Dynamical insights into the mechanism of a droplet detachment from a fiber

Dynamic Drop Penetration of Horizontally Oriented Fiber Arrays

In this experimental study, we combine drop impact into porous media and onto a single fiber to study drop impact into fiber arrays inspired by mammalian fur coats. In our 3D-printed arrays, we vary the packing density, fiber alignment, strand cross-section, and wettability. Drops impact fibers fixed at both ends, penetrating over short periods of time by momentum and laterally spreading throughout the array. Using image analysis, we measure penetration depth and wetted width into the array. Impact Weber number and intrinsic porosity define penetration, retraction, and rebound regimes. On average, at an impact Weber number of ≈80, staggered fibers reduce penetration by 24% in hydrophilic fibers and 34% in hydrophobic fibers, and the penetration reduction percentage is expected to increase with increasing Weber number. Our results indicate that as density grows toward the density of mammalian pelts, penetration will reach a maximum value independent of drop impact velocity, thereby providing an effective rain barrier. Hydrophilicity at the densities we test, 50-150 strands/cm2, aids fiber array resistance to dynamic penetration by impacting drops through the promotion of lateral drop spreading and inhibition of drop fragmentation. Conversely, hydrophobic fibers best resist low-speed wicking. The fraction of a drop that infiltrates hydrophilic and hydrophobic fibers is nearly identical for a fixed Weber number because lateral spreading restricts the penetration depth into hydrophilic fibers but does not restrict mass infiltration. Above a critical Weber number, the entire drop mass penetrates fiber arrays regardless of strand wettability.

Dynamics of fog droplets on a harp wire

Fog harps effectively drain small droplets, which prevents clogging and results in more water harvested from fog compared to mesh nets. However, the dynamics of fog droplets coalescing and sliding down a vertical wire remain poorly understood. Here, we develop an analytical model that captures the physics of fog droplets draining down a single vertical wire. The driving forces are gravity and the surface energy released from coalescence events, whereas the dominant resisting forces are revealed to be inertia, contact angle hysteresis, and local viscous dissipation within the droplet's receding wedge. The average sliding velocity of fog droplets on a Teflon-coated wire was only half that of an uncoated stainless steel wire, due to non-coalescence events exclusive to the hydrophobic wire disrupting the momentum of droplet sliding.

Dynamic Contact Angle Measurement on a Microscopic Area and Application to Wettability Characterization of a Single Fiber

Dynamic contact angles on a microscopic area were measured using a specially developed system. Combining pulse injection equipment, a high-speed image capture system set on a microscope, and precise positioning stages, contact angles of typically 2 nL water droplets were measured at a repetition rate of 130 ms. Thereafter, measuring the series of the contact angles of a droplet on a planar silicon surface, contact angle hysteresis, defined as the difference between the advancing and receding contact angles, was measured, and the effect of droplet size was clarified. The system was then applied to characterize a single fiber wherein the contact angles of droplets suspended on a polypropylene fiber, typically 19 μm in diameter, were measured. Plasma treatment is often adopted to modify wettability and has directionality. By fixing a fiber while applying torsion and changing the measurement position along the fiber, the contact angles at different circumferential positions can be characterized. This effect was unraveled by comparing the contact angles on the treated side to its opposite side as well as the effect of fiber diameter.

Reversible electrowetting transitions on superhydrophobic surfaces

An electric field applied across the interface has been shown to enable transitions from the Cassie to the Wenzel state on superhydrophobic surfaces with miniature corrugations. Molecular dynamics (MD) simulations manifest the possibility of reversible cycling between the two states when narrow surface wells support spontaneous expulsion of water in the absence of the field. With approximately 1 nm sized wells between the surface asperities, the response times to changes in the electric field are of O(0.1) ns, allowing up to GHz frequency of the cycle. Because of the orientation preferences of interfacial water in contact with the solid, the phenomenon depends on the polarity of the field normal to the interface. The threshold field strength for the Cassie-to-Wenzel transition is significantly lower for the field pointing from the aqueous phase to the surface; however, once in the Wenzel state, the opposite field direction secures tighter filling of the wells. Considerable hysteresis revealed by the delayed water retraction at decreasing field strength indicates the presence of moderate kinetic barriers to expulsion. Known to scale approximately with the square of the length scale of the corrugations, these barriers preclude the use of increased corrugation sizes while the reduction of the well diameter necessitates stronger electric fields. Field-controlled Cassie-to-Wenzel transitions are therefore optimized by using superhydrophobic surfaces with nanosized corrugations. Abrupt changes indicate a high degree of cooperativity reflecting the correlations between the wetting states of interconnected wells on the textured surface.

