Comparison between two capillary forces models

The combined effect of cohesion and finite size on the collapse of wet granular columns

The collapse of low-saturation liquid-containing granular materials is prevalent in nature and industrial processes, and understanding the associated transient dynamics is extremely important for exploring such complex flow processes. In this paper, the collapse of a finite-size wet granular column is systematically studied and the determinants affecting its dynamics are analyzed based on the discrete element model for wet particles and the corresponding small-scale experiments. With the aid of parametric analysis, the dimensionless cohesion parameter containing the system size and grain-scale bond number is proposed, and its relevance in characterizing column stability and collapse dynamics of wet granular materials is further confirmed. For the collapse of wet granular columns with a fixed aspect ratio, the initial height contained in the cohesion parameter is verified to be a manifestation of the finite size effect, which is present in a wet granular collapse and is coupled with the cohesive effect. Such a coupling effect is taken into account in our proposed scaling laws that can be applied to uniformly describe the deposit morphology of wet granular columns after collapse.

Accelerated Water Transportation Phenomenon through a Hydrophilic Metal Roll

Passive water transport by taking advantage of capillary forces is vital for various applications such as solar-driven interfacial evaporation, evaporative cooling, and atmospheric water harvesting. Surface engineering and structure design with a hydrophilic surface and enhanced capillary force will facilitate passive water transport. Herein, we demonstrate a hydrophilic Cu/CuO foil-based roll for accelerated water transportation. The roll was fabricated by rolling up a typical 2D Cu/CuO film, which transforms the water climbing behavior by significantly enhancing the capillary force between each Cu/CuO film layer. The simple spatial transformation for a 2D film, from planar foil to 3D structure, has extensively facilitated water transportation performance and broadened its practical application potential. The Cu/CuO film with a blade-like nanostructure and excellent hydrophilicity ensures water supply to a limited area, while the capillary effect between different layers of the Cu/CuO foil extends the water transportation height. Consequently, the Cu/CuO foil-based roll demonstrated a high fluidic transport velocity. This design derived from the 2D planar film can be potentially employed for a large range of applications such as evaporating in a confined space and evaporation-driven energy harvest.

Study on the Manipulation Strategy of Metallic Microstructures Based on Electrochemical-Assisted Method

Microcomponent manipulation (MCM) technology plays a decisive role in assembling complex systems at the micro- and nanoscale. However, the existing micromanipulation methods are difficult to widely apply in the manufacturing of microelectromechanical systems (MEMSs) due to the limited manipulation space and complex application objects, and the manipulation efficiency is relatively low, which makes it difficult to industrialize these micromanipulating systems. To solve the above problems, this paper proposes an efficient metal MCM strategy based on the electrochemical method. To verify the feasibility and repeatability of the strategy, the finite element model (FEM) incorporating the hydrodynamic and electrochemical theories is used to calculate the local stress distribution of the contact position during the dynamic pick-up process. Based on the simulation results, we defined the relationship between the parameters, such as the optimal manipulating position and angle for picking, transferring and releasing. The failure behaviors of pick-up are built to realize the efficient three-dimensional manipulation of microcopper wire of 300 μm. By establishing a theoretical model and experimental verification, it was concluded that the middle point was the best manipulating position when picking up the microcopper wire, the most efficient picking angle was between 45 and 60 degrees for the pipette, and the average time was 480 s in three sets of picking-release manipulation experiments. This paper provides an achievable idea for different types of micro-object manipulations and promotes the rapid application of micromanipulation techniques in MEMSs.

Electrowetting: A Consideration in Electroadhesion

With the commercialization of haptic devices, understanding behavior under various environmental conditions is crucial for product optimization and cost reduction. Specifically, for surface haptic devices, the dependence of the friction force and the electroadhesion effect on the environmental relative humidity and the finger hydration level can directly impact their design and performance. This article presents the influence of relative humidity on the finger-surface friction force and the electroadhesion performance. Mechanisms including changes to Young's modulus of skin, contact angle change and capillary force were analyzed separately with experimental and numerical methods. Through comparison of the calculated capillary force in this paper and the electroadhesion force calculated in published papers, it was found that electrowetting at high voltage could contribute up to 60% of the total friction force increase in electroadhesion. Therefore, in future design of surface haptic devices, the effect of electrowetting should be considered carefully.

