Contact-line fluctuations and dynamic wetting

Unsteady wetting of soft solids

HYPOTHESIS

Spreading of liquids on soft solids often occurs intermittently, i.e., the liquid's wetting front switches between sticking and slipping. Studies of this so-called stick-slip wetting on soft solids mostly are confined within quasi-static or forced spreading conditions. In these situations, because the sticking duration is set much larger than the viscoelastic relaxation time of the solid, a ridge is persistently and fully developed at the wetting front as the soft solid yields to the liquid's surface tension. The sticking duration and spreading velocity, therefore, were shown to have little impact to the contact angle change required for stick-to-slip transitions. For unsteady wetting of soft solids, a commonly encountered but largely unexplored situation, we hypothesize that the stick-to-slip transition is controlled not only by a combination of sticking duration and the spreading velocity, but also by an increasing depinning threshold caused by the growing ridge at the wetting front.

EXPERIMENT

We performed unsteady wetting experiment on soft solids by letting water droplets spread freely on soft solid surfaces of various stiffness. We capture both the stick-slip spreading behavior and growing wetting ridges using synchronous high-speed imaging and high-speed interferometry. Recorded data of liquid spreading and solid deforming at the wetting front were analyzed to shed light on the relation between stick-slip characteristics and the growing wetting ridge.

FINDINGS

We find that intermittent wetting on a soft solid surface results from a competition between three key factors: liquid inertia, capillary force change during sticking, and growing pinning force caused by the solid's viscoelastic response. We theoretically formulate their quantitative contributions to predict how stick-to-slip transitions occur, i.e., how the contact angle change and sticking duration depend on the liquid's spreading velocity and the solid's viscoelastic characteristics. This provides a mechanistic understanding and methods to control unsteady wetting phenomena in diverse applications, from tissue engineering and fabrication of flexible electronics to biomedicine.

The receding contact line cools down during dynamic wetting

When a contact line (CL)-where a liquid-vapor interface meets a substrate-is put into motion, it is well known that the contact angle differs between advancing and receding CLs. Using non-equilibrium molecular dynamics simulations, we reveal another intriguing distinction between advancing and receding CLs: while temperature increases at an advancing CL-as expected from viscous dissipation, we show that temperature can drop at a receding CL. Detailed quantitative analysis based on the macroscopic energy balance around the dynamic CL showed that the internal energy change of the fluid due to the change of the potential field along the pathline out of the solid-liquid interface induced a remarkable temperature drop around the receding CL, in a manner similar to latent heat upon phase changes. This result provides new insights for modeling the dynamic CL, and the framework for heat transport analysis introduced here can be applied to a wide range of nanofluidic systems.

Dynamic wetting of various liquids: Theoretical models, experiments, simulations and applications

Dynamic wetting is a ubiquitous phenomenon and frequently observed in our daily life, as exemplified by the famous lotus effect. It is also an interfacial process of upmost importance involving many cutting-edge applications and has hence received significantly increasing academic and industrial attention for several decades. However, we are still far away to completely understand and predict wetting dynamics for a given system due to the complexity of this dynamic process. The physics of moving contact lines is mainly ascribed to the full coupling with the solid surface on which the liquids contact, the atmosphere surrounding the liquids, and the physico-chemical characteristics of the liquids involved (small-molecule liquids, metal liquids, polymer liquids, and simulated liquids). Therefore, to deepen the understanding and efficiently harness wetting dynamics, we propose to review the major advances in the available literature. After an introduction providing a concise and general background on dynamic wetting, the main theories are presented and critically compared. Next, the dynamic wetting of various liquids ranging from small-molecule liquids to simulated liquids are systematically summarized, in which the new physical concepts (such as surface segregation, contact line fluctuations, etc.) are particularly highlighted. Subsequently, the related emerging applications are briefly presented in this review. Finally, some tentative suggestions and challenges are proposed with the aim to guide future developments.

Thermal capillary waves on bounded nanoscale thin films

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.

Kinetic analysis of wetting and spreading at high temperatures: A review

The kinetic factors of the liquid-solid interface formation process are extremely useful in the design of composite preparation methods and the manufacture of comprehensive performance-controlled metal- or ceramic-based composites. Here, we review the available spreading dynamic models, focusing on wetting at high temperatures. There is yet to be developed a general spreading dynamic model with complete physical meaning that can accurately describe complicated surface-interface kinetic processes at high temperatures. In this work, we highlight common analysis errors in the description of the spreading dynamics for metal-ceramic and metal-metal systems. By unifying the expressions of the spreading dynamic models as the function f(v, θ_d) and fitting the experimental data reported in the literature, we discovered that the molecular-kinetic model commonly used to describe adsorption-controlled spreading at room temperature and reaction-limited spreading model used at high temperature have a certain range of overlap. When the condition σ_lv(cosθ_e-cosθ_d) < <2nk_BT is satisfied, these models are consistent in terms of mathematical functional expressions. As a result, distinguishing between them when the spreading behavior includes both adsorption and reaction is challenging.

