Rayleigh Instability Research Articles

Realization of a 2H–Si microneedle with an ultrafast growth rate of 6.7 × 104 Å·s-1

Abstract Nanomaterials have facilitated the development of innovative technologies in various industries. However, most research has been limited to nanoscale phenomena, and the effects of nanoscale phenomena on microscale crystal growth remain obscure. In this study, we demonstrated a straight 2H-Si microneedle with a longitudinal growth rate of 6.7 × 104 Å·s-1, which could not be explained by conventional crystal growth mechanisms, through AlN nanowires. The AlN nanowires were grown using the hydride vapor-phase epitaxy method, which induced the formation of Al membranes when NH3 supply was ceased. At this time, an elliptical Al membrane was created within 0.166 s, in accordance with the principle of Plateau–Rayleigh instability. The average spacing of the Al membrane was 4 μm, and approximately 10,000 elliptical Al membranes absorbed SiCl almost simultaneously to form a 40-mm 2H-Si microneedle within 100 min of growth time. Therefore, we realized straight 2H–Si microneedles with a growth rate of 6.7 × 104 Å·s-1. Differing from the conventional growth mechanism, this new growth method sheds light on the mechanism by which nanoscale phenomena contribute to the growth of microscale crystals.

Recirculatory Solvotaxis of a Nematic Droplet on Water Surface Enabling Miniaturization.

Self-organized contact line instabilities (CLI) of a macroscopic liquid crystal (LC) droplet can be an ingenious pathway to generate a large collection of miniaturized LC drops. For example, when a larger drop of volatile solvent (e.g., hexane) is dispensed near a smaller LC drop resting on a soft and slippery surface of a nonsolvent (e.g., water), unique self-organized locomotion in the form of a twin vortex has been observed within the droplets. This phenomenon is driven by the rapid counter diffusion of hexane and LC between the two droplets, resulting in the formation of a pair of vortices within the droplets before instigating a CLI at the three-phase contact line (TPCL) of the LC droplet. Initially, the higher Laplace pressure inside the LC droplet (PL,5CB) due to a net pressure gradient, PL,5CB > PL,Hex, drives the LC toward hexane. However, as the volatile solvent droplet shrinks due to rapid evaporation, a flow reversal happens owing to PL,5CB < PL,Hex. Subsequently, the diffusion of hexane into the LC droplet and its subsequent evaporation manifest a periodic oscillatory CLI expansion and retraction at the TPCL, which in turn form periodic finger-like structures. Following this, the fingers with a higher aspect ratio break into an array of miniaturized satellite LC droplets undergoing Rayleigh-Plateau instability (RPI). The observed deviation in the normalized satellite droplet spacing compared to theoretical value affirm the stabilizing influence of LC elasticity in such fingers, where λ and R5CB are experimentally calculated droplet spacing and 5CB droplet radius. Control experiments elucidate the specific contributions of capillary, drag, solutal Marangoni, and osmotic forces to the 5CB droplet locomotion phenomena. The experimentally and analytically consistent demonstration also supports and predicts pressure drop-induced droplet velocities as v ∼ t1.16.

The dynamical stability and instability of Rayleigh–Bénard problem for non-Newtonian fluids with power law type

We conduct a mathematical investigation into the dynamical stability and instability of the Rayleigh–Bénard (abbr. RB) problem for incompressible non-Newtonian fluids exhibiting power law type behavior, with p ⩾ 1 . We establish a critical threshold, denoted as R c , and endeavor to demonstrate that the RB problem exhibits exponential stability through the energy method when the Rayleigh number R (which is influenced by the non-Newtonian component) falls within the interval [ 0 , R c ) . Additionally, we formulate an instability criterion, R > R c , under which the RB problem is deemed unstable, we aim to prove this instability by employing a modified variational method. Our results show that non-Newtonian part has the stabilizing effect for thermal instability.

