Generation of Motion of Drops with Interfacial Contact

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.

Survey of Micro/Nanofabricated Chemical, Topographical, and Compound Passive Wetting Gradient Surfaces

Surface wetting gradients are desirable due to their ability to passively transport liquid droplets without the aid of gravity. Such surfaces can be prepared through topographical or chemical methods or a compound approach involving both methods. By altering the surface free energy across a surface, a droplet that contacts such a surface will experience an actuation force toward the hydrophilic region. Such transport properties make these surfaces attractive for a range of applications from thermal management to microfluidics to the investigation of biomolecular interactions. This paper reviews passive wetting gradients that have been demonstrated over the last three decades, focusing on the types of surfaces that have been developed to date along with the materials that have been used. The corresponding wetting ranges and physical lengths over which droplet mobility has been achieved on these various types of gradient surfaces are compared to guide future developments.

Upper Limit of Light-Levitated Droplet Motion

The light-enabled droplet levitation shows promising potential in applications in biotechnology, clinical medicine, and nanomaterials. In particular, light-levitated droplets have good followability with a moving laser beam, resulting in flexibility in manipulating their motion. However, it is still unclear whether there exists an upper limit to the light-levitated droplet motion with a moving laser beam. Therefore, the motion of light-levitated droplets above the free interface is studied to determine the upper limit of motions of the droplets with a moving laser beam. We demonstrate that an inefficient interface temperature response because of a very high moving speed of the laser beam and the resultant small upward vertical component of vapor flow are responsible for the existence of an upper-limit velocity. Above the upper limit, the light-levitated droplets are unable to stably move with the laser beam and finally disappear. By contrast, the droplets can stably move with the laser beam in a wide range at or below this upper limit. In addition, an almost linear relationship between the upper-limit velocity of the light-levitated droplets and the input laser power is presented. The findings of the present study are informative for the implementation of this light levitation technology.

Drop Spreading and Confinement in Swelling-Driven Folding of Thin Films

Surface instabilities are a versatile method for generating three-dimensional (3D) surface microstructure. When an elastomeric film weakly bonded to a substrate is swollen with solvent, buckle delamination and subsequent sliding of the film on the substrate lead to the formation of tall, self-contacting, and permanent folds. This paper explores the mechanics of fold development when such folding is induced by placing a drop on the surface of the film. We show that capillary effects can induce a strong coupling between folding and drop spreading: as folds develop, they wick the solvent toward the periphery of the drop, further propagating radially aligned folds. Accordingly, a solvent drop spreads far more on films that are weakly adhered to the substrate. As drop size reduces and folding becomes increasingly confined, debonding propagates along the perimeter of the wetted region, thus leading to corral-shaped fold patterns. On the other hand, as drop size increases and confinement effects weaken, isotropically oriented folds appear at a spacing that reduces as swelling increases. The spacing between the folds and the size of the corrals are both determined by the extent to which a single fold relieves compressive stress in its vicinity by sliding. We develop a model for folding which explicitly accounts for the fact that folds must initiate with near-zero volume under the buckle. The model shows that folds can appear even at very low swelling if there are large pre-existing debonded regions at the film-substrate interface.

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.

Directional Water Wicking on a Metal Surface Patterned by Microchannels

This work focuses on the simulation and experimental study of directional wicking of water on a surface structured by open microchannels. Stainless steel was chosen as the material for the structure motivated by industrial applications as fuel cells. Inspired by nature and literature, we designed a fin type structure. Using Selective Laser Melting (SLM) the fin type structure was manufactured additively with a resolution down to about 30 μm. The geometry was manufactured with three different scalings and both the experiments and the simulation show that the efficiency of the water transport depends on dimensionless numbers such as Reynolds and Capillary numbers. Full 3D numerical simulations of the multiphase Navier-Stokes equations using Volume of Fluid (VOF) and Lattice-Boltzmann (LBM) methods reproduce qualitatively the experimental results and provide new insight into the details of dynamics at small space and time scales. The influence of the static contact angle on the directional wicking was also studied. The simulation enabled estimation of the contact angle threshold beyond which transport vanishes in addition to the optimal contact angle for transport.