Binary mixture droplet wetting on micro-structure decorated surfaces

Liquid surface tension as well as solid structure play a paramount role on the intimate wetting and non-wetting regimes and interactions between liquids droplets and solid substrates. We hypothesise that the coupling of these two variables, independently addressed in the past, eventually offer a wider range of understanding to the surface science and interfacial communities. In this work, intrinsically hydrophobic micro-pillared surfaces varying in the spacing between structures, and pure ethanol, pure water and their binary mixtures (as well as acetone-water and ethylene glycol-water mixtures) are utilised, accessing a wide range of substrate solid fractions and liquid surface tensions experimentally. Wettability measurements are carried out at different azimuthal directions to exemplify the wetting/non-wetting behaviour as well as the droplet asymmetry function of both liquid composition and structure spacing. Our findings reveal that high water concentration droplets, i.e., high surface tension fluids, sit in the Cassie-Baxter regime while partial non-wetting Wenzel or mixed-mode regimes with enhanced droplet asymmetry ensuing for medium and high ethanol concentrations, i.e., low surface tension fluids, below certain micropillar spacing. Beyond micropillar spacing s ≥ 40 µm, the impact of the surface structure on the droplet shape is negligible, and droplets adopt a similar contact angle and circular shape as on a flat smooth hydrophobic surface. Wetting and non-wetting regimes are then supported by classical wetting theories and equations. A wetting regime map for a wide range of surface tension fluids and/or their mixtures on a wide domain of solid fractions is then proposed.

Local stress tensor calculation by the method-of-plane in microscopic systems with macroscopic flow: A formulation based on the velocity distribution function

In this work, we developed a calculation method of local stress tensor applicable to non-equilibrium molecular dynamics (NEMD) systems, which evaluates the macroscopic momentum advection and the kinetic term of the stress in the framework of the Method-of-Plane (MoP), in a consistent way to guarantee the mass and momentum conservation. From the relation between the macroscopic velocity distribution function and the microscopic molecular passage across a fixed control plane, we derived a method to calculate the basic properties of the macroscopic momentum conservation law including the density, the velocity, the momentum flux, and the two terms of the stress tensor, i.e., the interaction and the kinetic terms, defined on a surface with a finite area. Any component of the streaming velocity can be obtained on a control surface, which enables the separation of the kinetic momentum flux into the advection and stress terms in the framework of MoP, and this enables strict satisfaction of the mass and momentum conservation for an arbitrary closed control volume (CV) set in NEMD systems. We validated the present method through the extraction of the density, velocity, and stress distributions in a quasi-one-dimensional steady-state Couette flow system and in a quasi-2D steady-state NEMD system with a moving contact line. We showed that with the present MoP, in contrast to the volume average method, the conservation law was satisfied even for a CV set around the moving contact line, which was located in a strongly inhomogeneous region.

Roles of energy dissipation and asymmetric wettability in spontaneous imbibition dynamics in a nanochannel

HYPOTHESIS

The imbibition dynamics is controlled by energy dissipation mechanisms and influenced by asymmetric wettability in a nanochannel. We hypothesize that the imbibition dynamics can be described by a combined model of the Lucas-Washburn equation and the Cox-Voinov law considering velocity-dependent contact angles.

METHODS

Molecular dynamics simulations are utilized to investigate the imbibition dynamics. A wide range of wetting conditions is achieved via adjusting the liquid-solid interaction parameters, and the spontaneous imbibition processes are quantified and compared.

FINDINGS

The critical condition for the occurrence of spontaneous imbibition is analyzed from a surface energy perspective. The analyses of energy conversion and dissipation indicate that the viscous dissipation is dominant during spontaneous imbibition. The classical Lucas-Washburn equation is modified with the Cox-Voinov law considering the effect of the dynamic contact angle and an effective equilibrium contact angle. We show that the proposed theory well captures the imbibition dynamics embodied in the growth of imbibition length as well as the transient interface shape and velocity for both the symmetric and asymmetric wetting conditions. In nanochannels with asymmetric wettability, the imbibition length difference between the sidewalls and interface oscillations increases with wetting disparity. Our findings deepen the understanding of imbibition dynamics on the nanoscale, and provide a theoretical reference for relevant applications.

