Stability of a liquid bridge between nonparallel hydrophilic surfaces

Single Condensation Droplet Self-Ejection from Divergent Structures with Uniform Wettability

Coalescence-induced condensation droplet jumping has been extensively studied for anti-icing, condensation heat transfer, water harvesting, and self-cleaning. Another phenomenon that is gaining attention for potential enhancements is the self-ejection of individual droplets. However, the mechanism underlying this process remains elusive due to cases in which the abrupt detachment of an interface establishes an initial Laplace pressure difference. In this study, we investigate the self-ejection of individual droplets from uniformly hydrophobic microstructures with divergent geometries. We design, fabricate, and test arrays of truncated, nanostructured, and hydrophobic microcones arranged in a square pattern. High-speed microscopy reveals the dynamics of a single condensation droplet between four cones: after cycles of growth and stopped self-propulsion, the suspended droplet self-ejects without abrupt detachments. Through analytical modeling of the droplet in a conical pore as an approximation, we describe the slow isopressure growth phases and the rapid transients driven by surface energy release once a dynamic configuration is reached. Microcones with uniform wettability, in addition to being easier to fabricate, have the potential to enable the self-ejection of all nucleated droplets with a designed size, promising significant improvements in the aforementioned applications and others.

Spontaneous Separation of Immiscible Organic Droplets on Asymmetric Wedge Channels with Hierarchical Microchannels

Spontaneous separation of immiscible organic droplets has substantial research implications for environmental protection and resource regeneration. Compared to the widely explored separation of oil-water mixtures, there are fewer reports on separating mixed organic droplets on open surfaces due to the low surface tension differences. Efficient separation of mixed organic liquids by exploiting the rapid spontaneous transport of droplets on open surfaces remains a challenge. Here, through the fusion of inspiration from the fast droplet transport capability of Sarracenia trichome and the asymmetric wedge channel structure of shorebird beaks, this work proposes a spine with hierarchical microchannels and wedge channels (SHMW). Due to the synergistic effect of capillary force and asymmetric Laplace force, the SHMW can rapidly separate mixed organic droplets into two pure phases without requiring additional energy. In particular, the self-spreading of the oil solution on the open channel surface is utilized to amplify the surface energy difference between two droplets, and SHMW achieves the pickup of oil droplets floating on the surface of the organic solution. The maximum separation efficiency on 3-SHMW can reach 99.63%, and it can also realize the antigravity separation of mixed organic droplets with a surface tension difference as low as 0.87 mN·m-1. Furthermore, SHMW performs controllable separation, oil droplet pickup, and continuous separation and collection of mixed organic droplets. It is expected that this cooperative structure composed of hierarchical microchannels and wedge channels will be realized in resource recovery or chemical reactions in industrial production processes.

Chopstick-Like Structure for the Free Transfer of Microdroplets in Robot Chemistry Laboratory

As we all know, chopsticks can hold food, so can we use this method to carry Newtonian fluids such as droplets? This paper studies the process of this transfer and uses this method to realize the manipulation of open microfluidics by robots. To realize this transfer operation, we first analyzed the force of droplets in this chopstick-like structure and found that the bidirectional movement of droplets in this structure can be achieved by changing the structural parameters. Afterward, the whole process of the transfer of droplets using the chopstick-like structure was analyzed, and the parameter requirements for realizing this transfer were determined. The research in this paper provides a theoretical basis for the controllable manipulation of droplets which can be widely used in unmanned laboratories.

Evaporation-triggered directional transport of asymmetrically confined droplets

HYPOTHESIS

When a liquid droplet is confined between two non-parallel hydrophobic surfaces with dihedral angle α, its behavior is largely influenced by the asymmetric confinement. During evaporation, the droplet morphology under confinement will continuously evolve, leading to the directional transport of the droplet towards the cusp.

EXPERIMENTS AND SIMULATIONS

During the evaporation process, droplets at different initial locations l₀ from the cusp were experimentally observed to transport towards the cusp. A series of simulations using Surface Evolver were performed to obtain the three-dimensional morphologies of the confined droplets. Force and energy analyses were conducted to unveil the mechanisms dominating the evaporation-triggered actuation and transport.