Audible Sound from Vibrating Sessile Droplets for Monitoring Chemicals and Reactions in Liquid

To reduce environmental impact and sensor footprint, researchers need cost-effective and small-size surface tension and viscosity measurement devices. New measurement principles are needed for such sensors. We demonstrate that a sessile droplet's mechanical vibration can be transformed to audible sound, by recording the ultrasonic Doppler frequency shift in the form of an acoustic signal. The recorded sound wave reveals a droplet's surface tension and its viscosity, through its frequency spectrum and attenuation rate of the signal, respectively. Based on such sensors, two chemical measurements inside sessile droplets are shown: (I) titration of a Ni²⁺ and Co²⁺ mixture with a surface-active indicator (using surface tension) and (II) measurement of the molecular weight of a polymer in solution (using viscosity). Unlike the commercial technique, our ultrasound-based sensor is cost-effective in terms of equipment price and sample volume.

Light-Caused Droplet Bouncing from a Cavity Trap-Assisted Superhydrophobic Surface

Actuating droplet bouncing from a rigid surface is of considerable interest for potential applications, ranging from novel droplet microfluidics to self-cleaning and anti-icing. The photothermal effect and the accompanying phase change initiate a route for manipulating the tiny amount of liquid. In this work, we present a concept of droplet bouncing from a cavity trap-assisted superhydrophobic platform actuated by the photothermal effect-induced intense evaporation, which enables the purposeful manipulation of the droplet bouncing. It is demonstrated that such a design limits the vapor transport so that the vapor pressure under the droplet is considerably improved to overcome the gravity and liquid-solid adhesion force, leading to the droplet bouncing. Moreover, experimental results indicate that droplet bouncing behaviors can be easily tuned by simply adjusting the cavity dimension and the input laser power. This work provides a new method for the manipulation of droplet bouncing, presenting promising perspectives for future possible applications.

Counterintuitive Ballistic and Directional Liquid Transport on a Flexible Droplet Rectifier

Achieving the directional and long-range droplet transport on solid surfaces is widely preferred for many practical applications but has proven to be challenging. Particularly, directionality and transport distance of droplets on hydrophobic surfaces are mutually exclusive. Here, we report that drain fly, a ubiquitous insect maintaining nonwetting property even in very high humidity, develops a unique ballistic droplet transport mechanism to meet these demanding challenges. The drain fly serves as a flexible rectifier to allow for a directional and long-range propagation as well as self-removal of a droplet, thus suppressing unwanted liquid flooding. Further investigation reveals that this phenomenon is owing to the synergistic conjunction of multiscale roughness, structural periodicity, and flexibility, which rectifies the random and localized droplet nucleation (nanoscale and microscale) into a directed and global migration (millimeter-scale). The mechanism we have identified opens up a new approach toward the design of artificial rectifiers for broad applications.

Self-Excited Motions of Volatile Drops on Swellable Sheets

When a volatile droplet is deposited on a floating swellable sheet, it becomes asymmetric, lobed and mobile. We describe and quantify this phenomena that involves nonequilibrium swelling, evaporation and motion, working together to realize a self-excitable spatially extended oscillator. Solvent penetration causes the film to swell locally and eventually buckle, changing its shape and the drop responds by moving. Simultaneously, solvent evaporation from the swollen film causes it to regain its shape once the droplet has moved away. The process repeats and leads to complex pulsatile spinning and/or sliding movements. We use a one-dimensional experiment to highlight the slow swelling of and evaporation from the film and the fast motion of the drop, a characteristic of excitable systems. Finally, we provide a phase diagram for droplet excitability as a function of drop size and film thickness and scaling laws for the motion of the droplet.

Rectification of Mobile Leidenfrost Droplets by Planar Ratchets

The self-transportation of mobile Leidenfrost droplets with well-defined direction and velocity on millimetric ratchets is one of the most representative and spectacular phenomena in droplet dynamics. Despite extensive progress in the ability to control the spatiotemporal propagation of droplets, it remains elusive how the individual ratchet units, as well as the interactions within their arrays, are translated into the collective droplet dynamics. Here, simple planar ratchets characterized by uniform height normal to the surface are designed. It is revealed that on planar ratchets, the transport dynamics of Leidenfrost droplets is dependent not only on individual units, but also on the elegant coordination within their arrays dictated by their topography. The design of planar ratchets enriches the fundamental understanding of how the surface topography is translated into dynamic and collective droplet transport behaviors, and also imparts higher applicability in microelectromechanical system based fluidic devices.