Plateau–Rayleigh instability in a capillary: assessing the importance of inertia

Liquid plug formation in thin channels due to the Plateau–Rayleigh instability of a liquid film is observed in a variety of fields. In this paper, complementarity between theoretical solutions and direct numerical simulations (DNS) based on a front-tracking algorithm is explored to evaluate the importance of inertia for the case of a cylindrical capillary. A linear stability analysis is first performed and DNS results are then used to investigate the spatial distributions of inertial, convective and viscous terms of the Navier–Stokes equation. The existence of both viscous and inertial regimes is evidenced with a threshold given by the film thickness. The presence of the core fluid slows down the instability. In the viscous regime, predictions of the lubrication theory are verified. An example of liquid water as the outer fluid film and water vapour as the inner core fluid is simulated with application to the fuel cells.

Additive manufacturing of 3D flow-focusing millifluidics for the production of curable microdroplets.

Microfluidics plays a crucial role in the generation of mono-sized microdroplet emulsions. Traditional glass microfluidic chips typically lack versatility in generating curable droplets of arbitrary liquids due to the inherent hydrophilic nature of glass and to fabrication constraints. To overcome this, we designed a microdroplet generator with 3D flow-focusing capabilities that can be 3D-printed. The chip can handle oil-in-water emulsions despite its lipophilicity. Operating in the jetting regime, the chip exploits the Rayleigh-Plateau instability to enable high throughput. With its versatile design, the chip is capable of producing both single and double emulsions within the same channel. We utilize a thermoset (epoxy-melamine) based system to test its ability to handle curable chemicals and to produce in a post-processing step both solid particles and filled capsules. With a low solvent concentration in the curable material, the present system can encapsulate water-based cores of a wide range of sizes.

A long-wave model for a falling upper convected Maxwell film inside a tube

A long-wave asymptotic model is developed for a viscoelastic falling film along the inside of a tube; viscoelasticity is incorporated using an upper convected Maxwell model. The dynamics of the resulting model in the inertialess limit is determined by three parameters: Bond number Bo, Weissenberg number We and a film thickness parameter $a$ . The free surface is unstable to long waves due to the Plateau–Rayleigh instability; linear stability analysis of the model equation quantifies the degree to which viscoelasticity increases both the rate and wavenumber of maximum growth of instability. Elasticity also affects the classification of instabilities as absolute or convective, with elasticity promoting absolute instability. Numerical solutions of the nonlinear evolution equation demonstrate that elasticity promotes plug formation by reducing the critical film thickness required for plugs to form. Turning points in travelling wave solution families may be used as a proxy for this critical thickness in the model. By continuation of these turning points, it is demonstrated that in contrast to Newtonian films in the inertialess limit, in which plug formation may be suppressed for a film of any thickness so long as the base flow is strong enough relative to surface tension, elasticity introduces a maximum critical thickness past which plug formation occurs regardless of the base flow strength. Attention is also paid to the trade-off of the competing effects introduced by increasing We (which increases growth rate and promotes plug formation) and increasing Bo (which decreases growth rate and inhibits plug formation) simultaneously.

Plateau-Rayleigh Instability in Soft-Lattice Inorganic Solids.

Plateau-Rayleigh instability─a macroscopic phenomenon describing the volume-constant breakup of one-dimensional continuous fluids─has now been widely observed in adatoms, liquids, polymers, and liquid metals. This instability enables controlled wetting-dewetting behavior at fluid-solid interfaces and, thereby, the self-limited patterning into ordered structures. However, it has yet to be observed in conventional inorganic solids, as the rigid lattices restrict their "fluidity". Here, we report the general fluid-like Plateau-Rayleigh instability of silver-based chalcogenide semiconductors featuring soft-lattice ionic crystals. It enables postsynthetic morphing from conformal core-shell nanowires to periodically coaxial ones. We reveal that such self-limited reconstruction is thermodynamically driven by the surface energy and interface energy and kinetically favored by the high ionic diffusion coefficients of subnanoscale soft-lattice shells. The resulting periodic heterostructures can be topotactically transformed for epitaxial combinations of functional semiconductors free from the lattice-matching rule. This fluid-like behavior in soft inorganic solids thus offers routes toward sophisticated nanostructures and controllable patterning at all-inorganic solid-solid interfaces.

Electrospinning of LaB6/PEDOT:PSS/PEO Fiber Composites of Unique Morphologies.

