Efficient transport of droplet sandwiched between saw-tooth plates

Coalescence-Induced Droplet Jumping on Superhydrophobic Surfaces with Annular Wedge-Shaped Micropillar Arrays

The coalescence-induced droplet jumping on superhydrophobic surfaces has extensive application potential in water harvesting, thermal management of electronic devices, and microfluidics. The rational design of the surface structure can influence the interaction between the droplet and the surface, thereby controlling the velocity and direction of the droplet's jumping. In this study, we fabricate the superhydrophobic surface with annular wedge-shaped micropillar arrays, examine the dynamic behavior of condensate droplets on the surface, and measure the temporal and spatial variations of droplet density, average radius, and surface coverage with wedge-shaped micropillars of varying sizes. In addition, the energy analysis of the coalescence-induced droplet jumping reveals that the two primary factors influencing the jumping are the relative size and position of the droplets and micropillars. Further numerical simulations find that the wedge-shaped micropillars cause an asymmetric distribution of pressure within the droplet and at the solid-liquid contact surface, which generates an unbalanced force driving the droplet in the gradient direction of the wedge-shaped micropillar, causing the droplet to jump off the surface with both vertical and gradient-direction velocities. The capacity of the wedge-shaped micropillar surface to transport droplets in the gradient direction increases and then decreases as the relative size of the droplets and micropillars increases. The relative position of the droplet center-of-mass line perpendicular to the bottom edge of the wedge micropillars' trapezoidal shape is more favorable for droplet transport. This work reveals the influence mechanism of surface structure on the velocity and direction of droplet jumping, and the results can guide the microstructure design of superhydrophobic surfaces, which has significant implications for the application of droplet jumping.

Long-Distance Continuous Self-Transport of a Droplet by Merging Droplets on a Graphene-Covered Multibranch Gradient Groove Surface

Although the self-transport of liquid droplets by a gradient-textured substrate can break away from the energy input, the long distance and even continuous spontaneous motion of droplets will be limited by the length in the surface-gradient direction. This article introduces a novel design with a monolayer graphene-covered multibranch gradient groove surface (GMGGS). The design aims to achieve long-distance, continuous self-transport of a mercury (Hg) droplet by merging with other mercury droplets, and the process is carried out using molecular dynamics (MD) simulation. This method achieves the merging of mercury droplets through the structure of multibranch gradient grooves, and we have observed that the merged mercury droplet can be reaccelerated in the gradient groove. The results demonstrate that droplet merging allows for control over the surface morphology variations of mercury droplets within the gradient groove. This creates a forward pressure difference, which leads to reacceleration of the mercury droplets. In light of this mechanism, the trunk droplet can achieve long-distance continuous self-transport on the GMGGS by continuously merging with branch droplets. These findings will broaden our comprehension of droplet merging and self-transport behavior, offering corresponding theoretical support for the long-distance continuous self-transport of droplets.

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.

High-speed directional transport of condensate droplets on superhydrophobic saw-tooth surfaces

HYPOTHESIS

Most droplets on high-efficiency condensing surfaces have radii of less than 100 μm, but conventional droplet transport methods (such as wettability-gradient surfaces and structural-curvature-gradient surfaces) that rely on the unbalanced force of three-phase lines can only transport millimeter-sized droplets efficiently. Regulating high-speed directional transport of condensate droplets is still challenging. Therefore, we present a method for condensate droplet transportation, based on the reaction force of the superhydrophobic saw-tooth surfaces to the liquid bridge, the condensate droplets could be transported at high speed and over long distances.

EXPERIMENTS

The superhydrophobic saw-tooth surfaces are fabricated by femtosecond laser ablation and chemical etching. Condensation experiments and luminescent particle characterization experiments on different surfaces are conducted. Aided by the theoretical analysis, we illustrate the remarkable performance of condensate droplet transportation on saw-tooth surfaces.

