Modeling of Menisci and Capillary Forces from the Millimeter to the Micrometer Size Range

Effect of Particle Size on the Orientation and Order of Assemblies of Functionalized Microscale Cubes Formed at the Water/Air Interface

The impact of the particle size and wettability on the orientation and order of assemblies obtained by self-organization of functionalized microscale polystyrene cubes at the water/air interface is reported. An increase in the hydrophobicity of 10- and 5-μm-sized self-assembled monolayer-functionalized polystyrene cubes, as assessed by independent water contact angle measurements, led to a change of the preferred orientation of the assembled cubes at the water/air interface from face-up to edge-up and further to vertex-up, irrespective of microcube size. This tendency is consistent with our previous studies with 30-μm-sized cubes. However, the transitions among these orientations and the capillary force-induced structures, which change from flat plate to tilted linear and further to close-packed hexagonal arrangements, were observed to shift to larger contact angles for smaller cube size. Likewise, the order of the formed aggregates decreased significantly with decreasing cube size, which is tentatively attributed to the small ratio of inertial force to capillary force for smaller cubes in disordered aggregates, which results in more difficulties to reorient in the stirring process. Experiments with small fractions of larger cubes added to the water/air interface increased the order of smaller homo-aggregates to values similar to neat 30 μm cube assemblies. Hence, collisions of larger cubes or aggregates are shown to play a decisive role in breaking metastable structures to approach a global energy minimum assembly.

Locomotion of Miniature Soft Robots

Miniature soft robots are mobile devices, which are made of smart materials that can be actuated by external stimuli to realize their desired functionalities. Here, the key advancements and challenges of the locomotion producible by miniature soft robots in micro- to centimeter length scales are highlighted. It is highly desirable to endow these small machines with dexterous locomotive gaits as it enables them to easily access highly confined and enclosed spaces via a noninvasive manner. If miniature soft robots are able to capitalize this unique ability, they will have the potential to transform a vast range of applications, including but not limited to, minimally invasive medical treatments, lab-on-chip applications, and search-and-rescue missions. The gaits of miniature soft robots are categorized into terrestrial, aquatic, and aerial locomotion. Except for the centimeter-scale robots that can perform aerial locomotion, the discussions in this report are centered around soft robots that are in the micro- to millimeter length scales. Under each category of locomotion, prospective methods and strategies that can improve their gait performances are also discussed. This report provides critical analyses and discussions that can inspire future strategies to make miniature soft robots significantly more agile.

Self-powered locomotion of a hydrogel water strider

Hydrogels are an exciting class of materials for new and emerging robotics. For example, actuators based on hydrogels have impressive deformability and responsiveness. Studies into hydrogels with autonomous locomotive abilities, however, are limited. Existing hydrogels achieve locomotion through the application of cyclical stimuli or chemical modifications. Here, we report the fabrication of active hydrogels with an intrinsic ability to move on the surface of water without operated stimuli for up to 3.5 hours. The active hydrogels were composed of hydrophobic and hydrophilic groups and underwent a dynamic wetting process to achieve spatial and temporal control of surface tension asymmetry. Using surface tension, the homogeneous active hydrogels propelled themselves and showed controlled locomotion on water, similar to common water striders.

Modeling ternary fluids in contact with elastic membranes

We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modeling approach for the fluid phases, we derive the governing equations for the dynamics of the ternary fluid flow and membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method for the ternary fluid (Eulerian description) and a finite difference representation of the membrane (Lagrangian description). The ternary fluid and membrane solvers are coupled through the immersed boundary method. For validation purposes, we consider the relaxation dynamics of a two-dimensional elastic capsule placed at a fluid-fluid interface. The capsule shapes, resulting from the balance of surface tension and elastic forces, are compared with equilibrium numerical solutions obtained by surface evolver. Furthermore, the Galilean invariance of the proposed model is proven. The proposed approach is versatile, allowing for the simulation of a wide range of geometries. To demonstrate this, we address the problem of a capillary bridge formed between two deformable capsules.

