Droplet motion in one-component fluids on solid substrates with wettability gradients

Velocity-Switched Droplet Rebound Direction on Anisotropic Superhydrophobic Surfaces

Droplet well-controlled directional motion being an essential function has attracted much interest in academic and industrial applications, such as self-cleaning, micro-/nano-electro-mechanical systems, drug delivery, and heat-transferring. Conventional understanding has it that a droplet impacted on an anisotropic surface tends to bounce along the microstructural direction, which is mainly dictated by surface properties rather than initial conditions. In contrast to previous findings, it demonstrates that the direction of a droplet's rebound on an anisotropic surface can be switched by designing the initial impacting velocity. With an increase in impacting height from 2 to 10 cm, the droplet successively shows a backward, vertical, and forward motion on anisotropic surfaces. Theoretical demonstrations establish that the transition of droplet bouncing on the anisotropic surface is related to its dynamic wettability during impacting process. Characterized by the liquid-solid interaction, it is demonstrated that the contact state at small and large impacting heights induces an opposite resultant force in microstructures. Furthermore, energy balance analysis reveals that the energy conversion efficiency of backward motion is almost three times as that of traditional bouncing. This work, including experiments, theoretical models, and energy balance analysis provides insight view in droplet motions on the anisotropic surfaces and opens a new way for the droplet transport.

The Effects of Viscoelasticity on Droplet Migration on Surfaces with Wettability Gradients

A finite-volume method based on the OpenFOAM is used to numerically study the factors affecting the migration of viscoelastic droplets on rigid surfaces with wettability gradients. Parameters investigated include droplet size, relaxation time, solvent viscosity, and polymer viscosity of the liquid comprising droplets. The wettability gradient is imposed numerically by assuming a linear change in the contact angle along the substrate. As reported previously for Newtonian droplets, the wettability gradient induces spontaneous migration from hydrophobic to hydrophilic region on the substrate. The migration of viscoelastic droplets reveals the increase in the migration speed and distance with the increase in the Weissenberg number. The increase in droplet size also shows the increase in both the migration speed and distance. The increase in polymer viscosity exhibits the increase in migration speed but the decrease in migration distance.

Directional Liquid Transport from the Cold Region to the Hot Region on a Topological Surface

Manifested from the "tears of wine" to the "coffee-ring effect", the directional transport of a liquid governed by the Marangoni effect is highly pervasive in our daily life and has brought a great number of applications. Similar to this surface tension gradient-dominated process, the fluid preferentially flows from the hot region to the cold region. In contrast to this perception, in this study, we report that water liquid deposited on a specially designed topological surface can flow from the low-temperature region to the high-temperature region in a spontaneous, long-range, and unidirectional manner. We show that such a behavior is mainly owing to a strong topological effect that outweighs the thermal gradient imposed along the surface. Moreover, the specific temperature range applied on the topological surface for the occurrence of such a unidirectional liquid transport phenomenon is also identified. Our findings would find important insights for developing next-generation cooling devices where a rapid flow from the condensation region to the evaporation/boiling region is preferred.

Bioinspired Topological Surface for Directional Oil Lubrication

Directional droplet transport widely exists in biological surfaces that greatly inspire the development of a great deal of engineered devices allowing for directional liquid transport in diverse energy and water applications. Despite extensive advances in this area, it remains a challenge to guide the directional spreading of lubricating oils by virtue of the bioinspired design of surface topography in the lubricity field. In this paper, we develop a bioinspired topological surface textured with simple V-shaped posts elegantly distributed in the parallel channels, which allows for an efficient and unidirectional transport of various lubricating oils. We also clarify the propagation of a precursor film and the coalescence effect between the original droplet and the precursor film in the preferential direction, as well as the pinning effect in the reverse direction, which integrate seamlessly to create a long-range directional oil transportation. The directional oil transportation promises a potential application of directional lubrication, creating a functional surface consisting of two zones with different lubrication properties as evidenced by different friction coefficients.

Designing biomimetic liquid diodes

Just as the innovation of electronic diodes that allow the current to flow in one direction provides a foundation for the development of digital technologies, the engineering of surfaces or devices that allow the directional and spontaneous transport of fluids, termed liquid diodes, is highly desired in a wide spectrum of applications ranging from medical microfluidics, advanced printing, heat management and water collection to oil-water separation. Recent advances in manufacturing, visualization techniques, and biomimetics have led to exciting progress in the design of various liquid diodes. In spite of exciting progress, formulating a general framework broad enough to guide the design, optimization and fabrication of engineered liquid diodes remains a challenging task to date. In this review, we first present an overview of the development of biological and engineered liquid diodes to elucidate how to control the surface chemistry and topography to regulate the transport of liquids without the need for external energy. Then the latest design strategies allowing for the creation of longitudinal and transverse liquid diodes are discussed and compared. We also define some figures of merit such as the rectification coefficient and the transport velocity and distance to quantify the performance of liquid diodes. Finally, we highlight perspectives on the development of engineered liquid diodes that transcend nature and adapt to various practical applications.