Modification of the Fluctuation Dynamics of Ultrathin Wetting Films

We report on the effect of intermolecular forces on the fluctuations of supported liquid films. Using an optically induced thermal gradient, we form nanometer-thin films of wetting liquids on glass substrates, where van der Waals forces are balanced by thermocapillary forces. We show that the fluctuation dynamics of the film interface is strongly modified by intermolecular forces at lower frequencies. Data spanning three frequency decades are in excellent agreement with theoretical predictions accounting for van der Waals forces. Our results emphasize the relevance of intermolecular forces on thermal fluctuations when fluids are confined at the nanoscale.

Taking a closer look: A molecular-dynamics investigation of microscopic and apparent dynamic contact angles

HYPOTHESIS

Molecular dynamics (MD) may be used to investigate the velocity dependence of both the microscopic and apparent dynamic contact angles (θ_m and θ_app).

METHODS

We use large-scale MD to explore the steady displacement of a water-like liquid bridge between two molecularly-smooth solid plates under the influence of an external force F⁰. A coarse-grained model of water reduces the computational demand and the solid-liquid affinity is varied to adjust the equilibrium contact angle θ⁰. Protocols are devised to measure θ_m and θ_app as a function of contact-line velocity U_cl.

FINDINGS

For all θ⁰, θ_m is velocity-dependent and consistent with the molecular-kinetic theory of dynamic wetting (MKT). However, θ_app diverges from θ_m as F⁰ is increased, especially at the receding meniscus. The behavior of θ_app follows that predicted by Voinov: (θ_app)³ = (θ_m)³ + 9Ca·ln(L/L_m), where Ca is the capillary number and L and L_m are suitably-chosen macroscopic and microscopic length scales. For each θ⁰, there is a critical velocity U_crit and contact angle θ_crit at which θ_app→0 and the receding meniscus deposits a liquid film. Setting θ_app=0, θ_m=θ_crit and U_cl=U_crit in the Voinov equation yields the value of L/L_m. The predicted values of θ_app then agree well with those measured from the simulations. Since θ_m obeys the MKT, we have, therefore, demonstrated the utility of the combined model of dynamic wetting proposed by Petrov and Petrov.

Spreading and receding of oil droplets on silanized glass surfaces in water: Role of three-phase contact line flow direction in spontaneous displacement

HYPOTHESIS

The spontaneous displacement of both spreading and receding droplets on surfaces are extensively involved in numerous technical applications. We hypothesize that the spreading and receding displacement behaviors could be interpreted differently due to opposite flow directions at the three-phase contact line.

EXPERIMENTS

We performed two groups of displacement experiments using different initial setups of oil droplets on silanized glass surfaces in aqueous surroundings.

FINDINGS

The different initial configurations mostly resulted in oil displacement in opposite directions: either spreading or receding of the oil droplet. Different static states were observed at the end of the spreading and receding processes on surfaces with the same wettability due to the contact angle hysteresis. The dynamic displacement was analyzed using the hydrodynamic and molecular kinetic models, which showed distinct applicabilities for the data description of the spreading and receding possesses. The model analysis further indicated the different nature of these possesses, in particular, the resistance to displacement dynamics, which was illustrated by the interpretation of the microscopic slip length and contact line friction in the respective models. This study can shed light on the fundamental role of the displacement direction in the spontaneous liquid-liquid displacement.

Nanoscale thin-film flows with thermal fluctuations and slip

The combined effects of thermal fluctuations and liquid-solid slip on nanoscale thin-film flows are investigated using stochastic lubrication equations (SLEs). The previous no-slip SLE for films on plates is extended to consider slip effects and a new SLE for films on fibers is derived, using a long-wave approximation to fluctuating hydrodynamics. Analytically derived capillary spectra, which evolve in time, are found from the new SLEs and compared to molecular dynamics simulations. It is shown that thermal fluctuations lead to the generation and growth of surface waves, and slip accelerates this growth. SLEs developed here provide useful tools to study nanoscale film dewetting, nanofiber coating, and liquid transport using nanofibers.

Dynamic wetting of solid-liquid-liquid system by molecular kinetic theory

HYPOTHESIS

The mechanisms of dynamic wetting of solid-liquid-liquid (SLL) system, especially the viscosity effects of two liquids, can be investigated by the molecular kinetic theory (MKT).

METHODS

The molecular kinetic theory combined with published data was used to study the roles of a fluid viscosity and a solid surface in dynamic wetting.