Direct Measurement of Capillary Attraction between Floating Disks

Two bodies resting at a fluid interface may interact laterally due to the surface deformations they induce. Here we use an applied magnetic force to perform direct measurements of the capillary attraction force between centimetric disks floating at an air-water interface. We compare our measurements to numerical simulations that take into account the disk's vertical displacement and spontaneous tilt, showing that both effects are necessary to describe the attraction force for short distances. We characterize the dependence of the attraction force on the disk mass, diameter, and relative spacing, and develop a scaling law that captures the observed dependence of the capillary force on the experimental parameters.

THE INFLUENCE OF TEMPERATURE ON DISPERSION OF PARTICLES ON LIQUID SURFACES

It was shown recently that small particles and powders spontaneously disperse on liquid surfaces when they come in contact with the interface for the first time (Figure 2). This happens due to the combined effect of the capillary force, buoyant weight of the particle and the viscous drag that the particles experience when they encounter the liquid surface. The particles undergo oscillations normal to the interface before they come to the equilibrium position on the interface. These oscillations, in turn, induce a flow on the interface which disperses the particles radially outward. This phenomenon has a significant role in the pollination of sea plants such as “Ruppia” in which the formation of “pollen rafts” is the first step which results from the spontaneous dispersion of their pollens on the water surface. This work investigates, experimentally, the influence of temperature of the liquid on which this dispersion occurs. It was observed that the frequency of oscillations of the particles decreased with the increase in the temperature of the liquid. It is because the magnitude of capillary force that the particle experiences also decreased when the temperature of the liquid increased.

Control of Orientation, Formation of Ordered Structures, and Self-Sorting of Surface-Functionalized Microcubes at the Air-Water Interface

The dependence of the orientation of microscale PS cubes, which are surface functionalized on only five faces, at the water/air interface and the ordered aggregates formed by capillary force assembly are reported. Depending on the wettability of the faces, the cubes were shown to adopt a preferred orientation that changes with decreasing wettability from face up to edge up and further to vertex up. Concomitantly, stable aggregates with different structures were formed by capillary force self-assembly. The unmodified bottom face of the cubes was localized by fluorescence labeling. Finally, self-sorting of differently surface functionalized microcubes was realized for the first time, due to the stronger capillary interactions of quadrupole-quadrupole and hexapole-hexapole interactions compared to quadrupole-hexapole interaction.

Gibbsian Thermodynamic Study of Capillary Meniscus Depth

In the presence of gravity or other external fields, liquid surface curvature deviates from a spherical shape and the surface configuration can be found by numerical integration of the Young–Laplace equation and the typical initial point for integration is the apex of the interface. The meniscus shape in large Bond number systems, which have the central portion of the interface flattened, cannot be determined with the apex as the initial point for integration. Here we find the depth of capillary menisci by considering an initial point for integration to be at the three-phase-contact-line (TPCL) and evaluate the curvature at the TPCL by free energy analysis and inspect the effect of different parameters on the interface shape. A new parameter—which is the deviation of equilibrium curvature at the TPCL from the spherical shape (SR)—is introduced and inspected and it was found that at a Bond number of 13 the maximum deviation, approximately 0.8 of spherical curvature, takes place while for large enough Bond numbers the curvature at the three-phase contact line is near the spherical shape (0.95 < SR < 1). A potential application of this approach is to measure the capillary rise at the TPCL to find the surface tension in high Bond number systems such as those with low surface/interfacial tensions.

Capillarity-driven migration of small objects: A critical review

The phenomena on the capillarity-driven migration of small objects are full of interest for both scientific and engineering communities, and a critical review is thereby presented. The small objects mentioned here deal with the non-deformable objects, such as particles, rods, disks and metal sheets; and besides them, the soft objects are considered, such as droplets and bubbles. Two types of interfaces are analyzed, i.e., the solid-fluid interface and the fluid-fluid interface. Due to the easily deformable properties of the soft objects and distorted interfacial shapes induced by small objects, a more convenient way to obtain the driving force is through the potential energy of the system. The asymmetric factors causing the object migration include the asymmetric configuration of the interface, and the difference between the interfacial tensions. Finally, a simple outlook on the potential applications of small object migration is made. These behaviors may cast new light on the design of microfluidics and new devices, environment cleaning, oil and gas displacement and mineral industries.