FINDINGS

The asymmetrically confined droplet of volume V would drift towards an equilibrium location of l_e from the cusp with the lowest energy. Its directional motion results from the consecutively decreasing l_e, which is scaled as l_e~α^-1V¹³ during evaporation. Herein, the creeping and slipping modes of transport could be characterized as the quasi-stable and unstable self-relaxation processes of droplet from the stretched regime to the equilibrium regime, respectively. Our findings on the intrinsic mechanism of droplet actuation shed light on a novel approach to manipulating the confined droplet behaviors in a passive and decisive fashion.

Energy harvesting performance of an EDLC power generator based on pure water and glycerol mixture: analytical modeling and experimental validation

A liquid droplet oscillating between two plane electrodes was visualized, and the electrical power generation based on the reverse-electrowetting-on-dielectric (REWOD) phenomenon was measured. For the upper plate, a hydrophobic surface treated by PTFE was used, and the lower plate was tested using the hydrophilic surface properties of ITO glass. To analyze the dynamic behavior of an oscillating liquid bridge, a modeling study was carried out using the phase field method based on the finite element method. The dynamic contact angle of the oscillating liquid bridge was modeled based on advancing and receding contact angles. The variable interfacial areas between the liquid and solid surfaces were calculated and agreed well with the experimental results within a 10% error band. Furthermore, experimental and analytical studies were carried out to examine the REWOD energy harvesting characteristics of the glycerol-water mixtures in various concentrations. As a result, the peak voltage output was obtained at a specific concentration of the glycerol mixture, and the power density of the oscillating liquid bridge at this point was up to 2.23 times higher than that of pure water.

Role of trapped liquid in flow boiling inside micro-porous structures: pore-scale visualization and heat transfer enhancement

Flow boiling is an important heat dissipation method for cooling high heat flux surfaces in many industrial applications. The heat transfer can be further enhanced by using porous media surfaces due to their high specific surface areas. However, although flow boiling in channels is well understood, the phase-change behavior with the additional capillary effect induced by the porous structures is not well understood, and the design of the porous structures is difficult to avoid dryout and over-temperature accidents. A pore-scale lab-on-a-chip method was used here to investigate the flow boiling heat transfer characteristics inside micro-porous structures. The flow patterns, captured in the two-phase region with a uniform pore-throat size of 30 μm, showed that liquid was trapped in the pore-throat structures as both dispersed liquid bridges and liquid films. Moreover, the liquid film was shown to be moving on the wet solid surface by laser-induced fluorescence and particle tracking. A theoretical analysis showed that the capillary pressure difference between adjacent liquid bridges could drive the liquid film flows, which helped maintain the coolant supply in the two-phase region. The pore-throat parameters could be designed to enhance the capillary pressure difference with multiple throat sizes of 10 - 90 μm which would enhance the heat transfer 5% - 10% with a 5% - 23% pressure drop reduction. This research provides another method for improving the flow boiling heat transfer through the porous structure design besides changing the surface wettability.

Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping

The capillary action between two solid surfaces has drawn significant attention in micro-objects manipulation. The axisymmetric capillary bridges and capillary forces between a spherical concave gripper and a spherical particle are investigated in the present study. A numerical procedure based on a shooting method, which consists of double iterative loops, was employed to obtain the capillary bridge profile and bring the capillary force subject to a constant volume condition. Capillary bridge rupture was characterized using the parameters of the neck radius, pressure difference, half-filling angle, and capillary force. The effects of various parameters, such as the contact angle of the spherical concave gripper, the radius ratio, and the liquid bridge volume on the dimensionless capillary force, are discussed. The results show that the radius ratio has a significant influence on the dimensionless capillary force for the dimensionless liquid bridge volumes of 0.01, 0.05, and 0.1 when the radius ratio value is smaller than 10. The effectiveness of the theorical approach was verified using simulation model and experiments.

