Rayleigh Instability Research Articles

Stability criteria for the 2D α-Euler equations

Abstract We derive analogues of the classical Rayleigh, Fjortoft and Arnold stability and instability theorems in the context of the 2D α-Euler equations.

Advective Removal of Localized Convective Structures in a Porous Medium

Thermal convection in a planar horizontal layer of a porous medium, which is saturated with a viscous incompressible liquid pumped along the layer and has solid impermeable boundaries with a set heat flux at them, is considered. In certain physical systems, the first instability in Rayleigh–Benard convection between thermally insulated horizontal plates is long-wave. The equations characterizing large-scale thermal convection in a horizontal layer in a homogeneous liquid and in a porous medium are similar: they differ in just one term, which vanishes under certain conditions (e.g., for two-dimensional flows or an infinite Prandtl number). In the system in question with a vertical heat flux that is nonuniform along the layer, localized convective structures may emerge in the region where the heat flux exceeds the critical value corresponding to uniform heating from below and to the onset of convection within the layer. When the rate of the longitudinal pumping of a liquid through the layer changes, the system may enter either a state with stable localized convective structures and a monotonic (or oscillatory) instability or a state in which the localized convective flow is removed completely from the region of its excitation. Calculations are carried out based on the amplitude equations in the long-wave approximation using the Darcy–Boussinesq model and the approximation of small deviations of the heat flux across the boundaries from the critical values under uniform heating. The results of the numerical modeling of the process of the removal of a localized flow from the region of its excitation at higher rates of the longitudinal pumping of the liquid through the layer are detailed. Stability maps for monotonic and oscillatory instabilities of the base state of the system are presented.

Patterning Bubbles by the Stick–Slip Motion of the Advancing Triple Phase Line on Nanostructures

The stick-slip motion of the triple phase contact line (TCL) has wide applications in inkjet printing, surface coatings, functional material assembly, and device fabrication. Here, for the first time, we report that on an alumina substrate with nanostructures, the stick-slip motion of the advancing TCL during spreading of an emulsion droplet can serve as an effective nanopatterning process. Air enclosed in the substrate nanostructures can be exchanged with liquid during the "stick" phase, resulting in the formation of bubbles arranged in a ring pattern. The process takes place in two stages: rings of air form first and then, as the volume of air increases, they separate into air bubbles as a result of the Plateau Rayleigh instability. During the first stage, the rings form due to the stick-slip of the advancing TCL and are ascribed to hydrogen-bonding interactions. Ultimate bubble size is dependent on the substrate pore dimensions. The process was simulated using finite-element analysis to elucidate the mechanism associated with subsequent bubble formation. The simulations corroborate well with the experimental results. This stick-slip motion of the advancing TCL provides new insights into the phenomena associated with droplet spreading and wetting, and the ability to control the formation of patterned bubbles will be promising in applications ranging from microfluidics to printing of functional materials and devices based on bubble templates and applications requiring submerged hydrophobic surface.

Formation of silicon nanocrystal chains induced via Rayleigh instability in ultrathin Si/SiO2 core/shell nanowires synthesized by an inductively coupled plasma torch process

A new class of silicon (Si) nanohybrids is formed exploiting the Rayleigh instability experienced by Si nanowires (SiNWs) synthesized via inductively coupled plasma. These nanohybrids consist of three main categories of Si nanostructures: (i) core/shell silicon/silicon oxide nanowires (where the inner Si cores have diameters as small as 2–3 nm), (ii) sequences of almond-shaped silicon nanocrystals (SiNCs), having diameters in the range of 4–5 nm, connected by an ultrathin silicon nanowire (diameter of 1–2 nm) and embedded in a silica nanowire, and (iii) sequences of isolated spherical SiNCs (having diameters in the range of 4–7 nm) embedded in an otherwise continuous silica nanowire. The predominance of one morphology over the others can be tuned via post-synthesis thermal treatments, with a clear predominance of the spherical SiNC chain configuration after high-temperature annealing (1200 °C). It is demonstrated that the Rayleigh model describes very well the morphological transformations undergone by the Si core of the nanostructures when subject to the capillarity-related instability induced by the thermal annealing. More interestingly, we have been able, for the first time to our knowledge, to follow in situ the occurrence of Rayleigh instability in SiNWs leading to the breakage of their inner core and formation of smaller SiNCs. Finally, the optoelectronic properties of the Si nanohybrids, studied via photoluminescence measurements, have confirmed the occurrence of quantum confinement effects in the ultra-small SiNCs present in these new nanohybrids.

