Droplet Impact on Asymmetric Hydrophobic Microstructures.

Textured hydrophobic surfaces that repel liquid droplets unidirectionally are found in nature such as butterfly wings and ryegrass leaves and are also essential in technological processes such as self-cleaning and anti-icing. In many occasions, surface textures are oriented to direct rebounding droplets. Surface macrostructures (>100 µm) have often been explored to induce directional rebound. However, the influence of impact speed and detailed surface geometry on rebound is vaguely understood, particularly for small microstructures. Here, we study, using a high-speed camera, droplet impact on surfaces with inclined micropillars. We observed directional rebound at high impact speeds on surfaces with dense arrays of pillars. We attribute this asymmetry to the difference in wetting behavior of the structure sidewalls, causing slower retraction of the contact line in the direction against the inclination compared to with the inclination. The experimental observations are complemented with numerical simulations to elucidate the detailed movement of the drops over the pillars. These insights improve our understanding of droplet impact on hydrophobic microstructures and may be useful for designing structured surfaces for controlling droplet mobility.

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.

Vibration sorting of small droplets on hydrophilic surface by asymmetric contact-line friction.

Droplet spreading and transport phenomenon is ubiquitous and has been studied by engineered surfaces with a variety of topographic features. To obtain a directional bias in dynamic wetting, hydrophobic surfaces with a geometrical asymmetry are generally used, attributing the directionality to one-sided pinning. Although the pinning may be useful for directional wetting, it usually limits the droplet mobility, especially for small volumes and over wettable surfaces. Here, we demonstrate a pinning-less approach to rapidly transport millimeter sized droplets on a partially wetting surface. Placing droplets on an asymmetrically structured surfaces with micron-scale roughness and applying symmetric horizontal vibration, they travel rapidly in one direction without pinning. The key, here, is to generate capillary-driven rapid contact-line motion within the time-scale of period of vibration. At the right regime where a friction factor local at the contact line dominates the rapid capillary motion, the asymmetric surface geometry can induce smooth and continuous contact-line movement back and forth at different speed, realizing directional motion of droplets even with small volumes over the wettable surface. We found that the translational speed is selective and strongly dependent on the droplet volume, oscillation frequency, and surface pattern properties, and thus droplets with a specific volume can be efficiently sorted out.

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.

Droplet leaping governs microstructured surface wetting.

Microstructured surfaces that control the direction of liquid transport are not only ubiquitous in nature, but they are also central to technological processes such as fog/water harvesting, oil-water separation, and surface lubrication. However, a fundamental understanding of the initial wetting dynamics of liquids spreading on such surfaces is lacking. Here, we show that three regimes govern microstructured surface wetting on short time scales: spread, stick, and contact line leaping. The latter involves establishing a new contact line downstream of the wetting front as the liquid leaps over specific sections of the solid surface. Experimental and numerical investigations reveal how different regimes emerge in different flow directions during wetting of periodic asymmetrically microstructured surfaces. These insights improve our understanding of rapid wetting in droplet impact, splashing, and wetting of vibrating surfaces and may contribute to advances in designing structured surfaces for the mentioned applications.

Revealing How Topography of Surface Microstructures Alters Capillary Spreading.

Wetting phenomena, i.e. the spreading of a liquid over a dry solid surface, are important for understanding how plants and insects imbibe water and moisture and for miniaturization in chemistry and biotechnology, among other examples. They pose fundamental challenges and possibilities, especially in dynamic situations. The surface chemistry and micro-scale roughness may determine the macroscopic spreading flow. The question here is how dynamic wetting depends on the topography of the substrate, i.e. the actual geometry of the roughness elements. To this end, we have formulated a toy model that accounts for the roughness shape, which is tested against a series of spreading experiments made on asymmetric sawtooth surface structures. The spreading speed in different directions relative to the surface pattern is found to be well described by the toy model. The toy model also shows the mechanism by which the shape of the roughness together with the line friction determines the observed slowing down of the spreading.

Early Onset of Nucleate Boiling on Gas-covered Biphilic Surfaces.

For phase-change cooling schemes for electronics, quick activation of nucleate boiling helps safeguard the electronics components from thermal shocks associated with undesired surface superheating at boiling incipience, which is of great importance to the long-term system stability and reliability. Previous experimental studies show that bubble nucleation can occur surprisingly early on mixed-wettability surfaces. In this paper, we report unambiguous evidence that such unusual bubble generation at extremely low temperatures-even below the boiling point-is induced by a significant presence of incondensable gas retained by the hydrophobic surface, which exhibits exceptional stability even surviving extensive boiling deaeration. By means of high-speed imaging, it is revealed that the consequently gassy boiling leads to unique bubble behaviour that stands in sharp contrast with that of pure vapour bubbles. Such findings agree qualitatively well with numerical simulations based on a diffuse-interface method. Moreover, the simulations further demonstrate strong thermocapillary flows accompanying growing bubbles with considerable gas contents, which is associated with heat transfer enhancement on the biphilic surface in the low-superheat region.