Drying-induced stresses before solidification in colloidal dispersions: in situ measurements

We first report an original setup that enables continuous measurements of stresses induced by the drying of confined drops of complex fluids. This setup is mainly based on a precision scale working with an electromagnetic force compensation technique that provides accurate measurements of forces, while allowing simultaneously controlled evaporation rates, in situ microscopic observations, and thus quantitative estimates of normal stresses. We then performed an extensive study of the drying of a charged colloidal dispersion using this setup. Stress measurements clearly show the emergence of large tensile stresses during drying, well-before the solidification stage evidenced by the invasion of the porous colloidal material by air. Combined measurements of solid deformation and concentration profiles (particle tracking, Raman micro-spectroscopy) help us to demonstrate that these stresses are due to the formation of a solid at a low volume fraction, which further undergoes drying-induced shear deformations up to the colloid close-packing, as also supported by large deformation poroelastic modeling. Above all, our results highlight the importance of repulsive colloidal interactions in the build-up of mechanical stresses during drying.

Controlling Normal Stiffness in Droplet-Based Linear Bearings

While capillary forces are negligible relative to gravity at the macroscale, they provide adequate force to effectively manipulate millimeter to micro meter objects. The fluidic actuation can be accomplished using droplets that also act as bearings. While rotary droplet bearings have been previously demonstrated, this paper addresses the positioning accuracy of a droplet-based bearing consisting of a droplet between a moving plate and a stationary substrate with constrained wetting region under a normal load. Key wetting cases are analyzed using both closed form analytical approximations and numerical simulations. The vertical force and stiffness characteristics are analyzed in relation to the wetting boundaries of the supporting surface. Case studies of different wetting boundaries are presented and summarized. Design strategies are presented for maximizing load carrying capability and stiffness. These results show that controlled wetting and opposing droplet configurations can create much higher stiffness fluidic bearings than simple droplets.

Unraveling the solvent induced welding of silver nanowires for high performance flexible transparent electrodes

A solution processed metal nanowire network is a promising flexible transparent electrode to replace brittle metal oxides for printable optoelectronics applications, but suffers from the issue of pseudo contact between nanowires. Herein, using volatile solvent mists as a powerful "zipper", we demonstrate a simple and rapid method to effectively weld silver nanowires, which dramatically improves the conductivity and robustness of the silver nanowire network based flexible transparent electrodes. We reveal that for a stacked network structure, the unique wedge-shaped nanogaps between the long nanowires and substrate provide a strong capillary force during solvent evaporation, which is much larger than that between zero-dimensional nanoparticles and gives a decisive contribution for nanowire junction welding, and this nanowire-substrate interplay force is positively related to the wettability of the substrate. At the same time, the dissolution-reprecipitation of the capping agent on the silver nanowire surface as the natural adhesive can fix the network on the substrate tightly, which enhances the robustness of the network. Our approach solves two key issues in solution-processed transparent electrodes in one simple step, and is compatible with various mild solution-processed optoelectronic devices, especially those containing heat-sensitive or chemical-sensitive materials. Moreover, a new type of invisible infrared encryption display is demonstrated based on this approach.

High-performance surface-enhanced Raman scattering substrate prepared by self-assembling of silver nanoparticles into the nanogaps of silver nanoislands

We report an effective and simple method to further enhance the surface-enhanced Raman scattering (SERS) by silver (Ag) nanoparticles (AgNPs) self-assembling into the nanogaps of an Ag nanoisland (AgNIs). The AgNIs prepared by dewetting of Ag film created a nanorough surface, which induced the Ag nanoparticles to regularly deposit into the nanogaps. AgNPs and AgNIs samples were also prepared for comparative analysis. Their SERS activities were investigated theoretically and experimentally. Experimental enhancement factors (EFs) for AgNPs, AgNIs, and AgNPs decorated AgNIs substrate (AgNPs-AgNIs) were ∼10⁷, ∼10⁶, ∼10⁸, respectively, with relative standard deviation (RSD) of 66.1%, 12.9%, and 13.2%. Remarkable enhancement (EF≈10⁸) and excellent reproducibility (RSD=13.2%) indicated the AgNPs-AgNIs had a high potential in practical application. Electromagnetic simulation using COMSOL Multiphysics demonstrated that the additional enhancement of the SERS effect could be mainly attributed to the improvement of the local electromagnetic field. Moreover, the deposition process of Ag nanoparticles was analyzed in detail to understand the reproducibility of AgNPs-AgNIs.