Identification of Deposited Oil Structures on Thin Porous Oil Mist Filter Media Applying µ-CT Imaging Technique

The identification of microscale oil structures formed from deposited oil droplets on the filter front face of a coalescence filter medium is essential to understand the initial state of the coalescence filtration process. Using µ-CT imaging and a deep learning tool for segmentation, this work presents a novel approach to visualize and identify deposited oil structures as oil droplets on fibers or oil sails between adjacent fibers of different sizes, shapes and orientations. Furthermore, the local and global porosity, saturation and fiber ratios of different fiber material of the oleophilic filter medium was compared and evaluated. Especially the local and global porosity of the filter material showed great accordance. Local and global saturation as well as the fiber ratios on local and global scale had noticeable differences which can mainly be attributed to the small field of view of the µ-CT scan (350 µm on 250 µm) or the minimal resolution of approximately 1 µm. Finally, fiber diameters of the investigated filter material were analyzed, showing a good agreement with the manufacturer’s specifications. The analytical approach to visualize and analyze the deposited oil structures was the main emphasis of this work.

Fabrication of Eutectic Ga-In Nanowire Arrays Based on Plateau-Rayleigh Instability

We have developed a simple method of fabricating liquid metal nanowire (NW) arrays of eutectic GaIn (EGaIn). When an EGaIn droplet anchored on a flat substrate is pulled perpendicular to the substrate surface at room temperature, an hourglass shaped EGaIn is formed. At the neck of the shape, based on the Plateau–Rayleigh instability, the EGaIn bridge with periodically varying thicknesses is formed. Finally, the bridge is broken down by additional pulling. Then, EGaIn NW is formed at the surface of the breakpoint. In addition, EGaIn NW arrays are found to be fabricated by pulling multiple EGaIn droplets on a substrate simultaneously. The average diameter of the obtained NW was approximately 0.6 μm and the length of the NW depended on the amount of droplet anchored on the substrate. The EGaIn NWs fabricated in this study may be used for three-dimensional wiring for integrated circuits, the tips of scanning probe microscopes, and field electron emission arrays.

Centrifugal Detachment of Compound Droplets from Fibers

This article presents the first experimental-computational study on the centrifugal detachment of a compound droplet (e.g., a primary water droplet cloaked by an immiscible oil) from a fiber. The work was intended to establish a method for quantifying the force needed to detach compound droplets of different compositions from a fiber. More importantly, our study was aimed at improving the understanding of the interplay between interfacial and external forces acting on a compound droplet during forceful detachment. The experiments were conducted using DI water, for the primary droplet, and silicone or mineral oil, for the cloaking fluid. It was observed from the experiments that the silicone-oil-cloaked droplets behave differently from the mineral-oil-cloaked droplets. It was also observed that detachment force decreases with increasing the oil-to-water volume ratio. The simulations were performed using the Surface Evolver (SE) finite element code programmed for the complicated four-phase (air, water, oil, and solid) interfacial problem at hand. Our simulations revealed the evolution of the interfacial forces between the interacting phases under an increasing external body force on the droplet. The simulations also allowed us to define effective interfacial tensions and contact angles for detaching compound droplets, for the first time. Reasonable agreement was observed between the experimental measurements and computational results.

Solvent-Solvent Correlations across Graphene: The Effect of Image Charges

Wetting experiments show pure graphene to be weakly hydrophilic, but its contact angle (CA) also reflects the character of the supporting material. Measurements and molecular dynamics simulations on suspended and supported graphene often reveal a CA reduction due to the presence of the supporting substrate. A similar reduction is consistently observed when graphene is wetted from both sides. The effect has been attributed to transparency to molecular interactions across the graphene sheet; however, the possibility of substrate-induced graphene polarization has also been considered. Computer simulations of CA on graphene have so far been determined by ignoring the material's conducting properties. We improve the graphene model by incorporating its conductivity according to the constant applied potential molecular dynamics. Using this method, we compare the wettabilities of suspended graphene and graphene supported by water by measuring the CA of cylindrical water drops on the sheets. The inclusion of graphene conductivity and concomitant polarization effects leads to a lower CA on suspended graphene, but the CA reduction is significantly bigger when the sheets are also wetted from the opposite side. The stronger adhesion is accompanied by a profound change in the correlations among water molecules across the sheet. While partial charges on water molecules interacting across an insulator sheet attract charges of the opposite sign, apparent attraction among like charges is manifested across the conducting graphene. The change is associated with graphene polarization, as the image charges inside the conductor attract equally signed partial charges of water molecules on both sides of the sheet. Additionally, using a nonpolar liquid (diiodomethane), we affirm a detectable wetting translucency when liquid-liquid forces are dominated by dispersive interactions. Our findings are important for predictive modeling toward a variety of applications including sensors, fuel cell membranes, water filtration, and graphene-based electrode materials in high-performance supercapacitors.