Comprehensive Stability Improvement of Silver Nanowire Networks via Self-Assembled Mercapto Inhibitors.

Instability of silver nanowire (AgNW) has been regarded as a major obstacle to its practical applications in optoelectrical devices as transparent electrodes. Physical barrier layers such as polymer, metal, and graphene have been generally employed to improve the stability of AgNW in previous study. Herein, we first report self-assembled organothiols as an inhibitor for AgNW to achieve an overall enhancement in antioxidation, antisulfidation, thermal stability, and anti-electromigration. The self-assembled monolayers (SAMs) of phenyl azoles, methoxy silane, and methyl alkane were formed on the surface of AgNW via Ag-S covalent bond as barrier layers which provided protective effects against corrosives (e.g., O2, H2S). In particular, the decoration of 2-mercaptobenzimidazole (MBI) offered the best resistance to H2S and excellent stability under a high-temperature and high-humidity environment (85 °C and 85 RH %) for 4 months. Moreover, different SAMs exhibited a stabilizing or destabilizing effect on Plateau-Rayleigh instability of AgNW, which realized the tunability of degradation temperature of AgNWs, for example, increasing by ≥100 °C with MBI SAM or decreasing by ∼50 °C with octadecanethiol SAM compared with pristine AgNWs. Notably, the MBI-decorated AgNWs could survive at 400 °C which is by far the highest bearing temperature for solution-processed AgNW film. As a result, a transparent heater made of the MBI-AgNWs exhibited superior heating characteristics (higher working temperature and durability), as compared with the pristine AgNW-based heater. Our findings on the organothiols decoration not only provide a new paradigm in overall stability improvement of NW of noble metals but also show the potential in morphology controllability of metal NW.

Laser-Induced Dewetting of Metal Thin Films for Template-Free Plasmonic Color Printing

Plasmonic color laser printing has several advantages over pigment-based technology, including the absence of ink and toner and the production of nonfading colors. However, the current printing method requires a template that should be prepared via nanofabrication processes, making it impractical for large-area color images. In this study, we show that laser-induced dewetting of metal thin films by a nanosecond pulsed laser can be effectively utilized for plasmonic color printing. Ag, Au, and their complex films deposited on a glass substrate were dewetted into different surface structures such as droplets, rods, and ripples, depending on the incident laser energy. The resulting morphological evolutions could be explained by Rayleigh and capillary instabilities. For a bimetallic film comprising Ag nanowires coated on a Au layer, a few different plasmonic colors were generated from a single sample simply by changing the laser fluence. This provides a possible method for implementing plasmonic color laser printing without using a prepatterned template.

Cellular Automata Modeling of Ostwald Ripening and Rayleigh Instability.

A cellular automata (CA) approach to modeling both Ostwald ripening and Rayleigh instability was developed. Curvature-driven phase interface migration was implemented to CA model, and novel CA rules were introduced to ensure the conservation of phase volume fraction of nearly equilibrium two-phase system. For transient Ostwald ripening, it is shown that the temporal growth exponent m is evolving with time and non-integer temporal exponents between 2 and 3 are predicted. The varying temporal growth exponent m is related to the particle size distributions (PSDs) evolution. With an initial wide PSD, it becomes narrowed toward steady state. With an initial narrow PSD, it becomes widened at first and then narrowed toward steady state. For Rayleigh instability, two cases (one with sinusoidal perturbation on the surface of the long cylinder, and the other with grain boundaries in the interior of the long cylinder) were simulated, and the breakup of the long cylinder was shown for both cases. In the end, a system containing long cylinders with interior grain boundaries was simulated, which demonstrated the integration of Rayleigh instability and Ostwald ripening relating to the spheroidization of the lamellar structure.