On the Thermocapillary Migration on Radially Microgrooved Surfaces

Thermocapillary migration describes the phenomenon in which a droplet placed on a nonuniformly heated surface can migrate from warm to cold regions. Herein, we report an experimental investigation of the migration of silicone oil droplets on radially microgrooved surfaces subjected to a thermal gradient; the effects of the initial divergence angle and divergent direction on the migration behavior are highlighted. A theoretical model is established to predict the migration velocity considering the thermocapillary, viscous resistance, and radial structure-induced forces; furthermore, the proposed theoretical derivation is validated. This study advances the understanding of this interfacial phenomenon, which has great potential for regulating and controlling liquid motion in lubrication systems, condensation and heat-transfer devices, and open microfluidics.

Biological and Engineered Topological Droplet Rectifiers

The power of the directional and spontaneous transport of liquid droplets is revealed through ubiquitous biological processes and numerous practical applications, where droplets are rectified to achieve preferential functions. Despite extensive progress, the fundamental understanding and the ability to exploit new strategies to rectify droplet transport remain elusive. Here, the latest progress in the fundamental understanding as well as the development of engineered droplet rectifiers that impart superior performance in a wide variety of working conditions, ranging from low temperature, ambient temperature, to high temperature, is discussed. For the first time, a phase diagram is formulated that naturally connects the droplet dynamics, including droplet formation modes, length scales, and phase states, with environmental conditions. Parallel approaches are then taken to discuss the basic physical mechanisms underlying biological droplet rectifiers, and a variety of strategies and manufacturing routes for the development of robust artificial droplet rectifiers. Finally, perspectives on how to create novel man-made rectifiers with functionalities beyond natural counterparts are presented.

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.

Directional Droplet Propulsion on Gradient Boron Nitride Nanosheet Grid Surface Lubricated with a Vapor Film below the Leidenfrost Temperature

Controlled propulsion of liquid droplets on a solid surface offers important applications in various fields, including fog harvesting, heat transfer, microfluidics, and microdevice technologies. The propulsion of the liquid droplet is realized only if the driven force exceeds the resistance force. Sometimes the directional propulsion of droplets only takes place at the Leidenfrost state to achieve enough lubrication for a vapor cushion. The thick vapor cushions levitate liquid droplets to reduce resistance force. However, it is still challenging to reduce the vapor cushion thickness and simultaneously realize the directional droplet's motion, especially below the Leidenfrost temperature. Here, a structurally hydrophobic boron nitride nanosheet (BNNS) grid surface was constructed with a two-direction topographical gradient, i. e., the perpendicular altitude gradient and the horizontal density gradient. The polar nature of the B-N bonds results in intrinsic hydrophilicity of the boron nitride layer, which increases the Leidenfrost point and facilitates wetting even at high temperature. Much thinner vapor-lubricating layers are competent in the droplet's directional motion below the Leidenfrost temperature of the BNNS grid surface because the air gap trapped within boron nitride nanosheet grids acts as a part of the lubrication layer.

The effect of the orientation and the height of periodic sub-micrometric texturing on dropwise condensation

Controlling condensation conditions by surface topography is of prime interest. The aim of this work is to investigate the behavior of water droplets condensing on oriented sub-micrometric structures representing ripples with wavelengths around 800 nm. Droplet behavior was studied on different ripples heights and on untextured surfaces. It was specifically looked at how the presence of ripples creates geometrical confinement, and how that influences the deformation and the orientation of single droplets. Results show that the condensed droplets follow the orientation of textured features, especially with high structures height (150 nm). This is shown by the decreasing of droplet roundness with ripples height. The relative number of circular droplets (roundness near to 1) is around 0.6 for 70 nm high ripples and decrease to around 0.2 for 150 nm high ripples. The corresponding relative number on untextured surface is around 0.5. A mechanism, based on droplets pinning and hysteresis, is proposed to explain the influence of the ripples orientation in a vertical plane, onto the droplet deformation during coalescence step. Finally, the presence of ripples is shown to barely impact breath figure dynamics. Number of droplets and mean droplet radius for the textured and untextured surfaces present a comparable evolution.

Wetting of flat gradient surfaces

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed.

Mapping microscale wetting variations on biological and synthetic water-repellent surfaces

Droplets slip and bounce on superhydrophobic surfaces, enabling remarkable functions in biology and technology. These surfaces often contain microscopic irregularities in surface texture and chemical composition, which may affect or even govern macroscopic wetting phenomena. However, effective ways to quantify and map microscopic variations of wettability are still missing, because existing contact angle and force-based methods lack sensitivity and spatial resolution. Here, we introduce wetting maps that visualize local variations in wetting through droplet adhesion forces, which correlate with wettability. We develop scanning droplet adhesion microscopy, a technique to obtain wetting maps with spatial resolution down to 10 µm and three orders of magnitude better force sensitivity than current tensiometers. The microscope allows characterization of challenging non-flat surfaces, like the butterfly wing, previously difficult to characterize by contact angle method due to obscured view. Furthermore, the technique reveals wetting heterogeneity of micropillared model surfaces previously assumed to be uniform.