Electrostatic cloaking of surface structure for dynamic wetting.

Dynamic wetting problems are fundamental to understanding the interaction between liquids and solids. Even in a superficially simple experimental situation, such as a droplet spreading over a dry surface, the result may depend not only on the liquid properties but also strongly on the substrate-surface properties; even for macroscopically smooth surfaces, the microscopic geometrical roughness can be important. In addition, because surfaces may often be naturally charged or electric fields are used to manipulate fluids, electric effects are crucial components that influence wetting phenomena. We investigate the interplay between electric forces and surface structures in dynamic wetting. Although surface microstructures can significantly hinder spreading, we find that electrostatics can "cloak" the microstructures, that is, deactivate the hindering. We identify the physics in terms of reduction in contact-line friction, which makes the dynamic wetting inertial force dominant and insensitive to the substrate properties.

Diffuse interface method for a compressible binary fluid.

Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO_{2} + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO_{2} + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO_{2} the smaller the surface tension and the easier the drop deforms.

Dynamic wetting of viscoelastic droplets.

We conduct numerical experiments on spreading of viscoelastic droplets on a flat surface. Our work considers a Giesekus fluid characterized by a shear-thinning viscosity and an Oldroyd-B fluid, which is close to a Boger fluid with constant viscosity. Our results qualitatively agree with experimental observations in that both shear thinning and elasticity enhances contact line motion, and that the contact line motion of the Boger fluid obeys the Tanner-Voinov-Hoffman relation. Excluding inertia, the spreading speed shows strong dependence on rheological properties, such as the viscosity ratio between the solvent and the polymer suspension, and the polymeric relaxation time. We also discuss how elasticity can affect contact line motion. The molecular migration theory proposed in the literature is not able to explain the agreement between our simulations and experimental results.

Thermohydrodynamics of boiling in binary compressible fluids.

We numerically study the thermohydrodynamics of boiling for a CO(2) + ethanol mixture on lyophilic and lyophobic surfaces in both closed and open systems, based on a diffuse interface model for a two-component system. The corresponding wetting boundary conditions for an isothermal system are proposed and verified in this paper. New phenomena due to the addition of another component, mainly the preferential evaporation of the more volatile component, are observed. In the open system and the closed system, the physical process shows very different characteristics. In the open system, except for the movement of the contact line, the qualitative features are rather similar for lyophobic and lyophilic surfaces. In the closed system, the vortices that are observed on a lyophobic surface are not seen on a lyophilic surface. More sophisticated wetting boundary conditions for nonisothermal, two-component systems might need to be further developed, taking into account the variations of density, temperature, and surface tension near the wall, while numerical results show that the boundary conditions proposed here also work well even in boiling, where the temperature is nonuniform.

Multirelaxation-time lattice Boltzmann model for droplet heating and evaporation under forced convection.

We investigate the evaporation of a droplet surrounded by superheated vapor with relative motion between phases. The evaporating droplet is a challenging process, as one must take into account the transport of mass, momentum, and heat. Here a lattice Boltzmann method is employed where phase change is controlled by a nonideal equation of state. First, numerical simulations are compared to the D(2) law for a vaporizing static droplet and good agreement is observed. Results are then presented for a droplet in a Lagrangian frame under a superheated vapor flow. Evaporation is described in terms of the temperature difference between liquid-vapor and the inertial forces. The internal liquid circulation driven by surface-shear stresses due to convection enhances the evaporation rate. Numerical simulations demonstrate that for higher Reynolds numbers, the dynamics of vaporization flux can be significantly affected, which may cause an oscillatory behavior on the droplet evaporation. The droplet-wake interaction and local mass flux are discussed in detail.

Surface structure determines dynamic wetting.

Liquid wetting of a surface is omnipresent in nature and the advance of micro-fabrication and assembly techniques in recent years offers increasing ability to control this phenomenon. Here, we identify how surface roughness influences the initial dynamic spreading of a partially wetting droplet by studying the spreading on a solid substrate patterned with microstructures just a few micrometers in size. We reveal that the roughness influence can be quantified in terms of a line friction coefficient for the energy dissipation rate at the contact line, and that this can be described in a simple formula in terms of the geometrical parameters of the roughness and the line-friction coefficient of the planar surface. We further identify a criterion to predict if the spreading will be controlled by this surface roughness or by liquid inertia. Our results point to the possibility of selectively controlling the wetting behavior by engineering the surface structure.

Dynamic wetting at the nanoscale.

Although the capillary spreading of a drop on a dry substrate is well studied, understanding and describing the physical mechanisms that govern the dynamics remain challenging. Here we study the dynamics of spreading of partially wetting nanodroplets by combining molecular dynamics simulations and continuum phase field simulations. The phase field simulations account for all the relevant hydrodynamics, i.e., capillarity, inertia, and viscous stresses. By coordinated continuum and molecular dynamics simulations, the macroscopic model parameters are extracted. For a Lennard-Jones fluid spreading on a planar surface, the liquid slip at the solid substrate is found to be significant, in fact crucial for the motion of the contact line. Evaluation of the different contributions to the energy transfer shows that the liquid slip generates dissipation of the same order as the bulk viscous dissipation or the energy transfer to kinetic energy. We also study the dynamics of spreading on a substrate with a periodic nanostructure. Here it is found that a nanostructure with a length scale commensurate with molecular size completely inhibits the liquid slip. The dynamic spreading is thus about 30% slower on a nanostructured surface compared to one that is atomically smooth.