Reliable and Accurate Release of Micro-Sized Objects with a Gripper that Uses the Capillary-Force Method

There have been recent developments in grippers that are based on capillary force and condensed water droplets. These are used for manipulating micro-sized objects. Recently, one-finger grippers have been produced that are able to reliably grip using the capillary force. To release objects, either the van der Waals, gravitational or inertial-forces method is used. This article presents methods for reliably gripping and releasing micro-objects using the capillary force. The moisture from the surrounding air is condensed into a thin layer of water on the contact surfaces of the objects. From the thin layer of water, a water meniscus between the micro-sized object, the gripper and the releasing surface is created. Consequently, the water meniscus between the object and the releasing surface produces a high enough capillary force to release the micro-sized object from the tip of the one-finger gripper. In this case, either polystyrene, glass beads with diameters between 5–60 µm, or irregularly shaped dust particles of similar sizes were used. 3D structures made up of micro-sized objects could be constructed using this method. This method is reliable for releasing during assembly and also for gripping, when the objects are removed from the top of the 3D structure—the so-called “disassembling gripping” process. The accuracy of the release was lower than 0.5 µm.

Surface tension-driven self-alignment

Surface tension-driven self-alignment is a passive and highly-accurate positioning mechanism that can significantly simplify and enhance the construction of advanced microsystems. After years of research, demonstrations and developments, the surface engineering and manufacturing technology enabling capillary self-alignment has achieved a degree of maturity conducive to a successful transfer to industrial practice. In view of this transition, a broad and accessible review of the physics, material science and applications of capillary self-alignment is presented. Statics and dynamics of the self-aligning action of deformed liquid bridges are explained through simple models and experiments, and all fundamental aspects of surface patterning and conditioning, of choice, deposition and confinement of liquids, and of component feeding and interconnection to substrates are illustrated through relevant applications in micro- and nanotechnology. A final outline addresses remaining challenges and additional extensions envisioned to further spread the use and fully exploit the potential of the technique.

Direct numerical simulation of gas-solid-liquid flows with capillary effects: An application to liquid bridge forces between spherical particles

In this study, a numerical method is developed to perform the direct numerical simulation (DNS) of gas-solid-liquid flows involving capillary effects. The volume-of-fluid method employed to track the free surface and the immersed boundary method is adopted for the fluid-particle coupling in three-phase flows. This numerical method is able to fully resolve the hydrodynamic force and capillary force as well as the particle motions arising from complicated gas-solid-liquid interactions. We present its application to liquid bridges among spherical particles in this paper. By using the DNS method, we obtain the static bridge force as a function of the liquid volume, contact angle, and separation distance. The results from the DNS are compared with theoretical equations and other solutions to examine its validity and suitability for modeling capillary bridges. Particularly, the nontrivial liquid bridges formed in triangular and tetrahedral particle clusters are calculated and some preliminary results are reported. We also perform dynamic simulations of liquid bridge ruptures subject to axial stretching and particle motions driven by liquid bridge action, for which accurate predictions are obtained with respect to the critical rupture distance and the equilibrium particle position, respectively. As shown through the simulations, the strength of the present method is the ability to predict the liquid bridge problem under general conditions, from which models of liquid bridge actions may be constructed without limitations. Therefore, it is believed that this DNS method can be a useful tool to improve the understanding and modeling of liquid bridges formed in complex gas-solid-liquid flows.

Nanocapillary Adhesion between Parallel Plates

Molecular dynamics simulations are used to study capillary adhesion from a nanometer scale liquid bridge between two parallel flat solid surfaces. The capillary force, Fcap, and the meniscus shape of the bridge are computed as the separation between the solid surfaces, h, is varied. Macroscopic theory predicts the meniscus shape and the contribution of liquid/vapor interfacial tension to Fcap quite accurately for separations as small as two or three molecular diameters (1-2 nm). However, the total capillary force differs in sign and magnitude from macroscopic theory for h ≲ 5 nm (8-10 diameters) because of molecular layering that is not included in macroscopic theory. For these small separations, the pressure tensor in the fluid becomes anisotropic. The components in the plane of the surface vary smoothly and are consistent with theory based on the macroscopic surface tension. Capillary adhesion is affected by only the perpendicular component, which has strong oscillations as the molecular layering changes.

