Predicting the wetting dynamics of a two-liquid system

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.

Antifouling graphene oxide membranes for oil-water separation via hydrophobic chain engineering

Engineering surface chemistry to precisely control interfacial interactions is crucial for fabricating superior antifouling coatings and separation membranes. Here, we present a hydrophobic chain engineering strategy to regulate membrane surface at a molecular scale. Hydrophilic phytic acid and hydrophobic perfluorocarboxylic acids are sequentially assembled on a graphene oxide membrane to form an amphiphilic surface. The surface energy is reduced by the introduction of the perfluoroalkyl chains while the surface hydration can be tuned by changing the hydrophobic chain length, thus synergistically optimizing both fouling-resistance and fouling-release properties. It is found that the surface hydration capacity changes nonlinearly as the perfluoroalkyl chain length increases from C₄ to C₁₀, reaching the highest at C₆ as a result of the more uniform water orientation as demonstrated by molecular dynamics simulations. The as-prepared membrane exhibits superior antifouling efficacy (flux decline ratio <10%, flux recovery ratio ~100%) even at high permeance (~620 L m^-2 h^-1 bar^-1) for oil-water separation.

Molecular Dynamics Study of Wetting and Adsorption of Binary Mixtures of the Lennard-Jones Truncated and Shifted Fluid on a Planar Wall

The wetting of surfaces is strongly influenced by adsorbate layers. Therefore, in this work, sessile drops and their interaction with adsorbate layers on surfaces were investigated by molecular dynamics simulations. Binary fluid model mixtures were considered. The two components of the fluid mixture have the same pure component parameters, but one component has a stronger and the other a weaker affinity to the surface. Furthermore, the unlike interactions between both components were varied. All interactions were described by the Lennard-Jones truncated and shifted potential with a cutoff radius of 2.5σ. The simulations were carried out at constant temperature for mixtures of different compositions. The parameters were varied systematically and chosen such that cases with partial wetting as well as cases with total wetting were obtained and the relation between the varied molecular parameters and the phenomenological behavior was elucidated. Data on the contact angle as well as on the mole fraction and thickness of the adsorbate layer were obtained, accompanied by information on liquid and gaseous bulk phases and the corresponding phase equilibrium. Also, the influence of the adsorbate layer on the wetting was studied: for a sufficiently thick adsorbate layer, the wall's influence on the wetting vanishes, which is then only determined by the adsorbate layer.

Dramatic Slowing Down of Oil/Water/Silica Contact Line Dynamics Driven by Cationic Surfactant Adsorption on the Solid

We report on the contact line dynamics of a triple-phase system silica/oil/water. When oil advances onto silica within a water film squeezed between oil and silica, a rim forms in water and recedes at constant velocity. We evidence a sharp (three orders of magnitude) decrease of the contact line velocity upon the addition of cationic surfactants above a threshold concentration, which is slightly smaller than the critical micellar concentration. We show that, with or without surfactant, and within the range of small capillary numbers investigated, the contact line dynamics can be described by a friction term that does not reduce to pure hydrodynamical effects. In addition, we derive a model that successfully accounts for the selected contact line velocity of the rim. We further demonstrate the strong increase of the friction coefficient with surfactant bulk concentration results from the strongly nonlinear adsorption isotherm of surfactants on silica. From the variations of the friction coefficient and spreading parameter with surface concentration, we suggest a picture in which the part of the adsorbed surfactants that are strongly bound to the silica interface is trapped under the oil droplet and is responsible for the large increase in line friction.

A generalized examination of capillary force balance at contact line: On rough surfaces or in two-liquid systems

We investigate the capillary force balance at the contact line on rough solid surfaces and in two-liquid systems. Our results confirm that solid-liquid interactions perpendicular to the interface have a significant influence on the lateral component of the capillary force exerted on the contact line. Surface roughness of the solid substrate reduces the mobility of liquid and alters how the perpendicular solid-liquid interactions transfer into a force acting parallel to the interface. A quantitative relation between surface roughness and the transfer strategy is proposed. Moreover, when a liquid is in coexistence with another immiscible liquid on a solid, the capillary forces exerted on liquids of both sides are involved in our theoretical model. The contact angle can be predicted by calculating three interfacial tensions. These arguments are then verified by molecular dynamics simulations. Our findings set up the generalized theoretical framework for the capillary force balance at the contact line and broaden its application in more realistic scenarios.