Locomotion of arthropods in aquatic environment and their applications in robotics

Many bio-inspired robots have been developed so far after careful investigation of animals' locomotion. To successfully apply the locomotion of natural counterparts to robots for efficient and improved mobility, it is essential to understand their principles. Although a lot of research has studied either animals' locomotion or bio-inspired robots, there have only been a few attempts to broadly review both of them in a single article. Among the millions of animal species, this article reviewed various forms of aquatic locomotion in arthropods including relevant bio-inspired robots. Despite some previous robotics research inspired by aquatic arthropods, we found that many less-investigated or even unexplored areas are still present. Therefore, this article has been prepared to identify what types of new robotics research can be carried out after drawing inspiration from the aquatic locomotion of arthropods and to provide fruitful insights that may lead us to develop an agile and efficient aquatic robot.

Gravity-Drawn Silicone Filaments: Production, Characterization, and Wormlike Chain Dynamics

We introduce a method to produce continuous polydimethylsiloxane (PDMS) silicone filaments on the order of 0.5 m long and 100 μm in diameter. The approach overcomes traditional limitations in silicone drawing by partially precuring the polymer and drawing through a tube furnace. We characterize the filaments' mechanical properties, and their ability to switch hydrophobicity by UV-ozone and corona discharge patterning. The flexible filaments' dynamic properties were evaluated by way of athermal acoustic excitation at the air-water interface, revealing conformational reconfigurability consistent with a wormlike chain model. We envision applications in rapid prototyping and as a platform for model foldamer studies.

Motility of active nematic films driven by "active anchoring"

We provide a minimal model for an active nematic film in contact with both a solid substrate and a passive isotropic fluid, and explore its dynamics in one and two dimensions using a combination of hybrid Lattice Boltzmann simulations and analytical calculations. By imposing nematic anchoring at the substrate while active flows induce a preferred alignment at the interface ("active anchoring"), we demonstrate that directed fluid flow spontaneously emerges in cases where the two anchoring types are opposing. In one dimension, our model reduces to an analogue of a loaded elastic column. Here, the transition from a stationary to a motile state is akin to the buckling bifurcation, but offers the possibility to reverse the flow direction for a given set of parameters and boundary conditions solely by changing initial conditions. The two-dimensional variant of our model allows for additional tangential instabilities, and it is found that undulations form in the interface above a threshold activity. Our results might be relevant for the design of active microfluidic geometries or curvature-guided self-assembly.

The influence of particle size and residual charge on electrostatic interactions between charged colloidal particles at an oil-water interface

Electrostatic repulsive interaction forces between charged spherical colloidal particles at an oil-water interface are numerically studied by solving the standard three-dimensional Poisson-Nernst-Planck model. We directly compute the electrostatic force on a finite-size spherical particle and our results are applicable to all inter-particle distances without distinguishing short ranges and long ranges. The model successfully captures the scaling relationship of the force and the separation distance (d) between two charged particles at both short ranges (exponential dependence) and long ranges (∼d(-4)). The model also bridges these two ranges and provides quantitative information in the middle range. In addition, by assuming that there is a small residual electric charge at the particle-oil interface, the standard model is capable of quantitatively predicting the repulsive particle-particle interaction force over a large range of the separation distance between two particles. The favorable agreement between experiments and theoretical predictions also leads one to conclude that the standard model adequately describes the particle-particle interactions trapped at the oil-water interface.