How pinning and contact angle hysteresis govern quasi-static liquid drop transfer

This paper presents both experimental and numerical simulations of liquid transfer between two solid surfaces with contact angle hysteresis (CAH). Systematic studies on the role of the advancing contact angle (θa), receding contact angle (θr) and CAH in determining the transfer ratio (volume of the liquid transferred onto the acceptor surface over the total liquid volume) and the maximum adhesion force (Fmax) were performed. The transfer ratio was found to be governed by contact line pinning at the end of the transfer process caused by CAH of surfaces. A map based on θr of the two surfaces was generated to identify the three regimes for liquid transfer: (I) contact line pinning occurs only on the donor surface, (II) contact line pinning occurs on both surfaces, and (III) contact line pinning occurs only on the acceptor surface. With this map, an empirical equation is provided which is able to estimate the transfer ratio by only knowing θr of the two surfaces. The value of Fmax is found to be strongly influenced by the contact line pinning in the early stretching stage. For symmetric liquid bridges between two identical surfaces, Fmax may be determined only by θa, only by θr, or by both θa and θr, depending on the magnitude of the contact angles. For asymmetric bridges, Fmax is found to be affected by the period when contact lines are pinned on both surfaces.

Fast Liquid Transfer between Surfaces: Breakup of Stretched Liquid Bridges

In this work, a systematic experimental study was performed to understand the fast liquid transfer process between two surfaces. According to the value of the Reynolds number (Re), the fast transfer is divided into two different scenarios, one with negligible inertia effects (Re ≪ 1) and the other with significant inertia effects (Re > 1). For Re ≪ 1, the influences of the capillary number (Ca) and the dimensionless minimum separation (H(min)* = H(min)/V(1/3), where H(min) is the minimum separation between two surfaces and V is the volume of liquid) on the transfer ratio (α, the volume of liquid transferred to the acceptor surface over the total liquid volume) are discussed. On the basis of the roles of each physical parameter, an empirical equation is presented to predict the transfer ratio, α = f(Ca). This equation involves two coefficients which are affected only by the surface contact angles and H(min)* but not by the liquid viscosity or surface tension. When Re > 1, it is shown for the first time that the transfer ratio does not converge to 0.5 with the increase in the stretching speed.

Capillary adhesion at the nanometer scale

Molecular dynamics simulations are used to study the capillary adhesion from a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The atomic structure of the tip, the tip radius, the contact angles of the liquid on the two surfaces, and the volume of the liquid bridge are varied. The capillary force between the tip and substrate is calculated as a function of their separation h. The force agrees with continuum predictions based on macroscopic theory for h down to ∼5 to 10 nm. At smaller h, the force tends to be less attractive than predicted and has strong oscillations. This oscillatory component of the capillary force is completely missed in the macroscopic theory, which only includes contributions from the surface tension around the circumference of the meniscus and the pressure difference over the cross section of the meniscus. The oscillation is found to be due to molecular layering of the liquid confined in the narrow gap between the tip and substrate. This effect is most pronounced for large tip radii and/or smooth surfaces. The other two components considered by the macroscopic theory are also identified. The surface tension term, as well as the meniscus shape, is accurately described by the macroscopic theory for h down to ∼1 nm, but the capillary pressure term is always more positive than the corresponding continuum result. This shift in the capillary pressure reduces the average adhesion by a factor as large as 2 from its continuum value and is found to be due to an anisotropy in the pressure tensor. The component in the plane of the substrate is consistent with the capillary pressure predicted by the macroscopic theory (i.e., the Young-Laplace equation), but the normal pressure that determines the capillary force is always more positive than the continuum counterpart.

Simulation of capillary bridges between nanoscale particles

Capillary forces are very important as they exceed in general other adhesion forces. But at the same time the exact calculation of these forces is very complex, so often assumptions and approximations are used. Previous research was done with regard to micrometer sized particles, but the behavior of nanoscale particles is different. Hence, the results for micrometer sized particles cannot be directly transferred when considering nanoscale particles. Therefore, a simulation method was developed to calculate numerically the shape of a rotationally symmetrical capillary bridge between two spherical particles or a particle and a plate. The capillary bridge in the gap between the particles is formed due to capillary condensation and is in thermodynamic equilibrium with the gas phase. Hence the Kelvin equation and the Young-Laplace equation can be used to calculate the profile of the capillary bridge, depending on the relative humidity of the surrounding air. The bridge profile consists of several elements that are determined consecutively and interpolated linearly. After the shape is determined, the volume and force, divided into capillary pressure force and surface tension force, can be calculated. The validation of this numerical model will be shown by comparison with several different analytical calculations for micrometer-sized particles. Furthermore, it is demonstrated that two often used approximations, (1) the toroidal approximation and (2) the use of an effective radius, cannot be used for nanoscale particles without remarkable mistake. It will be discussed how the capillary force and its components depend on different parameters, like particle size, relative humidity, contact angle, and distance, respectively. The rupture of a capillary bridge due to particle separation will also be presented.