Effect of Wetting and Dewetting Dynamics on Atomic Force Microscopy Measurements

Water bridge dynamics between an atomic force microscopy (AFM) tip and a flat substrate is studied by using a multibody dissipative particle dynamics (MDPD) model. First, the numerical model is validated by comparing the present results of droplet contact angles and liquid bridges with those reported in the literature. Then, the ability of MDPD to capture the meniscus shape and behavior for different operating conditions and geometric parameters is examined for both static and dynamic cases. Hence, several parametric studies and analyses of the AFM tip configuration and its operating conditions are reported. It is found that a critical capillary number of about 0.001 is calculated based on 5% change on the force measurements between the static and dynamic results. It is also demonstrated that the hysteresis behavior in the capillary force exerted on the AFM tip can be successfully predicted by using the MDPD model when the tip approaches or retracts from the substrate. Moreover, there is an excellent agreement in the results of breakup distance for different water bridge volumes between the predictions of the MDPD model and the theory. Also, the hysteresis of capillary force exerted on an AFM tip composed of multibody design is studied. The prediction on the transition of the capillary force vs distance between the AFM tip and the substrate is in good agreement with the experimental results. Therefore, we demonstrate a validated MDPD model which can successfully capture liquid bridge dynamics. This model can be used as a powerful design tool for meniscus manipulation technology, such as dip-pen nanolithography, as well as for studying dynamic, e.g., tapping mode AFM tip, interactions with a liquid bridge.

Competing forces on a liquid bridge between parallel and orthogonal dissimilar fibers

This paper presents a detailed investigation on the mechanical forces acting on a liquid bridge between dissimilar fibers in parallel and orthogonal configurations. These forces were measured experimentally, using a sensitive scale, and were also predicted computationally, via numerical simulation. Special attention was paid to the fiber-fiber spacing at which the liquid bridge detached from the fibers, and to how a transition from an equilibrium liquid bridge to a spontaneously (time-dependent) detaching bridge took place. It was found that, while varying the spacing between the fibers affects a liquid bridge differently for fibers with different relative angles with respect to one another, the spacing at which the bridge detaches from the fibers is independent of the fibers' relative angle. This paper also formulates the contribution of the geometrical and wetting properties of the fibers competing for the droplet that results from a liquid bridge detachment, and presents a mathematical expression to predict the fate of that droplet.

Modes and break periods of electrowetting liquid bridge

In this paper, we propose a microscale liquid oscillator using electrowetting-on-dielectric (EWOD). Specifically, a mesoscale liquid bridge (LB) between two horizontal surfaces with EWOD is considered. When EWOD is applied, the solid surface becomes more hydrophilic, and hence the contact angle (CA) is reduced. Following the activation of EWOD, the LB can remain connected or it can break into either symmetric or asymmetric shapes depending on the initial liquid volume and wettability of the two surfaces. The LB dynamics activated by EWOD is studied using the multibody dissipative particle dynamics (MDPD) method. Our numerical results show that the behavior of an LB under EWOD can be interpreted via three modes. In the first mode, the LB does not break after applying EWOD. In the second mode, the LB breaks and does not reform. The third mode happens when, depending on the interplay of the volume of the liquid and CA manipulation, the LB continuously breaks, recoils, and reforms. For asymmetric cases, it was observed that the LB may completely detach from one surface and may not reform. It was also observed that decreasing the wettability of a surface, for cases with a continuous breaking and reformation behavior, increases the connecting time interval and decreases the breaking time interval in one break-reform cycle. The results provided in this investigation facilitate fundamental understanding of LB dynamics and their application for the design of microscale liquid oscillators using EWOD.

Using Magnetic Field to Measure Detachment Force between a Nonmagnetic Droplet and Fibers

The ability to predict and/or measure the force needed to detach a droplet from a fiber (or an assembly of fibers) is important in designing efficient droplet?air or droplet?fluid separation media for a variety of applications. This paper reports on the use of magnetic force to measure the force of detachment for nonmagnetic droplets for the first time. This is accomplished by adding a small amount of ferrofluid (the secondary fluid) to the original nonmagnetic droplet (the primary fluid) to create a compound droplet with the ferrofluid nesting inside or cloaking the nonmagnetic droplet. Either way, the secondary ferrofluid can be used to induce a body force to the resulting compound droplet and thereby detach it from the fiber(s). The recorded detachment force can be used directly (the case of nesting ferrofluid) or after scaling (the case of cloaking ferrofluid) to obtain the force of detachment for the original nonmagnetic droplet. The novelty of the proposed method lies in the fact that it circumvents the need for using an external object, an airflow, or a centrifugal device for force measurement. The accuracy of our measurements was examined through comparison with validated numerical simulations as well as experimental data in the literature and good agreement was observed.