Atmospheric-operable bioactuator powered by insect muscle packaged with medium

Despite attempts in a number of studies to utilize muscle tissue and cells as microactuators, all of the biohybrid microdevices have been operable only in the culture medium and none have worked in air due to the dry environment. This paper demonstrates an atmospheric-operable bioactuator (AOB) fabricated by packaging an insect dorsal vessel (DV) tissue with a small amount of culture medium inside a capsule. The AOB, consisting of microtweezers and the capsule, was designed based on a structural simulation that took into account the capillary effect. The base part of the microtweezers was deformed by spontaneous contractions of the DV tissue in the medium inside the capsule, by which the front edges of the microtweezer arms projecting above the medium surface were also deformed. First, we confirmed in the medium that the DV tissue was able to reduce the gap between the arm tips of the microtweezers. After taking the AOB out of the medium, as we expected, the AOB continued to work in air at room temperature. The gap reduction in air became larger than the one in the medium due to a surface tension effect, which was consistent with the simulation findings on the surface tension by the phase-field method. Second, we demonstrated that the AOB deformed a thin-wall ring placed between its tips in air. Third, we measured the lifetime of the AOB. The AOB kept working for around 40 minutes in air, but eventually stopped due to medium evaporation. As the evaporation progressed, the microtweezers were pressed onto the capsule wall by the surface tension and opening and closing stopped. Finally, we attempted to prevent the medium from evaporating by pouring liquid paraffin (l-paraffin) over the medium after lipophilic coating of the capsule. As a result, we succeeded in prolonging the AOB lifetime to more than five days. In this study, we demonstrated the significant potential of insect muscle tissue and cells as a bioactuator in air and at room temperature. By integrating insect tissue and cells not only into a microspace but also onto a substrate, we expect to realize a biohybrid MEMS device with various functions in the near future.

Electric field-induced self-assembly of micro- and nanoparticles of various shapes at two-fluid interfaces

Particle lithography which explores the capability of particles to self-assemble offers an attractive means to manufacture nanostructured materials. Although traditional techniques typically lead to the formation of dense crystals, adjustable non-close-packed crystals are crucial in a number of applications. We have recently proposed a novel method to assemble spherical micro- and nanoparticles into monolayers. The technique consists of trapping particles at a liquid-fluid interface and applying an electric field normal to the interface. Particles rearrange themselves under the influence of interfacial and electrostatic forces to form 2-D hexagonal arrays of long-range order and whose lattice constant depends on the electric field strength and frequency. Furthermore, the existence of an electric field-induced capillary force makes the technique applicable to submicron and nanosized particles. Although spherical particles are often used, non-spherical particles can be beneficial in practice. Here, we review the method, discuss its applicability to particles of various shapes, and present results for particles self-assembly on air-liquid and liquid-liquid interfaces. In the case of non-spherical particles, the self-assembly process, while still taking place, is more complex as particles experience a torque which causes them to rotate relative to one another. This leads to a final arrangement displaying either a dominant orientation or no well-defined orientation. We also discuss the possibility of dislodging the particles from the interface by applying a strong electric field such that the Weber number is of order 1 or larger, a phenomenon which can be utilized to clean particles from liquid-fluid surfaces.

Interface-directed self-assembly of cell-laden microgels

Cell-laden hydrogels show great promise for creating engineered tissues. However, a major shortcoming with these systems has been the inability to fabricate structures with controlled micrometer-scale features on a biologically relevant length scale. In this Full Paper, a rapid method is demonstrated for creating centimeter-scale, cell-laden hydrogels through the assembly of shape-controlled microgels or a liquid-air interface. Cell-laden microgels of specific shapes are randomly placed on the surface of a high-density, hydrophobic solution, induced to aggregate and then crosslinked into macroscale tissue-like structures. The resulting assemblies are cell-laden hydrogel sheets consisting of tightly packed, ordered microgel units. In addition, a hierarchical approach creates complex multigel building blocks, which are then assembled into tissues with precise spatial control over the cell distribution. The results demonstrate that forces at an air-liquid interface can be used to self-assemble spatially controllable, cocultured tissue-like structures.

Physics underlying controlled self-assembly of micro- and nanoparticles at a two-fluid interface using an electric field

The purpose of this paper is to investigate the physics underlying the controlled self-assembly of microparticles and nanoparticles at a two-fluid interface using an electric field. As shown in recent experiments, under certain conditions an externally applied electric field can cause particles floating at a two-fluid interface to assemble into a virtually defect free monolayer whose lattice spacing can be adjusted by varying the electric field strength. In this work, we assume that both fluids and particles are perfect dielectrics and for this case analyze the (capillary and electrical) forces acting on the particles, deduce an expression for the lattice spacing under equilibrium condition, and study the dependence of the latter upon the various parameters of the system, including the particles' radius, the dielectric properties of the fluids and particles, the particles' position within the interface, the particles' buoyant weight, and the applied voltage. While for relatively large sized particles whose buoyant weight is much larger than the vertical electrostatic force, the equilibrium distance increases with increasing electric field, for submicron sized particles whose buoyant weight is negligible, it decreases with increasing electric field. For intermediate sized particles, the distance first increases and then decreases with increasing electric field strength.

