Moving droplets on asymmetrically structured surfaces

Patterned Ultraslippery Surfaces of Stainless Steel Prepared by Femtosecond Laser Ablation for Directional Manipulation of Liquid Droplets

Slippery liquid-infused porous surfaces (SLIPS) have promising applications in chip laboratories, nanofriction power generation, and microfluidics due to their excellent properties such as good hydrophobicity and low adhesion. However, the self-driven stability of conventionally lubricated surfaces is not high, and the velocity of liquid droplets is difficult to regulate. This greatly limits the potential applications of SLIPS. A strategy is offered to prepare microporous structures of SLIPS directly on a stainless-steel substrate using femtosecond laser processing technology as the main means to realize exhibiting smoothness to liquids. At the same time, the principle of bionics is utilized, the porous structure of SLIPS is combined with the groove structure of rice leaves, or porous structures are combined with the wedge structure of shorebird beak to prepare the three-dimensional structure of SLIPS. Droplets exhibit significant individual anisotropy on three-dimensional (3D) SLIPS of leaf-like groove stripe structure in rice, enabling the precise control of droplet motion direction. When droplets are transported in wedge-shaped SLIPS with an asymmetric structure, the wedge edge can limit the direction of droplet motion while squeezing the droplet to generate Laplace pressure gradient, which achieves continuous self-driven transport of droplets. In addition, based on the above two processing strategies, an information transfer device is designed: the splicing of the self-driven transport surface with anisotropic topological channels enables the differential drive for liquid transport, which provides the conditions for the information transfer of the droplets. This strategy not only is simple and efficient but also provides new ideas for the effective development of multifunctional SLIPS as well as lab-on-a-chip and microfluidic domains.

Droplet Transportation on Liquid-Infused Asymmetrically Structured Surfaces by Mechanical Oscillation and Viscosity Control

The transportation of droplets on solid surfaces has received significant attention owing to its importance in biochemical analysis and microfluidics. In this study, we propose a novel strategy for controlling droplet motion by combining an asymmetric structure and infused lubricating oil on a vibrating substrate. The transportation of droplets with volumes ranging from 10 to 90 μL was realized, and the movement speed could be adjusted from 1.45 to 10.87 mm/s. Typical droplet manipulations, including droplet transportation along a long trajectory and selective movement of multiple droplets, were successfully demonstrated. Through experimental exploration and theoretical analysis, we showed that the adjustment of droplet transport velocity involves an intricate interaction among the Ohnesorge number, droplet volume, and input amplitude. It can potentially be used for the more complex manipulation of liquid droplets in microfluidic and biochemical analysis systems.

Fracture Diodes: Directional Asymmetry of Fracture Toughness

Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of a medium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. This paves the way for control of crack paths and direction, where fracture-when unavoidable-can be guided through predesigned paths to minimize loss of critical components.

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.

Long-range spontaneous droplet self-propulsion on wettability gradient surfaces

The directional and long-range droplet transportation is of great importance in microfluidic systems. However, it usually requires external energy input. Here we designed a wettability gradient surface that can drive droplet motion by structural topography. The surface has a wettability gradient range of over 150° from superhydrophobic to hydrophilic, which was achieved by etching silicon nanopillars and adjusting the area of hydrophilic silicon dioxide plane. We conducted force analysis to further reveal the mechanism for droplet self-propulsion, and found that the nanostructures are critical to providing a large driving force and small resistance force. Theoretical calculation has been used to analyze the maximal self-propulsion displacement on different gradient surfaces with different volumes of droplets. On this basis, we designed several surfaces with arbitrary paths, which achieved directional and long-range transportation of droplet. These results clarify a driving mechanism for droplet self-propulsion on wettability gradient surfaces, and open up new opportunities for long-range and directional droplet transportation in microfluidic system.

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).