Scalable In-Fiber Manufacture of Functional Composite Particles.

Advanced fabrication methods must be developed for magnetic-polymeric particles, which are used in medical diagnostics, drug delivery, separation, and environmental remediation. The development of scalable fabrication processes that enables simultaneously tuning of diameters and compositions of magnetic-polymeric particles remains a major challenge. Here, we proposed the production of high-quality magnetic-composite particles through a universal method based on the in-fiber Plateau-Rayleigh instability of polymeric fibers. This method can simultaneously control the particle diameter, hybrid configuration, and functional properties. The diameter of magnetic-polymeric particles can be reproducibly tuned from ∼20 nm to 1.25 mm, a wide range unachievable by conventional solution methods. The final diameter was controlled by the inner/outer fiber diameter ratio. We further showed that the prepared magnetic-polymeric composite particles can be used for the highly efficient recovery of heavy metals (98.2% for Cd2+) and for the precise separation of immune cells (CD4+ T cells). Overall, the in-fiber manufacture method can become a universal technology for the scalable preparation of different types of magnetic-polymeric composite particles with diverse functionalities.

Submerged injection of gas into a thin liquid sheet

Submerged injection of gas into a thin liquid sheet is frequently observed in industrial processes. Most studies on submerged gas injection, however, focus on the phenomena happened in deep liquid pool. Few studies have been devoted to a thin liquid layer with a thickness of a few millimeters. Here, we study submerged injection of gas into a thin liquid sheet, where we quantify the behaviors of bubbling/collapse and the resulting liquid jet with a high-speed video system. For the experimentally available range of liquid depths and gas velocities, three different flow regimes are identified and we build a phase diagram outlining these regimes in terms of the Weber number and Bond number. Particularly, the complete evolution of periodic bubbling-bursting behavior is investigated systematically. The bubbling characteristics, which show great differences with traditional bubbling in deep liquid, are depicted and analyzed. Using dimensional arguments, we propose a scaling law for the rupture radius of bubbles which brings out the effects of gravity and inertia. Focusing on the subsequent liquid jet dynamics, we unravel experimentally the intricate roles of capillary wave velocities, cavity morphology, liquid thickness and gas momentum in bubble collapse. With increase of the liquid sheet thickness, jets first become fat and small and then ends up thinner, detaching more and smaller droplets due to Rayleigh-Plateau instability. Our study firstly provides the quantitative overview of the events following submerged gas injection into thin quiescent liquid and provide guides for the control of the bursting-bubble jet.

Discussion on Rayleigh equation obtained for a Hall thruster plasma with dust

The present study focuses on the Rayleigh equation derived in the case of a Hall thruster plasma having dust contamination, produced near the exit of the channel due to the finite divergence of the accelerated ions and the sputtering of the walls. In the presence of negatively charged dust particles, a modified form of the well-known Rayleigh equation of fluid dynamics is realized. The modified equation takes the form of the Rayleigh equation for a particular band of oscillation frequency, revealing that the Rayleigh instability shall occur in the thruster only for the oscillations having frequencies within this band. For better understanding, the variation of frequency band with various parameters, viz. dust density, dust charge number, dust mass, electron temperature and ion density, has been traced out.

Observation and characterization of memristive silver filaments in amorphous zinc-tin-oxide

Abstract

The flow of thin liquid layers on circular cylinders

The time evolution of a coating layer of liquid on an inclined circular cylindrical substrate is studied experimentally and theoretically. For small-diameter cylinders, the motion of Newtonian liquids, driven by the combined influences of surface tension and gravity, is analyzed using the long-wave or “lubrication” approximation. Computed time-dependent solutions of the lubrication model are in general agreement with our experimental observations. Starting from a slightly-perturbed uniform coating, the full family of evolving flows is shown to depend only on three dimensionless parameters: the inclination angle of the cylinder from the vertical direction, the Bond number representing the ratio of gravity to surface tension effects, and a nondimensional measure of the initial coating thickness. Typically flow is initiated by the well-known Rayleigh-Plateau instability followed by drainage, and also wave propagation if the cylinder is not horizontal. Steady propagation of ring-like structures can occur as well as eventual overtaking, merging and reformation of the rings. We demonstrate that volumetric transport is maximized if the cylinder axis is inclined to, rather than aligned with, the direction of gravity. Results are relevant to the understanding, and potential optimization, of small-scale liquid transport. Such problems arise in the natural and industrial worlds.