Measuring Force of Droplet Detachment from Hydrophobic Surfaces via Partial Cloaking with Ferrofluids

This paper presents a new approach to measure the force required to detach a water (a polar liquid) droplet from a hydrophobic surface. This is done by partially cloaking the droplet with a high-surface-tension oil-based ferrofluid and using a magnet to apply a controllable body force to the resulting compound droplet. Placing the assembly on a sensitive scale, the magnet can then be brought closer to the droplet to detach it from the surface while recording the forces applied to the droplet. The work presented here is novel as it uses the concept of partial cloaking in which the solid-droplet contact area is not contaminated by the ferrofluid (and the measured forces do not need postprocessing). Our study is accompanied by numerical simulations aimed at improving our understanding of the interplay between the interfacial forces in a two-phase droplet under the influence of a strong (detaching) body force and at providing additional data for in-depth analyses of these forces. In particular, the minimum ferrofluid volume required for successful water droplet detachment from hydrophobic surfaces is computed for ferrofluids of different surface tensions, and they are compared to experimental data obtained from detaching water droplets from electrospun polystyrene coatings. It is also shown that the detachment force measured via partial cloaking is independent of the volume of the ferrofluid used for the experiment.

Influence of liquid bridge formation process on its stability in nonparallel plates

The formation of a liquid bridge in non-parallel plates is very common and the stability (whether or not it can move spontaneously) of such liquid bridges has been studied a lot for industry, e.g. in printing applications. It is generally considered that the liquid bridge stability is determined by Contact Angle (CA), Contact Angle Hysteresis (CAH), the position of the liquid bridge (represented as P) and the dihedral angle (θ) between non-parallel plates. The stability equation is θ = f(CA, CAH, P). Since P is a process quantity, which is difficult to determine, so it is also difficult to obtain the critical equation for the stability of the liquid bridge. In the previous study (J. Colloid Interface Sci., 2017, 492, 207–217), based on the fitting simulation results, the critical equation about CA, CAH and θ is obtained, as θ = f(CA, CAH). However, in some special cases, the results are still biased (e.g. the weak hydrophilic situation). In this paper, unlike simulation, we get the critical equation θ = f(CA, CAH) from a theoretical point of view. For the first time, by in-depth analysis of the process of liquid bridge formation, the theoretical calculation equation of P is obtained as P = f(CA, CAH, θ). And then, combining the equations θ = f(CA, CAH, P) and P = f(CA, CAH, θ), the theoretical equation is obtained. A lot of simulations and experiments were performed to verify our theoretical equation. Furthermore, comparing our equation with the previous equation, it was found that our equation is more consistent with the experimental results (error less than 0.2°). Finally, the importance of considering the liquid bridging process (the function of P) for stability analysis is illustrated by comparing the results with those not considered (the difference is more than 20% in some cases). The outputs of this paper provide in-depth theoretical support for the analysis and application of liquid bridges.

The effect of liquid bridge formation process on its stability was discussed to obtain the theoretical equation for determining the stability of the liquid bridge.

Evaporation and instability of an unbounded-axisymmetric liquid bridge between chemically similar and different substrates

HYPOTHESIS

In this manuscript we examine the stability of an evaporating-unbounded axisymmetric liquid bridge confined between parallel-planar similar or chemically different substrates using both theory and experiments. With a quasistatic assumption we use hydrostatics to estimate the minimum stable volume V_min via the Young-Laplace equation for Bond numbers 0⩽Bo⩽1, and top/bottom wall contact angles 5°<θ<175° although the primary focus is on wetting and partial wetting fluids. Solving the Young-Laplace equation requires knowledge of appropriate capillary pressure values, which appear as a constant, and may not provide unique solution. To examine uniqueness of numerical solutions and volume minima determined from the Young-Laplace equation for unbounded-axisymmetric liquid bridges we analyzed capillary pressure for large and small liquid volume-asymptotic limits at zero Bond number.

EXPERIMENTS

Experiments were performed to compare with the volume minima calculations for Bond numbers 0.04⩽Bo⩽0.65. Three substrates of varying surface energy were used, with purified water as the primary liquid. Volume estimates and contact angle data were extracted via image analysis and evaporation rates measured from this data are reported.

FINDINGS

Volume minima were in the range 0.1<V_min<20 μl depending on Bond number. There was good agreement when comparing predicted volume minima and those determined from experiments for the range of parameters studied.