Generation of Motion of Drops with Interfacial Contact

A liquid drop moves on a solid surface if it is subjected to a gradient of wettability or temperature. However, the pinning defects on the surface manifested in terms of a wetting hysteresis, or first-order nonlinear friction, limit the motion in the sense that a critical size has to be exceeded for a drop to move. The effect of hysteresis can, however, be mitigated by an external vibration that can be either structured or stochastic, thereby creating a directed motion of the drop. Many of the well-known features of rectification, amplification, and switching that are generic to electronics can be engineered with such types of movements. A specific case of interest is the random coalescence of drops on a surface that gives rise to self-generated noise. This noise overcomes the pinning potential, thereby generating a random motion of the coalesced drops. Randomly moving coalesced drops themselves exhibit a directed diffusive flux when a boundary is present to eliminate them by absorption. With the presence of a bias, the coalesced drops execute a diffusive drift motion that can have useful applications in various water and thermal management technologies.

Two-Dimensional Analysis of Air-Water Interface on Superhydrophobic Grooves under Fluctuating Water Pressure

We theoretically investigate the collapse (i.e., wetting) transition of the air-water interface on fully submerged superhydrophobic surfaces with micro-sized grooves under the fluctuating water pressure and the diffusion of the trapped air pockets. For the analysis, a nonlinear oscillator equation to describe the dynamics of the two-dimensional air-water interface on a single groove is derived, which is solved for a range of parameters of groove geometry and harmonically fluctuating water pressure. The results show that the pressure fluctuation across the interface encourages the early collapse of a plastron before reaching the critical hydrostatic pressure (i.e., maximum immersion depth) predetermined by the geometry. The dependence of plastron longevity on the surface geometry is found such that the plastron on a narrow groove (≤∼5 μm) (collapses mostly due to gas diffusion) lasts days while the ones on wider grooves (>∼35-45 μm, for example), more susceptible to the oscillating pressure, last a much shorter duration. The interplay between the air compression due to water impalement and the change of the volume of impaled water due to gas diffusion determines the response of plastron to fluctuating water pressure, which is analyzed in detail through the introduction of nondimensional parameters, and the critical groove width (most vulnerable to the external perturbations) is explained further. Finally, as a countermeasure to the fluctuating water pressure, it is suggested that the enhanced advancing contact angle of the groove sidewall (e.g., hierarchical structure) mitigates the negative effects.

A Fluidic Device with Polymeric Textured Ratchets

Nanotextured surfaces are widely used throughout nature for adhesion, wetting, and transport. Chemistry, geometry, and morphology are important factors for creating tunable textured surfaces, in which directionality of droplets can be controlled. Here, we fabricated nano textured polymeric surfaces, and studied the effect of tilting on the mobility of frequency modulated water droplet transported on asymmetric nano-PPX tracks. Plastically-deformed tracks guided water droplets for sorting, gating, and merging them as a function on their volume. Polymeric ratchets open up new avenues for the fields of digital fluidics and flexible device fabrication.

Grooved organogel surfaces towards anisotropic sliding of water droplets

Periodic micro-grooved organogel surfaces can easily realize the anisotropic sliding of water droplets attributing to the formed slippery water/oil/solid interface. Different from the existing anisotropic surfaces, this novel surface provides a versatile candidate for the anisotropic sliding of water droplets and might present a promising way for the easy manipulation of liquid droplets for water collection, liquid-directional transportation, and microfluidics.

In situ realization of asymmetric ratchet structures within microchannels by directionally guided light transmission and their directional flow behavior

An asymmetric ratchet structure within microchannels is demonstrated by directionally guided light transmission for controlled liquid flow. A direct and facile method is presented to realize programmed asymmetric structures, which control the fluid direction and speed.

Driving droplet by scale effect on microstructured hydrophobic surfaces

A new type of water droplet transportation mechanism on a microstructured hydrophobic surface is proposed and investigated experimentally and theoretically: a water droplet could be driven by scale effect under disturbance and vibration, which is different from the traditional contact angle-gradient-based method. A scale-gradient microstructured hydrophobic surface is fabricated in which the area fraction is kept constant, but the scales of the micropillars are monotonically changed. When additional water or horizontal vibration is applied, the original water droplet could move unidirectionally in the direction from the small scale to the large scale. A new model with line tension energy developed very recently could be used to explain these phenomena. When compared with the traditional contact angle-gradient smooth surface, it is also found that dynamic contact angle decreases with increasing the scale of the micropillars along the moving direction under disturbance. These new findings will deepen our understanding of the relationship between topology and dynamic wetting properties, and could be very helpful in designing liquid droplet transportation devices in microfluidic systems.