Converting Vertical Vibration of Anisotropic Ratchet Conveyors into Horizontal Droplet Motion

An anisotropic ratchet conveyor is an asymmetric, periodic, micropatterned surface that propels droplets when vibrated with a sinusoidal signal at certain frequencies and amplitudes. For each input frequency, there is a threshold amplitude beyond which the droplet starts to move. In this paper, we study the parameters that initiate droplet motion and the relationship between the input frequency and threshold amplitude among droplets with different volume, density, viscosity, and surface tension. Through this investigation we demonstrate how nondimensionalization reveals consistent behavior for droplets of different volumes. Finally, we propose a compact model that captures the essential features of the system to describe how a pure vertical vibration results in horizontal droplet motion. This model provides an intuitive understanding of the underlying physics and explains how the surface asymmetry is the key for lateral droplet motion.

Topological liquid diode

The last two decades have witnessed an explosion of interest in the field of droplet-based microfluidics for their multifarious applications. Despite rapid innovations in strategies to generate small-scale liquid transport on these devices, the speed of motion is usually slow, the transport distance is limited, and the flow direction is not well controlled because of unwanted pinning of contact lines by defects on the surface. We report a new method of microscopic liquid transport based on a unique topological structure. This method breaks the contact line pinning through efficient conversion of excess surface energy to kinetic energy at the advancing edge of the droplet while simultaneously arresting the reverse motion of the droplet via strong pinning. This results in a novel topological fluid diode that allows for a rapid, directional, and long-distance transport of virtually any kind of liquid without the need for an external energy input.

Mimicking wettability alterations using temperature gradients for water nanodroplets

A sessile droplet or a film usually moves from hotter regions to colder regions, due to variations in interfacial tension. This, known as the so-called Marangoni effect, is true for most pure liquids like water for which the surface tension decreases with an increase in temperature. In stark contrast to this existing understanding, we bring forth the coupled effect of wettability and temperature gradients on the dynamics of the three-phase contact line. By simultaneously tracking the dynamic evolution of the three-phase contact line due to the evaporation and diffusion of molecules through molecular dynamics simulations, we explore the coterminous effects of the change of surface tension coefficients and wetting parameters with temperature on sessile droplets residing on surfaces with different wettabilities. We demonstrate, for the very first time, that the inverse Marangoni effect, which is believed to be exclusively observed in mixtures and self-rewetting fluids, is feasible in pure water at scales where inertial effects are negligible. The results of the study find application in electronic chip cooling where by the combined tuning of surface characteristics and Marangoni forces, droplets can be passively transported to warmer regions for efficient thermal management.

Dynamics of a Water Droplet over a Sessile Oil Droplet: Compound Droplets Satisfying a Neumann Condition

We report the dynamics of compound droplets with a denser liquid (water) droplet over a less dense sessile droplet (mineral oil) that satisfies the Neumann condition. For a fixed size of an oil droplet, depending on the size of the water droplet, either it attains the axisymmetric position or tends to migrate toward the edge of the oil droplet. For a water droplet-to-oil droplet at volume ratio V_w/V_o ≥ 0.05, stable axisymmetric configuration is achieved; for V_w/V_o < 0.05, migration of water droplet is observed. The stability and migration of water droplets of size above and below critical size, respectively, are explained using the force balance at the three-phase contact line and film tension. The larger and smaller droplets that initially attain the axisymmetric position or some radial position, respectively, evaporate continuously and thus migrate toward the edge of the oil droplet. The radial location and migration of the water droplets of different initial sizes with respect to time are studied. Experiments with water droplets on a flat oil-air interface did not show migration, which signified the role of the curved oil-air interface for droplet migration. Finally, coalescence of water droplets of size above the critical size at the axisymmetric position is demonstrated. Our compound droplet studies could be beneficial for applications involving droplet transport where contamination due to direct contact and pinning of droplets on solid surfaces is of concern. Migration and coalescence of water droplets on curved oil-air interfaces could open new frontiers in chemical and biological applications including multiphase processing and biological interaction of cells and atmospheric chemistry.