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.

Forced Wetting and Dewetting of Water and Oil Droplets on Planar Microfluidic Grids

We experimentally study the wetting behavior of small water and oil droplets spreading and receding from textured surfaces made using a backside laser processing technique. A dual image acquisition system enables the three-dimensional characterization of both wetted area and dynamic contact angles. In particular, we compare droplet growth on smooth surfaces and planar microfluidic grids of various surface coverages and heights and discuss contact angle characterization. The surface texture is shown to trap liquid in microwells during the stick-and-slip motion of advancing contact lines. Receding wetting dynamics of liquid infused substrates shows similarity with forced spreading on smooth surfaces. Contact angle hysteresis is investigated as a function of surface parameters to better delineate specific wetting behaviors of water and oil on laser-processed surfaces.

Effects of Molecular Chain Length on the Contact Line Movement in Water/n-Alkane/Solid Systems

The movement of the contact line in liquid-liquid-solid systems is a major phenomenon in natural and industrial processes. In particular, n-alkanes are widely occurring in the oil, soil pollution, and chemical industries, yet there is little knowledge on the effects of molecular chain length on the contact line movement. Here, we studied the effects of molecular chain length on the contact line movement in water/n-alkane/solid systems with different surface wettabilities. We used n-heptane (C7), n-decane (C10), and n-hexadecane (C16) as alkanes and α-quartz as the solid surface. We calculated the time-variation contact line moving velocity and also analyzed the jump frequency and the mean distance of the molecular displacement occurring within the contact line zone by molecular-kinetic theory. Molecular dynamics simulation results show that the contact line velocity decreases with increasing the chain length, originally caused by the decreasing the jump frequency and mean distance. These variations with the molecular chain length are related to the more torsions and deformations of the molecules with a longer chain length. In addition, the moving mechanism of the contact line on the same solid surface does not change at different molecular chain lengths, implying that the moving mechanism mainly depends on the three-phase wettability.

Understanding the asymmetry between advancing and receding microscopic contact angles

By means of molecular dynamics simulation, the advancing and receding microscopic contact angles were analyzed for a shear flow of two mono-atomic fluids confined between parallel non-polar solid walls. We defined the microscopic dynamic contact angle based on the coarse-grained microscopic density distribution of the fluids (the instantaneous interface method [Willard and Chandler, J. Phys. Chem. B, 2010, 114, 1954-1958]) near the moving contact line. We have found that the asymmetric change of fluid density near the wall with respect to the moving contact line results in a different dependence between the advancing and receding contact angles on the contact line velocity in a system where the two fluids across the interface have unequal wettability to the solid wall. This difference between the advancing and receding contact angles leads to different flow resistance caused by the advancing and receding contact lines, which should have impact on the industrial applications of the fine fluid transportation with contact lines.

Moving mechanisms of the three-phase contact line in a water–decane–silica system

The movement of the three-phase contact line with chain molecules in the liquid phase displays more complex mechanisms compared to those in the usual liquid–liquid–solid systems and even to the gas–liquid–solid systems controlled by the traditional single-molecule adsorption–desorption mechanisms. By introducing decane molecules with chain structures, we demonstrate from molecular dynamics insights that the moving mechanism of the contact line in a water–decane–silica system is totally different from traditional mechanisms. Three different wettability-related moving mechanisms including “Roll up”, “Piston” and “Shear” are revealed corresponding to the hydrophilic, intermediate and hydrophobic three-phase wettability, respectively. In the “Roll up” mechanism, the decane molecules are rolled up by the competitively adsorbed water molecules and then move forward under the driving force; when the “Piston” mechanism happens, the decane molecules are pushed by the piston-like water phase owing to the comparable adsorption interactions of the two liquids on the solid surface; in the “Shear” mechanism, the contact line is hard to drive due to the stronger decane–silica interactions but the decane molecules far away from the solid surface will move forward. Besides, the time-averaged velocity of the moving contact line is greatly related to the moving mechanisms. For the “Roll up” mechanism, the contact line velocity increases first and then reaches a steady value; for the “Piston” mechanism, the contact line velocity has a maximum value at the start-up stage and then decreases to a stable value; for the “Shear” mechanism, the contact line velocity fluctuates around zero due to the thermal fluctuation of the molecules. Additionally, the mean distance from Molecular Kinetics Theory increases with decreasing hydrophilicity and the displacement frequency in “Roll up” mechanism is 2 orders of magnitude higher than that in the “Piston” mechanism, further demonstrating the different moving mechanisms from a quantitative point of view.