Drop motion induced by repeated stretching and relaxation on a gradient surface with hysteresis

The motion of a droplet can be induced by periodically compressing and extending it between two similar gradient surfaces possessing significant wetting hysteresis. The shape fluctuation of the drop during repeated compression-extension cycles leads to its ratchetlike motion toward the region of higher wettability. A simple model requiring the volume preservation of the drop during the compression-extension cycles is sufficient to account for the effect and predict drop velocity across the surface when drop size and cycle frequency are specified. In connection with this study, we also report a variation of the standard vapor phase adsorption method of preparing a chemically graded surface that allows for good control over the steepness and the length of the active zone. The method can be used to produce a linear or a radial gradient, both of which are employed here to drive droplet motion along these patterns. This type of discrete droplet motion can be used to move drops on surfaces to transport materials within miniaturized digital fluidic devices.

Directional self-cleaning superoleophobic surface

In this work, we report the creation of a grooved surface comprising 3 μm grooves (height ~4 μm) separated by 3 μm from each other on a silicon wafer by photolithography. The grooved surface was then modified chemically with a fluorosilane layer (FOTS). The surface property was studied by both static and dynamic contact angle measurements using water, hexadecane, and a polyethylene wax ink as the probing liquids. Results show that the grooved surface is both superhydrophobic and superoleophobic. Its observed contact angles agree well with the calculated Cassie-Baxter angles. More importantly, we are able to make a replica of the composite wax ink-air interface and study it by SEM. Microscopy results not only show that the droplet of the wax ink "sits" on air in the composite interface but also further reveal that the ink drop actually pins underneath the re-entrant structure in the side wall of the grooved structure. Contact angle measurement results indicate that wetting on the grooved surface is anisotropic. Although liquid drops are found to have lower static and advancing contact angles in the parallel direction, the drops are found to be more mobile, showing smaller hysteresis and lower sliding angles (as compared to the FOTS wafer surface and a comparable 3-μm-diameter pillar array FOTS surface). The enhanced mobility is attributable to the lowering of the resistance against an advancing liquid because 50% of the advancing area is made of a solid strip where the liquid likes to wet. This also implies that the contact line for advancing is no longer smooth but rather is ragged, having the solid strip area leading the wetting and the air strip area trailing behind. This interpretation is supported by imaging the geometry of the contact lines using molten ink drops recovered from the sliding angle experiments in both the parallel and orthogonal directions. Because the grooved surface is mechanically stronger against mechanical abrasion, the self-cleaning effect exhibited in the parallel direction suggests that groove texturing is a viable approach to create mechanically robust, self-cleaning, superoleophobic surfaces.

Bioinspired Directional Surfaces for Adhesion, Wetting and Transport

In Nature, directional surfaces on insect cuticle, animal fur, bird feathers, and plant leaves are comprised of dual micro-nanoscale features that tune roughness and surface energy. This feature article summarizes experimental and theoretical approaches for the design, synthesis and characterization of new bioinspired surfaces demonstrating unidirectional surface properties. The experimental approaches focus on bottom-up and top-down synthesis methods of unidirectional micro- and nanoscale films to explore and characterize their anomalous features. The theoretical component of the review focuses on computational tools to predict the physicochemical properties of unidirectional surfaces.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Emerging technologies for assembly of microscale hydrogels