Fabrication and visualization of capillary bridges in slit pore geometry

A procedure for creating and imaging capillary bridges in slit-pore geometry is presented. High aspect ratio hydrophobic pillars are fabricated and functionalized to render their top surfaces hydrophilic. The combination of a physical feature (the pillar) with a chemical boundary (the hydrophilic film on the top of the pillar) provides both a physical and chemical heterogeneity that pins the triple contact line, a necessary feature to create stable long but narrow capillary bridges. The substrates with the pillars are attached to glass slides and secured into custom holders. The holders are then mounted onto four axis microstages and positioned such that the pillars are parallel and facing each other. The capillary bridges are formed by introducing a fluid in the gap between the two substrates once the separation between the facing pillars has been reduced to a few hundred micrometers. The custom microstage is then employed to vary the height of the capillary bridge. A CCD camera is positioned to image either the length or the width of the capillary bridge to characterize the morphology of the fluid interface. Pillars with widths down to 250 µm and lengths up to 70 mm were fabricated with this method, leading to capillary bridges with aspect ratios (length/width) of over 100(1).

From concave to convex: capillary bridges in slit pore geometry

We investigate the morphological evolution of nonaxisymmetric capillary bridges in slit-pore geometry as the height of the pore and aspect ratio of the bridge are varied. The liquid bridges are formed between two hydrophobic surfaces patterned with hydrophilic strips. The aspect ratio of the capillary bridges (length/width) is varied from 2.5 to 120 by changing the separation between the surfaces, the width of the strips, or the fluid volume. As the bridge height is increased, the aspect ratio decreases and we observe a large increase in the mean curvature of the bridge. More specifically, the following counterintuitive result is observed: the mean curvature of the bridges changes sign and goes from negative (concave bridge) to positive (convex bridge) when the height is increased at constant volume. These experimental observations are in quantitative agreement with Surface Evolver simulations. Scaling shows a collapse of the data indicating that this transition in the sign of the Laplace pressure is universal for capillary bridges with high aspect ratios. Finally, we show that the morphology diagrams obtained from our 3D analysis are considerably different from those expected from a 2D analysis.

Capillary torque caused by a liquid droplet sandwiched between two plates

Capillary force makes a liquid droplet's surface have the minimum area. If the droplet is sandwiched between two plates, it exerts capillary force on the plates. The magnitude of the force depends on the shape of the sandwiched droplet, which is in turn determined by the shape of the plates and the volume of the liquid. The liquid's shape, however, is hard to determine analytically. In this paper, the torque caused by a droplet sandwiched between two noncircular plates is experimentally and theoretically analyzed. We patterned a magnetic material on the surface of the plates and used it to apply a magnetic force to the plates. The torque on the plates was measured. The torque caused by capillary force was calculated by observing the equilibrium between the capillary force and magnetic force. We obtained approximate theoretical solutions for the liquid's shape and torque and verified that they were in accordance with the experimental results. The experimental and theoretical results presented in this paper are useful for designing microdevices or self-assemblies actuated by capillary force.

Capillary forces during liquid nanodispensing

We present a comprehensive study of the capillary force measured during the liquid nanodispensing of attoliter droplets with an atomic force microscope tip. Due to the presence of a nanochannel drilled at the tip apex and connected to a reservoir droplet deposited on the cantilever, we observe a large variety of force curves during the deposition process. We propose a numerical method which accounts for most of the experimental observations. In particular, we clearly demonstrate the influence of the nanochannel diameter. This study leads to a better understanding of the mechanisms of liquid transfer from the tip to the surface and also provides a real time monitoring of the dispensing. Besides these applications, the method we use, which can handle a large variety of conditions and also complex geometries, may find a wide range of applications.