Wettability-related moving mechanisms of the three-phase contact line with one liquid phase composed of chain molecules are revealed.

Anomalous Wetting of Underliquid Systems: Oil Drops in Water and Water Drops in Oil

We have investigated the wetting phenomena of two underliquid systems, i.e., oil (drop) in water medium and water (drop) in oil medium for two different substrates, poly(methyl methacrylate) (PMMA) and glass. We have conducted detailed static (equilibrium) and dynamic contact angle measurements of drops on substrates kept in air, water, and oils of varying densities, viscosities, and surface tensions. We compared the experimentally observed contact angles with those predicted by the conventional wetting theories, namely, Young's equation and the Owens and Wendt approach. The results reported herein showed that experimental values vary in the range of 8-20% with the conventional theoretical model for water (drop) in oil (viscous surrounding medium) on PMMA substrate. However, oil (drop) in water medium on PMMA does not show such an anomaly. By taking into consideration a thin oil film between a water drop and PMMA originating from the surrounding oil medium, the modified Young's equation is proposed here. We found that the percentage difference between experimentally observed contact angles with modified Young's equation is in the range of 0.88-5.88%, which is very less compared to percentage difference with classic Young's equation. For glass substrates, the standard Young's equation does not translate to the underliquid systems whereas the Owens and Wendt theory could not correctly predict the underliquid contact angles. However, the modified Young's equation with thin-film consideration agrees very well with the experimental values and thereby demonstrated the presence of a thin film between a drop and glass substrate originating from the surrounding viscous medium. This present experimental study coupled with detailed theoretical analyses demonstrates the anomalous wetting signature of drops on substrates submerged in surrounding viscous medium, which is very different from the reported studies for drops on substrates kept in air (inviscid medium).

Wetting dynamics of polydimethylsiloxane mixtures on a poly(ethylene terephthalate) fiber

HYPOTHESIS

The wetting dynamics of liquids with identical surface tensions are mostly controlled by their viscosities. We therefore hypothesized that the wetting dynamics of one- (pure liquid) and two-component (mixture) polydimethylsiloxane (PDMS) on a poly(ethylene terephthalate) (PET) fiber with similar surface tensions and viscosities should be controlled by the same underlying physical mechanisms.

EXPERIMENTS

We studied the capillary rise of PDMS liquids on a PET fiber. We compared the different contact angle relaxations and characterized the transitions between the molecular-kinetic theory (MKT) and hydrodynamic approach (HD) for the PDMS mixtures and the pure liquids as a function of their viscosities.

FINDINGS

Compared to the pure PDMS liquid with a viscosity of 20 mm²/s that presents a contact angle relaxation following a t^-1/2 scale law in agreement with HD, the PDMS mixture with a higher viscosity (27.4 mm²/s) shows a t^-1 behavior predicted by the MKT. Moreover, the transition between MKT and HD appears in a regime with higher viscosities for PDMS mixtures than for pure liquids. Surface segregation of shorter PDMS chains or precursor film may be responsible for this shift.