Assembly of cell encapsulating building blocks (i.e., microscale hydrogels) has significant applications in areas including regenerative medicine, tissue engineering, and cell-based in vitro assays for pharmaceutical research and drug discovery. Inspired by the repeating functional units observed in native tissues and biological systems (e.g., the lobule in liver, the nephron in kidney), assembly technologies aim to generate complex tissue structures by organizing microscale building blocks. Novel assembly technologies enable fabrication of engineered tissue constructs with controlled properties including tunable microarchitectural and predefined compositional features. Recent advances in micro- and nano-scale technologies have enabled engineering of microgel based three dimensional (3D) constructs. There is a need for high-throughput and scalable methods to assemble microscale units with a complex 3D micro-architecture. Emerging assembly methods include novel technologies based on microfluidics, acoustic and magnetic fields, nanotextured surfaces, and surface tension. In this review, we survey emerging microscale hydrogel assembly methods offering rapid, scalable microgel assembly in 3D, and provide future perspectives and discuss potential applications.

Transport of a soft cargo on a nanoscale ratchet

Surface ratchets can guide droplet transport for microfluidic systems. Here, we demonstrated the actuation of microgels encapsulated in droplets using a unidirectional nanotextured surface, which moves droplets with low vibration amplitudes by a ratcheting mechanism. The nanofilm carries droplets along the ratchets with minimal drop shape deformation to move the encapsulated soft cargo, i.e., microscale hydrogels. The tilted nanorods of the nanofilm produce unidirectional wetting, thereby enabling droplet motion in a single direction. Maximum droplet translation speed on the nanofilm was determined to be 3.5 mm∕s, which offers a pathway towards high throughput microgel assembly applications to build complex constructs.

Light-controlled directional liquid drop movement on TiO2 nanorods-based nanocomposite photopatterns

Patterned polymeric coatings enriched with colloidal TiO(2) nanorods and prepared by photopolymerization are found to exhibit a remarkable increase in their water wettability when irradiated with UV laser light. The effect can be completely reversed using successive storage in vacuum and dark ambient environment. By exploiting the enhancement of the nanocomposites hydrophilicity upon UV irradiation, we prepare wettability gradients along the surfaces by irradiating adjacent surface areas with increasing time. The gradients are carefully designed to achieve directional movement of water drops along them, taking into account the hysteresis effect that opposes the movement as well as the change in the shape of the drop during its motion. The accomplishment of surface paths for liquid flow, along which the hydrophilicity gradually increases, opens the way to a vast number of potential applications in microfluidics.

An engineered anisotropic nanofilm with unidirectional wetting properties

Anisotropic textured surfaces allow water striders to walk on water, butterflies to shed water from their wings and plants to trap insects and pollen. Capturing these natural features in biomimetic surfaces is an active area of research. Here, we report an engineered nanofilm, composed of an array of poly(p-xylylene) nanorods, which demonstrates anisotropic wetting behaviour by means of a pin-release droplet ratchet mechanism. Droplet retention forces in the pin and release directions differ by up to 80 μN, which is over ten times greater than the values reported for other engineered anisotropic surfaces. The nanofilm provides a microscale smooth surface on which to transport microlitre droplets, and is also relatively easy to synthesize by a bottom-up vapour-phase technique. An accompanying comprehensive model successfully describes the film's anisotropic wetting behaviour as a function of measurable film morphology parameters.

Capillary motor driven by electrowetting

A micro-structure supported on a droplet is subjected to capillary force and aligned dependent on its shape. If the droplet's boundary conditions at the bottom and the micro-structure are non-circular, capillary torque is exerted on the structures. The direction of torque is determined by the boundary conditions and the position of the structure. By changing the boundary conditions continuously, rotational motion of a plate was achieved. The boundary conditions of the droplet were controlled by electrowetting. We patterned electrodes in an annular shape on the plate supporting the droplet. By changing the voltage-applied electrodes, the boundary conditions were changed and the plate is rotated. The droplet and the plate worked as a capillary motor with this method. We report the relationship between the characteristics of the capillary motor and its rotational motion. We sandwiched a 3.0-microL water droplet between two plates and achieved a rotational motion of 720 rpm at maximum.