FINDINGS

Compared with conventional methods, our method improves the transport velocity and relative transport distance by 1-2 orders of magnitude and achieves directional transport of the smallest condensate droplet of about 2 μm. Furthermore, the superhydrophobic saw-tooth surfaces enable multi-hop directional jumping of condensate droplets, leading to cross-scale increases in transport distances from microns to decimeters.

Surface behaviors of droplet manipulation in microfluidics devices

In recent years, the rapid development of microfluidic technology has caused a revolutionary impact in the fields of chemistry, medicine, and life sciences. Also, droplet control is one of the most important technologies in the field of microfluidics. In order to achieve different degrees of droplet transport, the dynamic balance of the competing processes of droplet driving force and fluid resistance should be controlled to achieve good selectivity of droplet transport. Here, we focus on the principles of droplet transport in microfluidic devices, including the driving forces for droplet transport in fluids and the effects of transport properties on droplet transport. After that, the effects of external fields on the directional transport of droplets and the advantages and disadvantages of each external field in droplet transport are discussed in detail. Finally, the applications and challenges of droplet microfluidics in chemical, biomedical, and mechanical systems are comprehensively introduced.

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.

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.

Motion of droplets into hydrophobic parallel plates

Due to the superior operability and good anti-interference, the prospect of controlling microdroplets using a parallel plate structure (PPS) is very promising. However, in practical applications, droplets in such structures are often affected by various factors, resulting in deformation, evaporation, stress rupture and other phenomena, leading to equipment failure. Therefore, how to simply and effectively transfer liquid droplets to PPS to maintain the stable and efficient operation of the system has become an urgent problem to be solved. In this paper, a simple and effective ratchet-like strategy (relaxing and squeezing actions) is introduced to transfer droplets. To analyze the mechanism of the strategy and optimize the control, we conduct this study from three aspects. First, the droplet movement trend is obtained by analyzing the pressure between SPS and PPS. Second, the reasons why the droplet can achieve this inward motion are investigated. Through theoretical analysis, which is also proven by simulations and experiments, we creatively put forward that the asymmetric change of the contact angle (CA) induced by the asymmetric structure is the fundamental cause of this kind of motion. Due to the asymmetric change of the contact angle, the CA in the PPS will reach the advancing angle first in the squeezing process, and the CA in the SPS will reach the receding angle first in the relaxing process, thus causing the inward movement of the droplet. Third, to optimize this strategy, the effects of the following governing parameters are researched individually based on the corresponding simulations and experiments: the control parameters (the initial gap width of the PPS H₀ and the amount of squeezing and relaxing of ΔH) and the thickness of the top plate. Subsequently, an optimized ratchet-like cycle is achieved. In summary, these findings not only provide a new method by which to realize the movement of droplets toward hydrophobic PPSs but also creatively point out the cause of the ratchet strategy, which can be applied in many microfluidics fields.

A simple and effective ratchet-like strategy is introduced to transfer droplets. We creatively put forward that the asymmetric change of the contact angle induced by the asymmetric structure is the fundamental cause of this kind of motion.

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.

Design of Nano Screw Pump for Water Transport and its Mechanisms

Nanopumps conducting fluids through nanochannels have attracted considerable interest for their potential applications in nanofiltration, water desalination and drug delivery. Here, we demonstrate by molecular dynamics (MD) simulations that a nano screw pump is designed with helical nanowires embedded in a nanochannel, which can be used to drive unidirectional water flow. Such helical nanowires have been successfully synthesized in many experiments. By investigating the water transport mechanism through nano screw pumps with different configuration parameters, three transport modes were observed: cluster-by-cluster, pseudo-continuous, and linear-continuous, in which the water flux increases linearly with the rotating speed. The influences of the nanowires’ surface energy and the screw’s diameter on water transport were also investigated. Results showed that the water flux rate increases as the decreasing wettability of helical nanowires. The deviation in water flux in screw pumps with smaller radius is attributed to the weak hydrogen bonding due to space confinement and the hydrophobic blade. Moreover, we also proposed that such screw pumps with appropriate diameter and screw pitch can be used for water desalination. The study provides an insight into the design of multifunctional nanodevices for not only water transport but water desalination in practical applications.