A numerical study on viscoelastic droplet migration on a solid substrate due to wettability gradient

This study investigates the viscoelastic effects on droplet migration induced by a wettability gradient on a rigid substrate by a numerical simulation based on OpenFOAM with the volume-of-fluid method. The droplets are set with different rheological properties to investigate the effect of the elastic parameters. The Oldroyd-B model was employed. Quantitative differences in the migration and deformation between Newtonian and viscoelastic droplets were investigated by changing the degree of elasticity. The droplet migration shows conspicuously higher mobility for high elasticity, especially during the accelerating period. Moreover, the displacement and velocity increased with the decrease of a viscoelasticity parameter, and the velocity enhancement was regulated by the elastic instability shown at a high Weissenberg number. In addition, the velocity of the droplet changes more significantly over the range of contact angles of 130° to 60° compared to other wettability-gradient surfaces.

Vapor-Induced Motion of Liquid Droplets on an Inert Substrate

Evaporating droplets are known to show complex motion that has conventionally been explained by the Marangoni effect (flow induced by the gradient of surface tension). Here, we show that the droplet motion can be induced even in the absence of the Marangoni effect due to the gradient of the evaporation rate. We derive an equation for the velocity of a droplet subject to the nonuniform evaporation rate and nonuniform surface tension placed on an inert substrate, where the wettability is uniform and unchanged. The equation explains the previously observed attraction-repulsion-chasing behaviors of evaporating droplets.

Surface-dependent scenarios for dissolution-driven motion of growing droplets

Nano-droplets on a foreign substrate have received increasing attention because of their technological possible applications, for instance to catalyse the growth of nanowires. In some cases the droplets can move as a result of a reaction with the substrate. In this work we show that the substrate orientation, the surface morphology and the shape of the pits etched in the substrate by the droplets affect the droplet motion, so that a single mechanism (droplet-induced substrate dissolution) may lead to several unexpected droplet dynamics. The experiments are carried out by low energy electron microscopy on Au-Si and Au-Ge, which are model systems for studying liquid droplet alloys. Studying in-situ the behaviour of Au droplets on various Si and Ge surfaces, we describe a subtle interplay between the substrate orientation, the surface defects, and the droplet motion. Our observations allow a deep understanding of the interfacial mechanisms at the origin of the alloy formation and the associated droplet motion. These mechanisms are based on events of substrate dissolution/recrystallization. The outcomes of this work highlight the importance of the etching anisotropy on the droplet-substrate behaviours, and are essential in the perspective of positioning liquid alloy droplets used for instance as nanowire catalysts.

Droplet migration on hydrophobic–hydrophilic hybrid surfaces: a lattice Boltzmann study

Droplet migration on textured hydrophobic–hydrophilic surfaces.

Thermal singularity and contact line motion in pool boiling: Effects of substrate wettability

The dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] is employed to model the growth of a single vapor bubble in a superheated liquid on a flat homogeneous substrate. The bubble spreading dynamics in the pool boiling regime has been numerically investigated for one-component van der Waals fluids close to the critical point, with a focus on the effect of the substrate wettability on bubble growth and contact line motion. The substrate wettability is found to control the apparent contact angle and the rate of bubble growth (the rate of total evaporation), through which the contact line speed is determined. An approximate expression is derived for the contact line speed, showing good agreement with the simulation results. This demonstrates that the contact line speed is primarily governed by (1) the circular shape of interface (for slow bubble growth), (2) the constant apparent contact angle, and (3) the constant bubble growth rate. It follows that the contact line speed has a sensitive dependence on the substrate wettability via the apparent contact angle which also determines the bubble growth rate. Compared to hydrophilic surfaces, hydrophobic surfaces give rise to a thinner shape of bubble and a higher rate of total evaporation, which combine to result in a much faster contact line speed. This can be linked to the earlier formation of a vapor film and hence the onset of boiling crisis.