In situ characterization of microdroplet interfacial properties in digital microfluidic systems

Real-time characterization of digital microfluidic lab-on-a-chip devices is important for biological and chemical applications in which the properties of the microdroplet are time variant. In this paper, a method for in situ characterization of microdroplet interfacial properties is introduced. The proposed characterization method relies on two submodules, namely the contact angle and capacitance sampling submodules, in a digital microfluidic system. In the contact angle measurement submodule, the microdroplet profile is acquired and an accurate contact angle is determined. In the capacitance sampling submodule, the capacitance of the system is measured by means of an activation voltage signal. For verification purposes, the results obtained from the proposed method are compared to the Lippmann-Young equation. The results are in excellent agreement with previously reported values. Finally, the proposed submodules are used to characterize the interfacial properties of a microdroplet containing an aqueous solution of bovine serum albumin (BSA) in which adsorption is a predominant effect. The results show the temporal behaviour of both microdroplet interfacial properties and dielectric characteristics.

Electrowetting on a lotus leaf

Electrowetting on dielectrics has been widely used to manipulate and control microliter or nanoliter liquids in micro-total-analysis systems and laboratory on a chip. We carried out experiments on electrowetting on a lotus leaf, which is quite different from the equipotential plate used in conventional electrowetting. This has not been reported in the past. The lotus leaf is superhydrophobic and a weak conductor, so the droplet can be easily actuated on it through electrical potential gradient. The capillary motion of the droplet was recorded by a high-speed camera. The droplet moved toward the counterelectrode to fulfill the actuation. The actuation speed could be of the order of 10 mms. The actuation time is of the order of 10 ms.

Droplet motion on designed microtextured superhydrophobic surfaces with tunable wettability

Superhydrophobic surfaces have shown promising applications in microfluidic systems as a result of their water-repellent and low-friction properties over the past decade. Recently, designed microstructures have been experimentally applied to construct wettability gradients and direct the droplet motion. However, thermodynamic mechanisms responsible for the droplet motion on such regular rough surfaces have not been well understood such that at present specific guidelines for the design of tunable superhydrophobic surfaces are not available. In this study, we propose a simple but robust thermodynamic methodology to gain thorough insight into the physical nature for the controllable motion of droplets. On the basis of the thermodynamic calculations of free energy (FE) and the free-energy barrier (FEB), the effects of surface geometry of a pillar microtexture are systematically investigated. It is found that decreasing the pillar width and spacing simultaneously is required to lower the advancing and receding FEBs to effectively direct droplets on the roughness gradient surface. Furthermore, the external energy plays a role in the actuation of spontaneous droplet motion with the cooperation of the roughness gradient. In addition, it is suggested that the so-called "virtual wall" used to confine the liquid flow along the undesired directions could be achieved by constructing highly advancing FEB areas around the microchannels, which is promising for the design of microfluidic systems.

Modeling microcapsules that communicate through nanoparticles to undergo self-propelled motion

Using simulation and theory, we demonstrate how nanoparticles can be harnessed to regulate the interaction between two initially stationary microcapsules on a surface and promote the self-propelled motion of these capsules along the substrate. The first microcapsule, the "signaling" capsule, encases nanoparticles, which diffuse from the interior of this carrier and into the surrounding solution; the second capsule is the "target" capsule, which is initially devoid of particles. Nanoparticles released from the signaling capsule modify the underlying substrate and thereby initiate the motion of the target capsule. The latter motion activates hydrodynamic interactions, which trigger the signaling capsule to follow the target. The continued release of the nanoparticles sustains the motion of both capsules. In effect, the system constitutes a synthetic analogue of biological cell signaling and our findings can shed light on fundamental physical forces that control interactions between cells. Our findings can also yield guidelines for manipulating the interactions of synthetic microcapsules in microfluidic devices.