Spontaneous Droplet Motion on a Periodically Compliant Substrate

Droplet motion arises in many natural phenomena, ranging from the familiar gravity-driven slip and arrest of raindrops on windows to the directed transport of droplets for water harvesting by plants and animals under dry conditions. Deliberate transportation and manipulation of droplets are also important in many technological applications, including droplet-based microfluidic chemical reactors and for thermal management. Droplet motion usually requires gradients of surface energy or temperature or external vibration to overcome contact angle hysteresis. Here, we report a new phenomenon in which a drying droplet placed on a periodically compliant surface undergoes spontaneous, erratic motion in the absence of surface energy gradients and external stimuli such as vibration. By modeling the droplet as a mass-spring system on a substrate with periodically varying compliance, we show that the stability of equilibrium depends on the size of the droplet. Specifically, if the center of mass of the drop lies at a stable equilibrium point of the system, it will stay there until evaporation reduces its size and this fixed point becomes unstable; with any small perturbation, the droplet then moves to one of its neighboring fixed points.

Interaction of Droplets Separated by an Elastic Film

The Laplace pressure of a droplet placed on one side of an elastic thin film can cause significant deformation in the form of a bulge on its opposite side. Here, we show that this deformation can be detected by other droplets suspended on the opposite side of the film, leading to interaction between droplets separated by the solid (but deformable) film. The interaction is repulsive when the drops have a large overlap and attractive when they have a small overlap. Thus, if two identical droplets are placed right on top of each other (one on either side of the thin film), they tend to repel each other, eventually reaching an equilibrium configuration where there is a small overlap. This observation can be explained by analyzing the energy landscape of the droplets interacting via an elastically deformed film. We further demonstrate this idea by designing a pattern comprising a big central drop with satellite droplets. This phenomenon can lead to techniques for directed motion of droplets confined to one side of a thin elastic membrane by manipulations on the other side.

Superhydrophobic Cones for Continuous Collection and Directional Transportation of CO2 Microbubbles in CO2 Supersaturated Solutions

Microbubbles are tiny bubbles with diameters below 50 μm. Because of their minute buoyant force, the microbubbles stagnate in aqueous media for a long time, and they sometimes cause serious damage. Most traditional methods chosen for elimination of gas bubbles utilize buoyancy forces including chemical methods and physical methods, and they only have a minor effect on microbubbles. Several approaches have been developed to collect and transport microbubbles in aqueous media. However, the realization of innovative strategies to directly collect and transport microbubbles in aqueous media remains a big challenge. In nature, both spider silk and cactus spines take advantage of their conical-shaped surface to yield the gradient of Laplace pressure and surface free energy for collecting fog droplets from the environment. Inspired by this, we introduce here the gradient of Laplace pressure and surface free energy to the interface of superhydrophobic copper cones (SCCs), which can continuously collect and directionally transport CO₂ microbubbles (from tip side to base side) in CO₂-supersaturated solution. A gas layer was formed when the microbubbles encounter the SCCs. This offers a channel for microbubble directional transportation. The efficiency of microbubble transport is significantly affected by the apex angle of SCCs and the carbon dioxide concentration. The former provides different gradients of Laplace pressure as the driving force. The latter represents the capacity, which offers the quantity of CO₂ microbubbles for collection and transportation. We believe that this approach provides a simple and valid way to remove microbubbles.

Linear Stepper Actuation Driving Drop Resonance and Modifying Hysteresis

In this work, 2 μL water drops are placed on substrates that are created to have a circular hydrophilic region bounded by superhydrophobicity so that they exhibit high contact angles. When the substrate is translated by a linear stepper actuator, the random force components present in the actuator are shown to cause the drop to rock resonantly. When the substrate is translated downward at inclination angles of up to 6° with respect to the horizontal, the contact angle hysteresis increases progressively to a limiting condition. When the substrate is moved up at inclined angles, alternatively, the contact angle hysteresis increases initially to the limiting condition before it is progressively restored to its static state. These behaviors are accounted for by the reversible micro-Cassie to Wenzel wetting state transformations that are made possible by the hierarchical microscale and nanoscale structures present in the superhydrophobic regions.

Thermocapillary Migration of Liquid Droplets Induced by a Unidirectional Thermal Gradient

A liquid droplet placed on a nonuniformly heated solid surface will migrate from a high-temperature region to a low-temperature region. This study reports the development of a theoretical model and experimental investigation on the migration behavior of paraffin oil droplets induced by the unidirectional thermal gradient. Thin-film lubrication theory is employed to determine the migration velocity of droplets, and temperature dependence of viscosity is taken into account. Comparisons between experimental and numerical results are presented. An effective approach for estimating the thermocapillary migration velocity of droplets on lubrication is proposed.