Micro- and nanoparticles self-assembly for virtually defect-free, adjustable monolayers

As chips further shrink toward smaller scales, fabrication processes based on the self-assembly of individual particles into patterns or structures are often sought. One of the most popular techniques for two-dimensional assembly (self-assembled monolayers) is based on capillary forces acting on particles placed at a liquid interface. Capillarity-induced clustering, however, has several limitations: it applies to relatively large (radius > approximately 10 microm) particles only, the clustering is usually non-defect-free and lacks long-range order, and the lattice spacing cannot be adjusted. The goal of the present article is to show that these shortcomings can be addressed by using an external electric field normal to the interface. The resulting self-assembly is capable of controlling the lattice spacing statically or dynamically, forming virtually defect-free monolayers, and manipulating a broad range of particle sizes and types including nanoparticles and electrically neutral particles.

Velocity Distributions of Camphor Particle Ensembles

The spatial distribution of ensembles of camphor particles on a water surface can be classified into four phases with the following properties, for increasing density: (I) no clustering of particles and a minimum distance distribution similar to that of a 2D ideal gas; (II) reminiscent of a gas with clustering of particles; (III) net-like structure with occasional rearrangements; and (IV) motionless. While single particles have varying velocity distributions, the overall velocity distribution is Laplacian (the width decreasing with increasing camphor density) for all phases.

Diffusion and Cluster Formation in One-Dimensional Systems with Attractive Interactions

We study cluster formation in a finite one-dimensional model system where the particles experience long-range attractive forces. The particles are first placed in equidistant positions by a repulsive potential, which then is turned off, and only a weak long-range potential acts between the particles. It is shown that the mean-square deviation in distance between the colloids at first increases due to normal Brownian motion, followed by a crossover to anomalous diffusion governed by the long-range forces. Moreover, we also found that the subsequent cluster formation could be described by a Poisson distribution. The results presented here may help us understand diffusion and cluster formation in one-dimensional systems.

Meniscus-climbing insects

Water-walking insects and spiders rely on surface tension for static weight support and use a variety of means to propel themselves along the surface. To pass from the water surface to land, they must contend with the slippery slopes of the menisci that border the water's edge. The ability to climb menisci is a skill exploited by water-walking insects as they seek land in order to lay eggs or avoid predators; moreover, it was a necessary adaptation for their ancestors as they evolved from terrestrials to live exclusively on the water surface. Many millimetre-scale water-walking insects are unable to climb menisci using their traditional means of propulsion. Through a combined experimental and theoretical study, here we investigate the meniscus-climbing technique that such insects use. By assuming a fixed body posture, they deform the water surface in order to generate capillary forces: they thus propel themselves laterally without moving their appendages. We develop a theoretical model for this novel mode of propulsion and use it to rationalize the climbers' characteristic body postures and predict climbing trajectories consistent with those reported here and elsewhere.

Reactive surface micropatterning by wet stamping

Hydrogel stamps are used to reactively micropattern various types of substrates. The method, called reactive wet stamping (r-WETS), is general in nature and overcomes several limitations of conventional soft-lithographic techniques. Illustrative applications of r-WETS in surface wettability modification, deposition of metallic microstructures, preparation of supports for electrostatic self-assembly, and multistep reactive patterning are discussed.

The interfacial torque on a partially submerged sphere

For a heavy spherical particle floating at the surface of a liquid, we show that the resultant torque exerted on the particle about its center by the interfacial forces is always zero, regardless of the position and shape of the contact line, provided only that the interfacial tension and the contact angle are constant. Interfacial tension therefore cannot rotate a spherical particle about its center.