Lateral vibration of a water drop and its motion on a vibrating surface

The resonant modes of sessile water drops on a hydrophobic substrate subjected to a small-amplitude lateral vibration are investigated using computational fluid dynamic (CFD) modeling. As the substrate is vibrated laterally, its momentum diffuses within the Stokes layer of the drop. Above the Stokes layer, the competition between the inertial and Laplace forces causes the formation of capillary waves on the surface of the drop. In the first part of this paper, the resonant states of water drops are illustrated by investigating the velocity profile and the hydrostatic force using a 3d simulation of the Navier-Stokes equation. The simulation also allows an estimation of the contact angle variation on both sides of the drop. In the second part of the paper, we investigate the effect of vibration on a water drop in contact with a vertical plate. Here, as the plate vibrates parallel to gravity, the contact line oscillates. Each oscillation is, however, rectified by hysteresis, thus inducing a ratcheting motion to the water droplet vertically downward. Maximum rectification occurs at the resonant states of the drop. A comparison between the frequency-dependent motion of these drops and the variation of contact angles on their both sides is made. The paper ends with a discussion on the movements of the drops on a horizontal hydrophobic surface subjected to an asymmetric vibration.

Vibration-actuated drop motion on surfaces for batch microfluidic processes

When a liquid drop is subjected to an asymmetric lateral vibration on a nonwettable surface, a net inertial force acting on the drop causes it to move. The direction and velocity of the drop motion are related to the shape, frequency, and amplitude of vibration, as well as the natural harmonics of the drop oscillation. Aqueous drops can be propelled through fluidic networks connecting various unit operations in order to carry out batch processing at the miniature scale. We illustrate the integration of several unit operations on a chip: drop transport, mixing, and thermal cycling, which are precursor steps to carrying out advanced biological processes at microscale, including cell sorting, polymerase chain reaction, and DNA hybridization.

Capillary bridges in electric fields

We analyzed the morphology of droplets of conductive liquids placed between two parallel plate electrodes as a function of the two control parameters electrode separation and applied voltage. Both electrodes were covered by thin insulating layers, as in conventional electrowetting experiments. Depending on the values of the control parameters, three different states of the system were found: stationary capillary bridges, stationary separated droplets, and periodic self-excited oscillations between both morphologies, which appear only above a certain threshold voltage. In the two stationary states, the morphology of the liquid is modified by the electric fields due to electrowetting and due to mutual electrostatic attraction, respectively. We determined a complete phase diagram within the two-dimensional phase space given by the control parameters. We discuss a model based on the interfacial and electrostatic contributions to the free energy. Numerical solutions of the model are in quantitative agreement with the phase boundaries found in the experiments. The dynamics in the oscillatory state are governed by electric charge relaxation and by contact angle hysteresis.

Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.

Soliton ratchets

The mechanism underlying the soliton ratchet, both in absence and in presence of noise, is investigated. We show the existence of an asymmetric internal mode on the soliton profile that couples, through the damping in the system, to the soliton translational mode. Effective soliton transport is achieved when the internal mode and the external force are phase locked. We use as a working model a generalized double sine-Gordon equation. The phenomenon is expected to be valid for generic soliton systems.

Phase locking effect and current reversals in deterministic underdamped ratchets

We study the transport properties (currents) of deterministic underdamped ratchets in terms of phase locking dynamics. The occurrence of reverse currents is interpreted in terms of different stability properties of the periodic rotating orbits and is shown to exist also in the absence of bifurcations from chaos to periodic motion. We briefly discuss the effects of noise on this phase locked dynamics.

Drift ratchet

We consider a silicon wafer, pierced by millions of identical pores with periodically varying diameters but without spatial inversion symmetry (ratchet profile). When a liquid is periodically pumped back and forth through the pores, our theory predicts a net transport of suspended micrometer-sized particles (drift ratchet). The direction of this particle current depends very sensitively on the size of the particles. For typical parameter values of the experiment, two different types of particles at an initially homogeneous 1:1 mixture are spatially separated with a purity beyond 1:1000 on a time scale of a few hours in comparably large quantities. This result is due to the highly parallel architecture of the device. The experimental realization of the setup, presently under construction, thus appears to be a promising new particle separation device, possibly superior to existing methods for particles sizes on the micrometer scale.