Unidirectional transport of water nanodroplets entrapped inside a nonparallel smooth surface: a molecular dynamics simulation study

The unidirectional transport of liquid nanodroplets is an important topic of research in the field of drug delivery, labs on chips, micro/nanofluidics, and water collection. Inspired by nature a nonparallel surface (NPS) is modelled in this study for pumpless water transport applications. The dynamics of water transport is analyzed with the aid of Molecular Dynamics (MD) simulations. There were five different types of NPSs namely A1, A2, A3, A4, and A5 utilized in this study, with separation angles equal to 5°, 7°, 9°, 11°, and 13° respectively. The water droplet was placed at the beginning of the open end of the NPS and it moved spontaneously towards the cusp of the surface in all cases except for the 13° NPS. The size of the water droplet, too, was altered and four different sizes of water droplets (3000, 4000, 5000, and 6000 molecules) were utilized in this study. Furthermore, the surface energy parameter of the NPS was also changed and four different values, i.e. 7.5 eV, 17.5 eV, 27.56 eV, 37.5 eV were assigned to the surface in order to represent a surface with hydrophobic to hydrophilic characteristics. In addition the importance of water bridge formation for its spontaneous propulsion with the influence of surface energy and droplet size is also discussed in this study. Moreover, a unique design is modelled for the practical application of water harvesting and a large size water droplet is formed by combining two water droplets placed inside a NPS.

Two water nanodroplets spontaneously move towards the cusp of nonparallel surfaces and coalesce to form a large size nanodroplet.

Directional Transport of a Liquid Drop between Parallel-Nonparallel Combinative Plates

Liquids confined between two parallel plates can perform the function of transmission, support, or lubrication in many practical applications, due to which to maintain liquids stable within their working area is very important. However, instabilities may lead to the formation of leaking drops outside the bulk liquid, thus it is necessary to transport the detached drops back without overstepping the working area and causing destructive leakage to the system. In this study, we report a novel and facile method to solve this problem by introducing the wedgelike geometry into the parallel gap to form a parallel-nonparallel combinative construction. Transport performances of this structure were investigated. The criterion for self-propelled motion was established, which seemed more difficult to meet than that in the nonparallel gap. Then, we performed a more detailed investigation into the drop dynamics under squeezing and relaxing modes because the drops can surely return in hydrophilic combinative gaps, whereas uncertainties arose in gaps with a weak hydrophobic character. Therefore, through exploration of the transition mechanism of the drop motion state, a crucial factor named turning point was discovered and supposed to be directly related to the final state of the drops. On the basis of the theoretical model of turning point, the criterion to identify whether a liquid drop returns to the parallel part under squeezing and relaxing modes was achieved. These criteria can provide guidance on parameter selection and structural optimization for the combinative gap, so that the destructive leakage in practical productions can be avoided.

Behavior of a Liquid Bridge between Nonparallel Hydrophobic Surfaces

When a liquid bridge is formed between two nonparallel identical surfaces, it can move along the surfaces. Literature indicates that the direction of bridge movement is governed by the wettability of surfaces. When the surfaces are hydrophilic, the motion of the bridge is always toward the cusp (intersection of the plane of the two bounding surfaces). On the other hand, the movement is hitherto thought to be always pointing away from the cusp when the surfaces are hydrophobic. In this study, through experiments, numerical simulations, and analytical reasoning, we demonstrate that for hydrophobic surfaces, wettability is not the only factor determining the direction of the motion. A new geometrical parameter, i.e., confinement (cf), was defined as the ratio of the distance of the farthest contact point of the bridge to the cusp, and that of the closest contact point to the cusp. The direction of the motion depends on the amount of confinement (cf). When the distance between the surfaces is large (resulting in a small cf), the bridge tends to move toward the cusp through a pinning/depinning mechanism of contact lines. When the distance between the surfaces is small (large cf), the bridge tends to move away from the cusp. For a specific system, a maximum cf value (cf_max) exists. A sliding behavior (i.e., simultaneous advancing on the wider side and receding on the narrower side) can also be seen when a liquid bridge is compressed such that the cf exceeds the cf_max. Contact angle hysteresis (CAH) is identified as an underpinning phenomenon that together with cf fundamentally explains the movement of a trapped liquid between two hydrophobic surfaces. If there is no CAH, however, i.e., the case of ideal hydrophobic surfaces, the cf will be a constant; we show that the bridge slides toward the cusp when it is stretched, while it slides away from the cusp when it is compressed (note sliding motion is different from motion due to pinning/depinning mechanism of contact lines). As such, the displacement is only related to geometrical parameters such as the amount of compression (or stretching) and the dihedral angle between the surfaces.