Numerical Simulations of the Digital Microfluidic Manipulation of Single Microparticles

Single-cell analysis techniques have been developed as a valuable bioanalytical tool for elucidating cellular heterogeneity at genomic, proteomic, and cellular levels. Cell manipulation is an indispensable process for single-cell analysis. Digital microfluidics (DMF) is an important platform for conducting cell manipulation and single-cell analysis in a high-throughput fashion. However, the manipulation of single cells in DMF has not been quantitatively studied so far. In this article, we investigate the interaction of a single microparticle with a liquid droplet on a flat substrate using numerical simulations. The droplet is driven by capillary force generated from the wettability gradient of the substrate. Considering the Brownian motion of microparticles, we utilize many-body dissipative particle dynamics (MDPD), an off-lattice mesoscopic simulation technique, in this numerical study. The manipulation processes (including pickup, transport, and drop-off) of a single microparticle with a liquid droplet are simulated. Parametric studies are conducted to investigate the effects on the manipulation processes from the droplet size, wettability gradient, wetting properties of the microparticle, and particle-substrate friction coefficients. The numerical results show that the pickup, transport, and drop-off processes can be precisely controlled by these parameters. On the basis of the numerical results, a trap-free delivery of a hydrophobic microparticle to a destination on the substrate is demonstrated in the numerical simulations. The numerical results not only provide a fundamental understanding of interactions among the microparticle, the droplet, and the substrate but also demonstrate a new technique for the trap-free immobilization of single hydrophobic microparticles in the DMF design. Finally, our numerical method also provides a powerful design and optimization tool for the manipulation of microparticles in DMF systems.

Wettability effects on contact line dynamics of droplet motion in an inclined channel

The present work discusses the implications of wall wettability and inclination of the surface on droplet dynamics. In this work, mesoscopic illustration of droplet dynamics in a duct with different inclination angles, based on the two-phase lattice Boltzmann model, is reported. Temporal evolution of wetted length, wetted area, and maximum height of the droplet for surfaces with different inclination angles and wettabilities is furnished in detail in order to elucidate the droplet displacement dynamics. It has been observed that the effect of inclination of the surface on droplet dynamics is more pronounced on a hydrophobic surface as compared to a hydrophilic surface. The time evolution of height and contact line motion of the droplet shows that higher angle of inclination of substrate affects the dynamics strongly irrespective of wettability.

Thermocapillary-actuated contact-line motion of immiscible binary fluids over substrates with patterned wettability in narrow confinement

We investigate thermocapillary-driven contact-line dynamics of two immiscible fluids in a narrow fluidic confinement comprising substrates with patterned wettability variations. Our study, based on phase field formalism, demonstrates that the velocity of the contact line is a strong function of the combined consequences of the applied thermal gradient and the substrate wetting characteristics. Finally, we evaluate different energy transfer rates and show that the dissipation due to fluid slip over the solid surface plays a dominating role in transferring energy into the contact-line motion. Our analysis, in effect, provides an elegant way of controlling the capillary filling rate in a narrow fluidic confinement by tailoring the applied temperature gradient and the substrate wettability in tandem.

Single-bubble dynamics in pool boiling of one-component fluids

We numerically investigate the pool boiling of one-component fluids with a focus on the effects of surface wettability on the single-bubble dynamics. We employed the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], a diffuse-interface model for liquid-vapor flows involving liquid-vapor transition in nonuniform temperature fields. We first perform simulations for bubbles on homogeneous surfaces. We find that an increase in either the contact angle or the surface superheating can enhance the bubble spreading over the heating surface and increase the bubble departure diameter as well and therefore facilitate the transition into film boiling. We then examine the dynamics of bubbles on patterned surfaces, which incorporate the advantages of both hydrophobic and hydrophilic surfaces. The central hydrophobic region increases the thermodynamic probability of bubble nucleation while the surrounding hydrophilic region hinders the continuous bubble spreading by pinning the contact line at the hydrophobic-hydrophilic intersection. This leads to a small bubble departure diameter and therefore prevents the transition from nucleate boiling into film boiling. With the bubble nucleation probability increased and the bubble departure facilitated, the efficiency of heat transfer on such patterned surfaces is highly enhanced, as observed experimentally [Int. J. Heat Mass Transfer 57, 733 (2013)]. In addition, the stick-slip motion of contact line on patterned surfaces is demonstrated in one-component fluids, with the effect weakened by surface superheating.