We present a direct electrospinning fabrication technique for the manufacture of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate)/poly(ethylene oxide) (PEDOT:PSS/PEO) polymer fibers containing embedded cubic lanthanum hexaboride (LaB6) particles. We focus on the impact of relative humidity on the formation of uniform polymer fibers and show that a relative humidity of 5% is optimal, resulting in an average fiber thickness of 266 ± 88 nm. As the relative humidity is increased, the fibers contain beads as a consequence of Rayleigh instabilities. The addition of lanthanum hexaboride cubic particles to the polymer solution before electrospinning results in the encapsulation of the LaB6 particles inside the fibers. We investigate the effect of LaB6 particle size on morphology and observe that particles of ∼500 nm yield a fiber-cube-fiber morphology, while 2 μm particles result in fewer embedded cubes along the length of the polymer fibers. This phenomenon likely arises from electrodynamic interactions between the LaB6 particles in the polymer solution and the electric field lines generated during electrospinning between the spinneret and the collector. Our results display the versatility of the electrospinning technique in the fabrication of unique polymer/hexaboride composite fibers.

Propagation behavior of wetting front and its fluctuation characteristics during subcooled jet impingement quenching

Jet impingement quenching as one of the most effective cooling methods is widely applied in many industrial fields. When a subcooled jet strikes the hot surface, the wetting front propagates outside after the wetting delay accompanied by high-frequency fluctuations. To elucidate the propagation behavior of the wetting front and its fluctuation characteristics, the quenching experiments that an upward water jet with different velocities and subcoolings impacted onto a hot nickel block with an initial temperature of 280°C were conducted. The transient transition boiling associated with the intermittent wet and dry situations around the wetting front was quantitatively analyzed based on the visual observation and fast response surface temperature measurement technique. The liquid-solid contact period near the wetting front, under the late transition boiling regime, spans the range of 494–590 µs. This time interval is comparable to the period of disturbance waves induced by the Plateau-Rayleigh instability of the jet. Furthermore, fluctuation amplitude of the wetting front diminishes from 0.8 to 0.2 mm as it propagates. The order of magnitude and the trend of variation in the fluctuation amplitude with respect to the wetting front radius align with theoretical calculations without considering boiling heat transfer effects.

“Halfway to Rayleigh” and Other Insights into the Rossby Wave Instability

The Rossby wave instability (RWI) is the fundamental nonaxisymmetric radial shear instability in disks. The RWI can facilitate disk accretion, set the shape of planetary gaps, and produce large vortices. It arises from density and/or temperature features, such as radial gaps, bumps, or steps. A general, sufficient condition to trigger the RWI is lacking, which we address by studying the linear RWI in a suite of simplified models, including incompressible and compressible shearing sheets and global, cylindrical disks. We focus on enthalpy amplitude and width as the fundamental properties of disk features with various shapes. We find analytic results for the RWI boundary and growth rates across a wide parameter space, in some cases with exact derivations and in others as a description of numerical results. Features wider than a scale height generally become unstable about halfway to Rayleigh instability, i.e., when the squared epicyclic frequency is about half the Keplerian value, reinforcing our previous finding. RWI growth rates approximately scale as enthalpy amplitude to the 1/3 power, with a weak dependence on width, across much of the parameter space. Global disk curvature affects wide planetary gaps, making the outer gap edge more susceptible to the RWI. Our simplified models are barotropic and height integrated, but the main results should carry over to more complex and realistic scenarios.