New Drop Fluidics Enabled by Magnetic-Field-Mediated Elastocapillary Transduction

This research introduces a new drop fluidics that uses a deformable and stretchable elastomeric film as the platform instead of the commonly used rigid supports. Such a soft film impregnated with magnetic particles can be modulated with an external electromagnetic field that produces a vast array of topographical landscapes with varying surface curvature, which, in conjunction with capillarity, can direct and control the motion of water droplets efficiently and accurately. When a thin layer of oil is present on this film that is deformed locally, a centrosymmetric wedge is formed. A water droplet placed on this oil-laden film becomes asymmetrically deformed, thus producing a gradient of Laplace pressure within the droplet and setting it in motion. A simple theory is presented that accounts for the droplet speed in terms of such geometric variables as the volume of the droplet and the thickness of the oil film covering the soft elastomeric film as well as material variables such as the viscosity of the oil and the interfacial tension of the oil-water interfaces. Following the verification of the theoretical result using well-controlled model systems, we demonstrate how the electromagnetically controlled elastocapillary force can be used to manipulate the motion of single and/or multiple droplets on the surface of the elastomeric film and how elementary operations such as drop fusion and thermally addressed chemical transformation can be carried out in aqueous droplets. It is expected that the resulting drop fluidics would be suitable for the digital control of drop motion by simply switching on and off the electromagnetic fields applied at different positions underneath the elastomeric film in a Boolean sequence. We anticipate that this method of directing and manipulating water droplets is poised for application in various biochemical reaction engineering situations, an example of which is the polymerase chain reaction (PCR).

A Surface Texture Design to Obstruct the Liquid Migration Induced by Omnidirectional Thermal Gradients

Thermo-capillary migration is a phenomenon in which surface thermal gradients drive a liquid to flow from warm to cold regions without external forces. It is important to prevent the migration of liquid lubricants on rubbing surfaces. In this paper, a pattern of microdimples was proposed to obstruct the liquid migration induced by an omnidirectional thermal gradient. Microdimple patterns were fabricated on the surfaces of SUS316 stainless steel. Experiments were performed to investigate the influence of microdimple patterns with different geometric parameters on the migration behavior of paraffin oil. In particular, this study focused on the interfacial flowing near the microdimples. The results demonstrated that microdimples have a significant obstructive effect on migration, whereas dimples have a retaining effect, and the adjacent dimples have an interacting effect.

Superhydrophobic-like tunable droplet bouncing on slippery liquid interfaces

Droplet impacting on solid or liquid interfaces is a ubiquitous phenomenon in nature. Although complete rebound of droplets is widely observed on superhydrophobic surfaces, the bouncing of droplets on liquid is usually vulnerable due to easy collapse of entrapped air pocket underneath the impinging droplet. Here, we report a superhydrophobic-like bouncing regime on thin liquid film, characterized by the contact time, the spreading dynamics, and the restitution coefficient independent of underlying liquid film. Through experimental exploration and theoretical analysis, we demonstrate that the manifestation of such a superhydrophobic-like bouncing necessitates an intricate interplay between the Weber number, the thickness and viscosity of liquid film. Such insights allow us to tune the droplet behaviours in a well-controlled fashion. We anticipate that the combination of superhydrophobic-like bouncing with inherent advantages of emerging slippery liquid interfaces will find a wide range of applications.

The impact of drops on surfaces is highly relevant to our daily life and many industrial applications, such as self-cleaning and ink printing. Here, Hao et al. show the transition from superhydrophobic-like drop bouncing, due to a trapped air layer, to substrate-dependent bouncing on a liquid thin film.

Adhesion-induced instabilities and pattern formation in thin films of elastomers and gels

A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film. While for a single film, the wavelength is entirely dependent on its thickness, a co-operative energy minimization dictates that the wavelength depends on both the elastic moduli and thicknesses of two contacting films. The wavelength can also depend on the material properties of a film if its surface tension has a pronounced effect in comparison to its elasticity. When such a confined film is subjected to a continually increasing normal displacement, the morphological patterns evolve into cracks, which, in turn, govern the adhesive fracture behavior of the interface. While, in general, the thickness provides the relevant length scale underlying the well-known Griffith-Kendall criterion of debonding of a rigid disc from a confined film, it is modified non-trivially by the elasto-capillary number for an ultra-soft film. Depending upon the degree of confinement and the spatial distribution of external stress, various analogs of the canonical instability patterns in liquid systems can also be reproduced with thin confined elastic films.