FINDINGS

First, the MKT on dynamic wetting was introduced and its limitation was analyzed. Second, a viscosity effect and a solid surface effect were considered. The viscosity effect was divided into three parts for the first time, including two pure liquid zones and a mixing zone. Third, a coefficient activation free energy model was proposed, considering the effects of mixing liquids and a solid surface. Finally, the key parameters in the MKT and the application and validation of the coefficient activation free energy model were discussed in detail. This model can explain the energy dissipation in a vicinity of a three-phase contact-line successfully in a SLL wetting system. This work sheds light on the physical mechanisms of fluid and solid surface properties on the dynamic wetting in a SLL system.

Controlling the pinning time of a receding contact line under forced wetting conditions

HYPOTHESIS

The contact line pinning that appears in a flow coating process over substrates patterned with chemical or physical heterogeneities has been recently applied to deposit micro- and nanoparticles with great precision. However, the mechanism underlying pinning of a receding contact line at the nanoscale is not yet well understood. In the case of a contact line pinned at a chemical heterogeneity, we hypothesise that it is possible to establish a relation between the pinning time, the contact line velocity and the liquid/plate/heterogeneity affinity that can help to optimize particle deposition.

METHODS

We use large-scale molecular dynamic (MD) simulations of a finite liquid bridge formed between two parallel, non-identical, smooth solid plates. The top plate slides relative to the bottom plate inducing a displacement of the four different contact lines of the liquid bridge. The introduction of a chemical heterogeneity on the bottom plate by modifying locally the liquid-solid affinity provokes the transient pinning of the contact line in contact with the bottom substrate. By means of this simple MD simulation, we can study the mechanism of contact line pinning and its relation with the liquid/heterogeneity affinity and the contact line velocity. Additionally, we compare this mechanism with the case of the receding contact line pinned on a physical heterogeneity (a simple step discontinuity).

FINDINGS

We propose an analytical model that predicts the values of the dynamic contact angles in the general case of a capillary liquid bridge confined between two parallel plates with different wettabilities versus the relative velocity of the top plate. These predictions are successfully validated by the results of the large-scale MD simulations. The model allows thus to predict the value of the dynamic contact angles for the different contact lines of the system versus the relative speed of the moving plate. Once the chemical heterogeneity is introduced in the bottom plate, we show that when the receding contact line reaches the patch it remains temporarily pinned while the receding contact angle evolves with time. Once the receding angle reaches the value of the equilibrium contact angle of the patch, the receding contact line overcomes pinning. A geometrical model able to predict the pinning time is proposed and validated by our MD simulations. The pinning time depends not only on the relative plate velocity and plate wettability properties but also on the separation distance between the plates confining the capillary bridge. The model can consequently be used to select the substrate wettability or meniscus geometry suitable to impose the pinning time required for specific applications.

Moving contact lines and Langevin formalism

HYPOTHESIS

In previous work [J.-C. Fernández-Toledano, T. D. Blake^, J. De Coninck, J. Colloid Interface Sci. 540 (2019) 322-329], **we used molecular dynamics (MD) to show that the thermal oscillations of a contact line formed between a liquid and a solid at equilibrium may be interpreted in terms of an overdamped 1-D Langevin harmonic oscillator. The variance of the contact-line position and the rate of damping of its self-correlation function enabled us to determine the coefficient of contact-line friction ζ and so predict the dynamics of wetting. We now propose that the same approach may be applied to a moving contact line.

METHODS

We use the same MD system as before, a liquid bridge formed between two solid plates, but now we move the plates at a steady velocity U_plate in opposite directions to generate advancing and receding contact lines and their associated dynamic contact angles θ^d. The fluctuations of the contact-line positions and the dynamic contact angles are then recorded and analyzed for a range of plate velocities and solid-liquid interaction.

FINDINGS

We confirm that the fluctuations of a moving contact line may also be interpreted in terms of a 1-D harmonic oscillator and derive a Langevin expression analogous to that obtained for the equilibrium case, but with the harmonic term centered about the mean location of the dynamic contact line x^d, rather than its equilibrium position x⁰, and a fluctuating capillary force arising from the fluctuations of the dynamic contact angle around θ^d, rather than the equilibrium angle θ⁰. We also confirm a direct relationship between the variance of the fluctuations over the length of contact line considered L_y, the time decay of the oscillations, and the friction ζ. In addition, we demonstrate a new relationship for our systems between the distance to equilibrium x^d-x⁰ and the out of equilibrium capillary force γ_Lcosθ⁰-cosθ^d, where γ_L is the surface tension of the liquid, and show that neither the variance of the fluctuations nor their time decay depend on U_plate. Our analysis yields values of ζ nearly identical to those obtained for simulations of spreading drops confirming the common nature of the dissipation mechanism at the contact line.