A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios

The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with moderate inertia. To date, the majority of interfacial-flow simulations are performed using an explicit surface-tension treatment, which restrains the performance of such simulations. Recently, an implicit treatment of surface tension able to breach the capillary time-step constraint using the volume-of-fluid (VOF) method was proposed, based on a fully-coupled pressure-based finite-volume algorithm. To this end, the interface-advection equation is incorporated implicitly into the linear flow solver, resulting in a tight coupling between all implicit solution variables (colour function, pressure, velocity). However, this algorithm is limited to uniform density and viscosity fields. Here, we present a fully-coupled algorithm for interfacial flows with implicit surface tension applicable to interfacial flows with large density and viscosity ratios. This is achieved by solving the continuity and momentum equations in conservative form, whereby the density is treated implicitly with respect to the colour function, and the advection term of the interface-advection equation is discretised using the THINC/QQ algebraic VOF scheme, yielding a consistent discretisation of the advective terms. This new algorithm is tested by considering representative surface-tension-dominated interfacial flows, including the Laplace equilibrium of a stationary droplet and the three-dimensional Rayleigh-Plateau instability of a liquid filament. The presented results demonstrate that interfacial flows with large density and viscosity ratios can be simulated and energy conservation is ensured, even with a time step larger than the capillary time-step constraint, provided that other time-step restrictions are satisfied.

Reconfigurable All-Oil Microfluidic Devices by 3D Printing.

Nanoparticle surfactants have been widely used to construct structured liquids in oil-water systems. Less attention, though, has been given in non-aqueous systems, for example, oil-oil systems, mainly due to the lack of suitable surfactants. Here, by using newly developed molecular brush surfactants (MBSs) that form at the DMSO-silicone oil interface, the construction of all-oil microfluidic devices is reported with advanced functions. Due to the high interfacial activity of MBSs, Plateau-Rayleigh instabilities of liquid jets can be completely suppressed, leading to the production of liquid threads with jammed MBSs at the interface. Taking advantage of the 3D printing technique, all-oil microfluidic devices with complex structures can be constructed, showing promising applications in mass transmission, chemical separation, and material synthesis.

The importance of initial extension rate on elasto-capillary thinning of dilute polymer solutions

This work focuses on inferring the molecular state of the polymer chain required to induce stress relaxation and the accurate measure of the polymer’s longest relaxation time in uniaxial stretching of dilute polymer solutions. This work is facilitated by the discovery that constant velocity applied at early times leads to initial constant extension rate before reaching the Rayleigh–Plateau instability. Such constant rate experiments are used to correlate initial stretching kinematics with the thinning dynamics in the final thinning regime. We show that there is a minimum initial strain-rate required to induce rate independent elastic effects, and measure the longest relaxation time of the material. Below the minimum extension rate, insufficient stretching of the chain is observed before capillary instability, such that the polymer stress is comparable to the capillary stress at long times and stress relaxation is not achieved. Above the minimum strain-rate, the chain reaches a critical stretch before instability, such that during the unstable filament thinning the polymer stress is significantly larger than the capillary stress and rate-independent stress relaxation is observed. Using a single relaxation mode FENE model, we show that the minimum strain rate leads to a required initial stretch of the chain before reaching the Rayleigh–Plateau limit. These results indicate that the chain conformation before entering the Rayleigh Instability Regime, and the stretching induced during the instability, determines the elastic behavior of the filament. Lastly, this work introduces a characteristic dimensionless group, called the stretchability factor, that can be used to quantitatively compare different materials based on the overall material deformation/kinematic behavior, not just the relaxation time. Overall, these results demonstrate a useful methodology to study the stretching of dilute solutions using a constant velocity stretching scheme.

Continuous Homogeneous Thin Liquid Film on a Single Cross-Shaped Profiled Fiber with High Off-Circularity: Toward Quick-Drying Fabrics.

Quick-drying fabrics, renowned for their rapid sweat evaporation, have witnessed various applications in strenuous exercise. Profiled fiber textiles exhibit enhanced quick-drying performance, which is attributed to the excellent wicking effect within fibrous bundles, facilitating the rapid transport of sweat. However, the evaporation process is not solely influenced by macroscopic liquid transport but also by microscopic liquid spreading on the fibers where periodic liquid knots induced by spontaneous fluidic instability significantly reduce the evaporation area. Here, a cross-shaped profiled fiber with high off-circularity, featured as multiple concavities along the fibrous longitude-axis, which enables the formation of a homogeneous thin liquid film on a single fiber without any periodic liquid knots, is developed. The high off-circularity cross-sections help overcoming Plateau-Rayleigh instability by tuning the Laplace pressure difference, further facilitated by capillary flow along the concave surface. The homogeneous thin liquid film on a single fiber is responsible for maximizing the evaporation area, resulting in excellent overall evaporation capacity. Consequently, fabrics made from such fibers exhibit rapid evaporation behavior, with evaporation rates ≈50% higher than those of cylindrical fabrics. It is envisioned that profiled fibers may provide inspiration for the manipulating homogeneous liquid films for applications in fluid coatings and functional textiles.