Wetting dynamics in two-liquid systems: Effect of the surrounding phase viscosity

This paper reports the experimental results of a water droplet spreading on a glass substrate submerged in an oil phase. The radius of the wetted area grows exponentially over time forming two distinct regimes. The early time dynamics of wetting is characterized with the time exponent of 1, referred to as the viscous regime, which is ultimately transitioned to the Tanner's regime with the time exponent of 0.1. It is revealed that an increase in the ambient phase viscosity over three decades considerably slows down the rate of three-phase contact line movement. A scaling law is developed where the three-phase contact line velocity is a function of both spreading radius and mean viscosity, close to the geometric mean of the droplet and ambient fluids' viscosities. Using the proposed scaling and mean viscosity, all plots of spreading radius for different viscosity ratios collapse to a master curve. Furthermore, several cases with multiple rupture and spreading points, i.e., wetting in a nonideal system, are considered. The growth of an equivalent wetting radius in a multiple point spreading system is predicted by the developed scaling law.

Analyzing the Molecular Kinetics of Water Spreading on Hydrophobic Surfaces via Molecular Dynamics Simulation

In this paper, we report molecular kinetic analyses of water spreading on hydrophobic surfaces via molecular dynamics simulation. The hydrophobic surfaces are composed of amorphous polytetrafluoroethylene (PTFE) with a static contact angle of ~112.4° for water. On the basis of the molecular kinetic theory (MKT), the influences of both viscous damping and solid-liquid retarding were analyzed in evaluating contact line friction, which characterizes the frictional force on the contact line. The unit displacement length on PTFE was estimated to be ~0.621 nm and is ~4 times as long as the bond length of C-C backbone. The static friction coefficient was found to be ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-3}$$\end{document}10−3 Pa·s, which is on the same order of magnitude as the dynamic viscosity of water, and increases with the droplet size. A nondimensional number defined by the ratio of the standard deviation of wetting velocity to the characteristic wetting velocity was put forward to signify the strength of the inherent contact line fluctuation and unveil the mechanism of enhanced energy dissipation in nanoscale, whereas such effect would become insignificant in macroscale. Moreover, regarding a liquid droplet on hydrophobic or superhydrophobic surfaces, an approximate solution to the base radius development was derived by an asymptotic expansion approach.

Young's Equation for a Two-Liquid System on the Nanometer Scale

We use large-scale molecular dynamics simulations to study the Lennard-Jones forces acting at the various interfaces of a liquid bridge (liquid 1) between two realistic solid plates on the scale of few nanometers when the two free surfaces are in contact with a second immiscible liquid (liquid 2) with an interfacial tension of γ₁₂. Each plate comprises a regular square planar lattice of atoms arranged in three atomic layers. To maintain rigidity while allowing momentum exchange with the liquid, solid atoms are allowed to vibrate thermally around their initial positions by a strong harmonic potential. By varying the solid-liquid coupling, we investigate a range of nonzero contact angles between the liquid-liquid interface and the solid. We first compute the forces when the plates are stationary (equilibrium case), from the perspectives of both the liquid and the solid. Our results confirm that the normal and tangential components of the computed interfacial forces at each contact line are consistent with Young's equation on this small scale. In particular, we show that the tangential force exerted by the liquid-liquid interface on the plates is given by the difference in the individual works of adhesion of the two liquids and equal to γ₁₂ cos θ_1,2⁰, where θ_1,2⁰ is the equilibrium contact angle measured through liquid 1. This result, which differs from that expected for a single liquid, is relevant to the interactions and behavior of two liquid-solid systems in nanotechnology. We then study the forces when the plates are translated at equal speeds in opposite directions over a range of steady velocities (dynamic case) and repeat the measurements of the force exerted by the liquid-liquid interface on the solid. We find that the normal and tangential components of this force are still correctly predicted by the normal and tangential components of the interfacial tension, provided only that the equilibrium contact angle is replaced by its dynamic analogue θ_1,2^D. Usually assumed without proof, this result is significant for our proper understanding of dynamic wetting at all scales.