Linear dependence of surface drag on surface viscosity

Flow at an air-water interface is limited by drag from both the two-dimensional surface and three-dimensional subphase. Separating these contributions to the interfacial drag is necessary to measure surface viscosity as well as to understand the influence of the interface on flow. In these experiments, a magnetic needle floating on a monolayer-covered air-water interface is put in motion by applying a constant magnetic force, F(m). The needle velocity varies exponentially with time, reaching a terminal velocity F(m)/C, in which C is the drag coefficient. C is shown to be linearly proportional to the monolayer surface viscosity, eta(s), for dipalmitoylphosphatidylcholine monolayers in the condensed phase by comparison to surface viscosity measured by channel viscometry.

Application of time-resolved linear dichroism spectroscopy: Intensity borrowing in charge transfer complex absorption spectra

Time-resolved linear dichroism spectroscopy has been used to study the influence of solvent on the charge transfer complex formed between hexamethylbenzene and 1,2,4,5-tetracyanobenzene. It was shown that cyano-substituted solvents induce a 1500 cm–1 increase in the charge transfer transition energies relative to those observed in chlorinated solvents. Furthermore, the angle between the charge transfer absorption transition moments and the photochemically produced radical anion absorption transition moment, after relaxation, has been measured for this complex in several solvents. A simple model was used to correlate the angles measured using time-resolved linear dichroism spectroscopy with the extent of localized excitation mixed into the charge transfer transitions. These measurements reveal that different charge transfer transitions borrow intensity from the localized excitation to different extents. By using different excitation wavelengths, the partitioning of the borrowed intensity among the charge transfer transitions of this complex could be evaluated for the first time.Key words: 1,2,4,5-tetracyanobenzene, hexamethylbenzene, donor–acceptor complex, photoinduced electron transfer, photoselection.

Electrostatic self-assembly of macroscopic crystals using contact electrification

Self-assembly of components larger than molecules into ordered arrays is an efficient way of preparing microstructured materials with interesting mechanical and optical properties. Although crystallization of identical particles or particles of different sizes or shapes can be readily achieved, the repertoire of methods to assemble binary lattices of particles of the same sizes but with different properties is very limited. This paper describes electrostatic self-assembly of two types of macroscopic components of identical dimensions using interactions that are generated by contact electrification. The systems we have examined comprise two kinds of objects (usually spheres) made of different polymeric materials that charge with opposite electrical polarities when agitated on flat, metallic surfaces. The interplay of repulsive interactions between like-charged objects and attractive interactions between unlike-charged ones results in the self-assembly of these objects into highly ordered, closed arrays. Remarkably, some of the assemblies that form are not electroneutral-that is, they possess a net charge. We suggest that the stability of these unusual structures can be explained by accounting for the interactions between electric dipoles that the particles in the aggregates induce in their neighbours.

Dynamic aggregation of chiral spinners

An object spinning at the surface of a liquid creates a chiral vortex. If the spinning object is itself chiral, its shape modifies the characteristics of the vortex; interactions between that vortex and other vortices then depend on the chirality of the objects that produce them. This paper describes the aggregation of millimeter-sized, chiral magnetized plates floating at a liquid-air interface and rotating under the influence of a rotating external magnetic field. This external field confines all the plates at densities that cause the vortices they generate to interact strongly. For one set of plates investigated, plates of one chirality attract one another, and plates of the other chirality repel other plates of both chiralities.

Beyond molecules: self-assembly of mesoscopic and macroscopic components

Self-assembly is a process in which components, either separate or linked, spontaneously form ordered aggregates. Self-assembly can occur with components having sizes from the molecular to the macroscopic, provided that appropriate conditions are met. Although much of the work in self-assembly has focused on molecular components, many of the most interesting applications of self-assembling processes can be found at larger sizes (nanometers to micrometers). These larger systems also offer a level of control over the characteristics of the components and over the interactions among them that makes fundamental investigations especially tractable.

Self-assembly at all scales

Self-assembly is the autonomous organization of components into patterns or structures without human intervention. Self-assembling processes are common throughout nature and technology. They involve components from the molecular (crystals) to the planetary (weather systems) scale and many different kinds of interactions. The concept of self-assembly is used increasingly in many disciplines, with a different flavor and emphasis in each.