Porous Spindle-Knot Fiber by Fiber-Microfluidic Phase Separation for Water Collection and Nanopatterning.

Porous spindle-knot structures have been found in many creatures, such as spider silk and the root of the soybean plant, which show interesting functions such as droplet collection or biotransformation. However, continuous fabrication of precisely controlled porous spindle-knots presents a big challenge, particularly in striking a balance among good structural controllability, low-cost, and functions. Here, we propose a concept of a fiber-microfluidics phase separation (FMF-PS) strategy to address the above challenge. This FMF-PS combines the advantages of a microchannel regulated Rayleigh instability of polymer solution coated onto a fiber with the nonsolvent-induced phase separation of the polymer solution, which enables continuous and cost-effective production of porous spindle-knot fiber (PSKF) with well-controlled size and porous structures. The critical factors controlling the geometry and the porous structures of the spindle-knot by FMF-PS have been systematically investigated. For applications, the PSKF exhibited faster water droplet nucleation, growth, and maximum water collection capability, compared to the control samples, as revealed by in situ water collection growth curves. Furthermore, high-level fabrics of the PSKFs, including a two-dimensional network and three-dimensional architecture, have been demonstrated for both large-scale water collection and art performance. Finally, the PSKF is demonstrated as a programmable building block for surface nanopatterning.

Drop breakup in bag regime under the impulsive condition

This study experimentally investigates the spatiotemporal evolution and associated local instabilities of a drop subjected to a weak shock wave. The front and side views of the drop are captured to understand its three-dimensional evolution and breakup. The interaction of shock causes the windward side of the drop to compress and generate a surface wave over it. Its temporal amplification is found to be governed by Kelvin–Helmholtz instability. The core of the deformed drop expands in a stream-wise direction, forming a Rayleigh–Taylor instability-driven bag structure. Consistent pressure gradients across the bag cause its continuous elongation until the pressure gradient overcomes the surface tension. This continuous elongation leads the sheet to undergo kinematic thinning, which causes the sheet to destabilize and nucleate the hole. This hole recedes and gathers liquid from upstream to thicken its interface, called the bag rim. The accelerating receding motion of the bag rim triggers Rayleigh–Taylor instability, and the corrugation that forms over it grows into ligaments and destabilizes to shed droplets through end pinching and ligament merging. Additionally, the accelerating rim undergoes radial expansion, with its further destabilization governed by the coupled effect of Rayleigh–Taylor and Rayleigh–Plateau instabilities, as well as the collision of the receding bag rim. This leads to the formation of corrugations, which grow into ligaments and further destabilize to shed drops via end pinching. Nonlinear effects dominate ligament dynamics and increase with the Weber number. The asymmetric ejection of the daughter drop from the rim causes it to evolve into a bag, undergoing tertiary breakup.

In Situ Growth of Gold Nanofilms with Branched Structures in the Presence of Organosulfur for High-Performance Flexible Electronics.

Herein, a novel method is presented for the in situ growth of gold nanofilms with branched structures in the presence of organosulfur. The key feature in this approach is the Rayleigh instability of ultrathin gold nanowires (AuNWs) without oleylamine (OAm), which allows the ultrathin AuNWs to decompose into gold nanoparticles (AuNPs) and the AuNPs to in situ grow into branched structures for high-performance stability and electrical conductivity. The sheet resistance of the gold nanofilms initially sharply decreased, whereas it subsequently slightly increased with the concentration of CS(NH2)2 until it exceeded the optimal range. After undergoing a 10 min heat treatment at 150 °C, the sheet resistance of the nanofilms was further reduced to 18 Ω/sq, which could be maintained for more than five months. The internal structure becomes fully grown and denser, forming a branched structure after heat treatment. Only certain organosulfurs can improve the electrical properties of the gold nanofilms, and the mechanism of organosulfur in the in situ growth of gold nanofilms with branched structures has also been presented. Overall, this novel method provides a straightforward and convenient approach to obtaining gold nanomaterials with branched structures, holding great potential promise for applications in flexible electronics, catalysis, and energy fields.