Universality in dynamic wetting dominated by contact-line friction.

We report experiments on the rapid contact-line motion present in the early stages of capillary-driven spreading of drops on dry solid substrates. The spreading data fail to follow a conventional viscous or inertial scaling. By integrating experiments and simulations, we quantify a contact-line friction µ(f) which is seen to limit the speed of the rapid dynamic wetting. A scaling based on this contact-line friction is shown to yield a universal curve for the evolution of the contact-line radius as a function of time, for a range of fluid viscosities, drop sizes, and surface wettabilities.

Numerical calculation of the dielectrophoretic force on a slender body.

In this paper, a model is proposed to numerically calculate the dielectrophoretic (DEP) force acting on a straight slender body in a non-uniform electric field. The induced charges are assumed to be located along the centerline of the slender body. By enforcing the boundary conditions at the interfaces of the two dielectrics, an integral equations system is obtained with the induced charge densities as unknowns. Based on the calculated induced charge densities, expressions to calculate the DEP force and torque are obtained. The calculated induced charge density of a prolate ellipsoid under a uniform electric field is compared with the analytic solution and an excellent agreement is achieved. The smaller the slenderness (the ratio of maximum radius to length of the slender body), the smaller the error is. The DEP force that a prolate ellipsoid experiences in a general electric field is numerically calculated and compared with the results obtained by the commonly accepted effective dipole moment method. The current model is expected to possess higher accuracy than the effective dipole moment method and to demand less calculation work than the Maxwell stress tensor method.

Multicomponent and multiphase modeling and simulation of reactive wetting.

A multicomponent and multiphase model with fluid motion is developed. The model is used to study reactive wetting in the case where concentration change of the spreading liquid and the substrate occurs. With the introduction of a Gibbs energy functional, the governing equations are derived, consisting of convective concentration and phase-field equations which are coupled to the Navier-Stokes equations with surface tension forces. The solid substrate is modeled hydrodynamically with a very high viscosity. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. An axisymmetric model with an adaptive finite element method is utilized. Numerical simulations were done revealing two stages in the wetting process. First, the convection-dominated stage where rapid spreading occurs. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Second, the diffusion-dominated stage where we observed depression of the substrate-liquid interface and elevation of the contact line region.

Microdroplet deposition under a liquid medium.

An experimental and numerical study of the factors affecting the reproducibility of microdroplet depositions performed under a liquid medium is presented. In the deposition procedure, sample solution is dispensed from the end of a capillary by the aid of a pressure pulse onto a substrate with pillar-shaped sample anchors. The deposition was modeled using the convective Cahn-Hilliard equation coupled with the Navier-Stokes equations with added surface tension and gravity forces. To avoid a severe time-step restriction imposed by the fourth-order Cahn-Hilliard equation, a semi-implicit scheme was developed. An axisymmetric model was used, and an adaptive finite element method was implemented. In both the experimental and numerical study it was shown that the deposited volume mainly depends on the capillary-substrate distance and the anchor surface wettability. A critical equilibrium contact angle has been identified below which reproducible depositions are facilitated.

Multi-step dielectrophoresis for separation of particles.

A new concept for separation of particles based on repetitive dielectrophoretic trapping and release in a flow system is proposed. Calculations using the finite element method have been performed to envision the particle behavior and the separation effectiveness of the proposed method. As a model system, polystyrene beads in deionized water and a micro-flow channel with arrays of interdigited electrodes have been used. Results show that the resolution increases as a direct function of the number of trap-and-release steps, and that a difference in size will have a larger influence on the separation than a difference in other dielectrophoretic properties. About 200 trap-and-release steps would be required to separate particles with a size difference of 0.2%. The enhanced separation power of dielectrophoresis with multiple steps could be of great importance, not only for fractionation of particles with small differences in size, but also for measuring changes in surface conductivity, or for separations based on combinations of difference in size and dielectric properties.

Superpositioned dielectrophoresis for enhanced trapping efficiency.

One of the major applications for dielectrophoresis is selective trapping and fractionation of particles. If the surrounding medium is of low conductivity, the trapping force is high, but if the conductivity increases, the attraction decreases and may even become negative. However, high-conductivity media are essential when working with biological material such as living cells. In this paper, some basic calculations have been performed, and a model has been developed which employs both positive and negative dielectrophoresis in a channel with interdigitated electrodes. The finite element method was utilized to predict the trajectories of Escherichia coli bacteria in the superpositioned electrical fields. It is shown that a drastic improvement of trapping efficiency can be obtained in this way, when a high conductivity medium is employed.