Molecular dynamics simulations for the motion of evaporative droplets driven by thermal gradients along nanochannels

For a one-component fluid on a solid substrate, a thermal singularity may occur at the contact line where the liquid-vapor interface intersects the solid surface. Physically, the liquid-vapor interface is almost isothermal at the liquid-vapor coexistence temperature in one-component fluids while the solid surface is almost isothermal for solids of high thermal conductivity. Therefore, a temperature discontinuity is formed if the two isothermal interfaces are of different temperatures and intersect at the contact line. This leads to the so-called thermal singularity. The localized hydrodynamics involving evaporation/condensation near the contact line leads to a contact angle depending on the underlying substrate temperature. This dependence has been shown to lead to the motion of liquid droplets on solid substrates with thermal gradients (Xu and Qian 2012 Phys. Rev. E 85 061603). In the present work, we carry out molecular dynamics (MD) simulations as numerical experiments to further confirm the predictions made from our previous continuum hydrodynamic modeling and simulations, which are actually semi-quantitatively accurate down to the small length scales in the problem. Using MD simulations, we investigate the motion of evaporative droplets in one-component Lennard-Jones fluids confined in nanochannels with thermal gradients. The droplet is found to migrate in the direction of decreasing temperature of solid walls, with a migration velocity linearly proportional to the temperature gradient. This agrees with the prediction of our continuum model. We then measure the effect of droplet size on the droplet motion. It is found that the droplet mobility is inversely proportional to a dimensionless coefficient associated with the total rate of dissipation due to droplet movement. Our results show that this coefficient is of order unity and increases with the droplet size for the small droplets (~10 nm) simulated in the present work. These findings are in semi-quantitative agreement with the predictions of our continuum model. Finally, we measure the effect of liquid-vapor coexistence temperature on the droplet motion. Through a theoretical analysis on the size of the thermal singularity, it can be shown that the droplet mobility decreases with decreasing coexistence temperature. This is observed in our MD simulations.

Hydrodynamics of Leidenfrost droplets in one-component fluids

Using the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], we numerically investigate the hydrodynamics of Leidenfrost droplets under gravity in two dimensions. Some recent theoretical predictions and experimental observations are confirmed in our simulations. A Leidenfrost droplet larger than a critical size is shown to be unstable and break up into smaller droplets due to the Rayleigh-Taylor instability of the bottom surface of the droplet. Our simulations demonstrate that an evaporating Leidenfrost droplet changes continuously from a puddle to a circular droplet, with the droplet shape controlled by its size in comparison with a few characteristic length scales. The geometry of the vapor layer under the droplet is found to mainly depend on the droplet size and is nearly independent of the substrate temperature, as reported in a recent experimental study [Phys. Rev. Lett. 109, 074301 (2012)]. Finally, our simulations demonstrate that a Leidenfrost droplet smaller than a characteristic size takes off from the hot substrate because the levitating force due to evaporation can no longer be balanced by the weight of the droplet, as observed in a recent experimental study [Phys. Rev. Lett. 109, 034501 (2012)].

Directional liquid spreading over chemically defined radial wettability gradients

We investigate the motion of liquid droplets on chemically defined radial wettability gradients. The patterns consist of hydrophobic fluorinated self-assembled monolayers (SAMs) on oxidized silicon substrates. The design comprises a central hydrophobic circle of unpatterned SAMs surrounded by annular regions of radially oriented stripes of alternating wettability, i.e., hydrophilic and hydrophobic. Variation in the relative width of the stripes allows control over the macroscopic wettability. When a droplet is deposited in the middle, it will start to move over to the radially defined wettability gradient, away from the center because of the increasing relative surface area of hydrophilic matter for larger radii in the pattern. The focus of this article is on a qualitative description of the characteristic motion on such types of anisotropic patterns. The influence of design parameters such as pattern dimensions, steepness of the gradient, and connection between different areas on the behavior of the liquid are analyzed and discussed in terms of advancing and receding contact lines, contact angles, spatial extent, and overall velocity of the motion.

Thermal singularity and droplet motion in one-component fluids on solid substrates with thermal gradients

Using a continuum model capable of describing the one-component liquid-gas hydrodynamics down to the contact line scale, we carry out numerical simulation and physical analysis for the droplet motion driven by thermal singularity. For liquid droplets in one-component fluids on heated or cooled substrates, the liquid-gas interface is nearly isothermal. Consequently, a thermal singularity occurs at the contact line and the Marangoni effect due to temperature gradient is suppressed. Through evaporation or condensation in the vicinity of the contact line, the thermal singularity makes the contact angle increase with the increasing substrate temperature. This effect on the contact angle can be used to move the droplets on substrates with thermal gradients. Our numerical results for this kind of droplet motion are explained by a simple fluid dynamical model at the droplet length scale. Since the mechanism for droplet motion is based on the change of contact angle, a separation of length scales is exhibited through a comparison between the droplet motion induced by a wettability gradient and that by a thermal gradient. It is shown that the flow field at the droplet length scale is independent of the statics or dynamics at the contact line scale.