Does a polymer film due to Rayleigh-instability affect interfacial properties measured by microbond test?

ABSTRACT The microbond (MB) test, which is primarily used to characterise the interface of fibrous composites, requires a large number of droplets to be tested and analysed in order to make a reliable conclusion about the fibre–droplet interface. The conventional method of depositing single droplets on fibre and performing the MB test can be improved by depositing multiple droplets using the Rayleigh plateau instability phenomenon (an additional film is formed between the droplets). Although the latter method has significant advantages and higher statistical reliability, the role of the additional film affecting MB test results has not been investigated. In this work, both methods are experimentally evaluated for glass and flax fibres with two different resin systems and the interfacial constants, namely critical stress for damage initiation and critical energy release rate, are validated by finite element (FE) models. The study reveals that the thickness of the additional film shows incorrect interfacial shear strength (IFSS) when determined from simple force-displacement data ( ≈ 18% increase for the fibre-droplet system in this study). The FE models confirm that the damage onset at the interface occurs at a higher force with this method, but the interfacial strength constants remain the same as with the conventional method.

Sandwich-structured bimodal fiber/bead-on-string fiber composite membrane for comfortable PM0.3 filter

Particulate matter (PM) pollution causes critical harm to human health and global environment. However, the protective respirators attain high-performance filtration of the most permeable PM0.3 by tight stacking of fibers and seriously compromising their wearing comfort. Herein, a fluffy sandwich-structured membrane (SSM) composed of bimodal fibrous layers and bead-on-string fibrous layer is designed to endow the air filter with both high-performance filtration and superior thermal-wet comfort. Based on the electrospinning technique, the bimodal fibers made of nano-/submicron-fibers (about 46 nm and 155 nm) are formed by inducing the jet splitting while the bead-on-string fibers consisting of submicron-fibers (≈ 120 nm) and micro-beads (≈ 3.37 μm) are prepared through manipulating the Rayleigh instability of jets. Due to the structural design of small pores and low packing density, the SSM exhibits excellent PM0.3 removal of 99.8%, low filtration resistance of 65 Pa, and high quality factor of 0.097 Pa-1. It also shows long-term filtration stability and durability under high humidity conditions. Moreover, the SSM simultaneously possesses superior thermal-wet comfort of heat dissipation, air permeability of 164 mm·s-1, and water vapor transmission of 7.6 kg·m-2·d-1. This work may offer a novel insight for exploiting high-performance and comfortable personal protective materials.

A surface quality optimization strategy based on a dedicated melt-pool control via the dashed-scan contouring technique in electron beam powder bed fusion

Electron beam powder bed fusion (EB-PBF) is a key metal additive manufacturing (AM) technology known for its high energy absorption and low heat stress. However, the high surface roughness of EB-PBF parts has limited its broader application. To address this issue, this paper proposes a dashed-scan contouring strategy to obtain lower surface roughness in EB-PBF. This strategy involves melting the contour in the form of segmented staggered scans and employing high-frequency jumping of the electron beam (EB) to melt multiple positions synchronously. A comprehensive analysis, combining experimental investigations and multi-physical simulations, elucidates the intrinsic connection between control processes and melt pool stability. Results show that by controlling the length-to-width ratio of the melt pool, regulating overlap distances between melt pools, and fine-tuning cooling times, balling phenomena and Plateau-Rayleigh instabilities can be suppressed. Additionally, these measures effectively mitigate irregularities in track formation when compared to the traditional process. Experimental validation demonstrates the efficacy of the approach, achieving reduced surface roughness (Ra) of thin-walled Ti-6Al-4 V parts from over 25 μm to below 12.6 μm, while enhancing dimensional accuracy and reducing melt anomalies at corners. The proposed dashed-scan contouring strategy opens new avenues for AM of highly reliable and intricate structures, such as lattice sandwich structures, thin walls, and internal flow passages.