area. We found the contact line speed to be highly anisotropic in this case. It is significantly faster in the azimuthal direction along the perimeter of the contact spot than in the radially inwards direction. We developed a three-dimensional, fully coupled numerical model that reproduces many features observed in the experiments.Graphical abstract

Wetting transitions in droplet drying on soft materials

Droplet interactions with compliant materials are familiar, but surprisingly complex processes of importance to the manufacturing, chemical, and garment industries. Despite progress—previous research indicates that mesoscopic substrate deformations can enhance droplet drying or slow down spreading dynamics—our understanding of how the intertwined effects of transient wetting phenomena and substrate deformation affect drying remains incomplete. Here we show that above a critical receding contact line speed during drying, a previously not observed wetting transition occurs. We employ 4D confocal reference-free traction force microscopy (cTFM) to quantify the transient displacement and stress fields with the needed resolution, revealing high and asymmetric local substrate deformations leading to contact line pinning, illustrating a rate-dependent wettability on viscoelastic solids. Our study has significance for understanding the liquid removal mechanism on compliant substrates and for the associated surface design considerations. The developed methodology paves the way to study complex dynamic compliant substrate phenomena.

Droplet Spreading and Wettability of Abrasive Processed Aluminum Alloy Surfaces

One of the main cause of a droplet metastable state is found to be surface roughness. This state is characterized by a large contact angle hysteresis and condition when the static contact angle is larger than the advancing dynamic contact angle. Besides the texture, other factors can influence the deviation from the equilibrium state, in particular, the fluid flow rate (the growth rate of a droplet) affecting the contact line speed. An experimental study was done to determine the effect of roughness and fluid flow rate on wetting of aluminum-magnesium alloy surfaces with random roughness processed by abrasive polishing. Three-dimensional roughness parameters were used to evaluate their texture. The correlations between these parameters, static, advancing and receding dynamic contact angles, hysteresis, and contact line speed were obtained. The molecular-kinetic theory of wetting was used to interpret the dynamic contact angle data.

Simulation of micron-scale drop impact

The numerical simulation of droplet impact is of interest for a vast variety of industrial processes, where practical experiments are costly and time-consuming. In these simulations, the dynamic contact angle is a key parameter, but the modeling of its behavior is poorly understood so far. One of the few models which considers the overall physical context of the involved ‘moving contact line problem’ is Shikhmurzaev’s interface formation model (Shikhmurzaev, 2008). In addition to keeping the problem well-posed, all surface and bulk parameters, such as the contact angle, are determined as part of the solution rather than being prescribed functions of contact line speed. In this article, we couple an asymptotic version of the interface formation model with our three-dimensional incompressible two-phase Navier–Stokes solver. Additionally, we employ a simple constant contact angle approach. We compare the results of these two numerical models with those from laboratory experiments for the micron-scale droplet impact on substrates with a variety of wetting characteristics. With our sophisticated asymptotic interface formation model, the droplet shapes, heights and diameters compare very well with practical experiments.

Contact-line fluctuations and dynamic wetting

HypothesisThe thermal fluctuations of the three-phase contact line formed between a liquid and a solid at equilibrium can be used to determine key parameters that control dynamic wetting. MethodsWe use large-scale molecular dynamics simulations and Lennard-Jones potentials to model a liquid bridge between two molecularly smooth solid surfaces and study the positional fluctuations of the contact lines so formed as a function of the solid–liquid interaction. FindingsWe show that the fluctuations have a Gaussian distribution and may be modelled as an overdamped one-dimensional Langevin oscillator. Our analysis allows us to extract the coefficients of friction per unit length of the contact lines ζ, which arise from the collective interaction of the contact-line’s constituent liquid atoms with each other and the solid surface. We then compare these coefficients with those obtained by measuring the dynamic contact angle as a function of contact-line speed in independent simulations and applying the molecular-kinetic theory of dynamic wetting. We find excellent agreement between the two, with the same dependence on solid–liquid interaction and, therefore, the equilibrium contact angle θ0. As well as providing further evidence for the underlying validity of the molecular-kinetic model, our results suggest that it should be possible to predict the dynamics of wetting and, in particular, the velocity-dependence of the local, microscopic dynamic contact angle, by experimentally measuring the fluctuations of the contact line of a capillary system at equilibrium. This would circumvent the need to measure the microscopic dynamic contact angle directly.

Thermocapillary rupture of a horizontal liquid layer on a silicon substrate

This paper is an experimental study of thermocapillary breakdown phenomenon in a horizontal film of liquid placed on a silicon nonisothermal substrate. With the help of a high-speed video camera the speed of the three-phase contact line was measured during the growth of a dry spot.