Understanding the Early Regime of Drop Spreading

We present experimental data to characterize the spreading of a liquid drop on a substrate kept submerged in another liquid medium. They reveal that drop spreading always begins in a regime dominated by drop viscosity where the spreading radius scales as r ∼ t with a nonuniversal prefactor. This initial viscous regime either lasts in its entirety or switches to an intermediate inertial regime where the spreading radius grows with time following the well-established inertial scaling of r ∼ t(1/2). This latter case depends on the characteristic viscous length scale of the problem. In either case, the final stage of spreading, close to equilibrium, follows Tanner's law. Further experiments performed on the same substrate kept in ambient air reveal a similar trend, albeit with limited spatiotemporal resolution, showing the universal nature of the spreading behavior. It is also found that, for early times of spreading, the process is similar to coalescence of two freely suspended liquid drops, making the presence of the substrate and consequently the three-phase contact line insignificant.

The molecular-kinetic approach to wetting dynamics: Achievements and limitations

The molecular-kinetic theory (MKT) of dynamic wetting was formulated almost 50 years ago. It explains the dependence of the dynamic contact angle on the speed of a moving meniscus by estimating the non-hydrodynamic dissipation in the contact line. Over the years it has been refined to account explicitly for the influence of (bulk) fluid viscosity and it has been applied successfully to both solid-liquid-vapour and solid-liquid-liquid systems. The free energy barrier for surface diffusion has been related to the energy of adhesion. The MKT provides a qualitative explanation for most effects in dynamic wetting. The theory is simple, flexible, and it is widely used to rationalize the physics of wetting dynamics and fit experimental data (dynamic contact angle versus contact line speed). The MKT predicts an intermediate wettability as optimal for high-speed coating as well as the maximum speeds of wetting and dewetting. Nevertheless, the values of the molecular parameters derived from experimental data tend to be scattered and not particularly reliable. This review outlines the main achievements and limitations of the MKT and highlights some common cases of misinterpretation.

The influence of topography on dynamic wetting

The paramount importance of wetting applications and the significant economic value of controlling wetting-based industrial processes has stimulated a deep interest in wetting science. In many industrial applications the motion of a complex liquid front over nano-textured surfaces controls the fate of the processes. However our knowledge of the impact of nano-heterogeneities on static and dynamic wetting is very limited. In this article, the fundamentals of wetting are briefly reviewed, with a particular focus on hysteresis and roughness issues. Present knowledge and models of dynamic wetting on smooth and rough surfaces are then examined, with particular attention devoted to the case of nano-topographical heterogeneities and solid-fluid-fluid systems.

Formation and dynamics of partially wetting droplets in square microchannels

Droplet motion and dynamic wetting transitions are experimentally investigated over a wide range of viscosities and flow rates in square microchannels

Can dynamic contact angle be measured using molecular modeling?

A method is presented for determining the dynamic contact angle at the three-phase contact between a solid, a liquid, and a vapor under an applied force, using molecular simulation. The method is demonstrated using a Lennard-Jones fluid in contact with a cylindrical shell of the fcc Lennard-Jones solid. Advancing and receding contact angles and the contact angle hysteresis are reported for the first time by this approach. The increase in force required to wet fully an array of solid cylinders (robustness) with decreasing separation distance between cylinders is evaluated. The dynamic contact angle is characterized by partial slipping of the three phase contact line when a force is applied.

Forced wetting of a reactive surface

The dynamic wetting of water on gelatin-coated poly(ethylene terephthalate) (GC-PET) has been investigated by forced wetting over a wide speed range and compared with earlier data obtained with unmodified PET. The results were analysed according to the molecular-kinetic theory of dynamic wetting (MKT). Both substrates show complex behaviour, with separate low- and high-speed modes. For the GC-PET, this is attributed to a rapid change in the wettability of the substrate on contact with water, specifically a surface molecular transformation from hydrophobic to hydrophilic. This results in a smooth wetting transition from one mode to the other. For the PET, the bimodal behaviour is attributed to surface heterogeneity, with the low-speed dynamics dominated by interactions with polar sites on the substrate that become masked at higher speeds. In this case, the transition is discontinuous. The study has general ramifications for the investigation of any wetting processes in which a physicochemical transformation takes place at the solid surface on contact with the liquid. In particular, it shows how forced wetting, combined with the MKT, can reveal subtle details of the processes involved. It is unlikely that similar insight could be gained from spontaneous wetting studies, such as spreading drops.