On the globularization of the shapes associated with alpha-precipitate of two phase titanium alloys: Insights from phase-field simulations

In two-phase titanium alloys, α-precipitate exhibits plate morphology which spheroidizes during static globularization. The stability of the 3-dimensional plates to withstand perturbation is well-established. However, based on Rayleigh instabilities, the current understanding rendered by ‘the modified perturbation theory’ holds that the spheroidization of the plates is governed by the stable growth of the ridges. To address this counterintuitive view, a multiphase-field model, which recovers the sharp interface solutions, is employed to investigate the morphological transformation accompanying globularization of shapes that resemble α-precipitate. The present investigation unravels an alternate mechanism, wherein the plates globularize by the successive formation and decay, by lateral expansion, of multiple terminal perturbations. This unique mode of spheroidization, distinctly, characterizes the temporal evolution of the driving force which contradicts the hitherto assumed conventional monotonic-decrease in the curvature-difference. Particularly, it is identified that the ellipsoidal plates exhibit a step-wise change in the curvature-difference while non-monotonic series of peaks are observed during the evolution of the pancake structures. To aid the optimization of the thermal cycle involved in the globularization treatment, a simplified relation between the aspect ratio and spheroidization time, which encompasses the influence of the transformation mechanism, is derived.

Nitrogen-doped SiC/SiOx nanowire heterostructure synthesized by pyrolysis deposition of phthalocyanine derivative

Nitrogen-doped SiC/SiOx nanowire heterostructure was synthesized successfully by chemical vapor deposition using phthalocyanine derivative as a precursor. Carbon and nitrogen atoms are provided simultaneously by the heterostructure, and nitrogen element was combined into the heterostructure effectively through pyrolysis of phthalocyanine derivative during the deposition. This special heterostructure exhibits a regular periodic cage-like SiOx bead decorated on SiC nanowires with diameter of 200 nm, whose formation mechanism could be primarily attributed to the combined effect from the vapor growth, Rayleigh instability and polar faces. The present method provides an alternative way for controllable fabrication of the nitrogen-doped SiC nanowire heterostructures for their tunable performances and nano-sized electronic devices application.

On the geometric stability of an inorganic nanowire and an organic ligand shell

The break-up of a nanowire with an organic ligand shell into discrete droplets is analysed in terms of the Rayleigh-Plateau instability. Explicit account is taken of the effect of the organic ligand shell upon the energetics and kinetics of surface diffusion in the wire. Both an initial perturbation analysis and a full numerical analysis of the evolution in wire morphology are conducted, and the governing non-dimensional groups are identified. The perturbation analysis is remarkably accurate in obtaining the main features of the instability, including the pinch-off time and the resulting diameter of the droplets. It is conjectured that the surface energy of the wire and surrounding organic shell depends upon both the mean and deviatoric invariants of the curvature tensor. Such a behaviour allows for the possibility of a stable nanowire such that the Rayleigh-Plateau instability is not energetically favourable. A stability map illustrates this. Maps are also constructed for the final droplet size and pinch-off time as a function of two non-dimensional groups that characterise the energetics and kinetics of diffusion in the presence of the organic shell. These maps can guide future experimental activity on the stabilisation of nanowires by organic ligand shells.

On Plateau–Rayleigh Instability of a Cylinder of Viscous Liquid

In 1892, in his classical work, L. Rayleigh considered the instability of a cylinder of viscous liquid under capillary force, the so-called Plateau‐Rayleigh instability. In this work, in linear approximation, he obtained a dispersion equation describing the increment of this instability as a function of wavelength, the radius of cylinder, the mass density, surface tension, and viscosity of the liquid. Hundreds of authors referred to this work, but none of them used his dispersion equation in its complete form; they used only the asymptotic solutions of his equation for zero or infinitely large viscosities. A reason for this is, probably, that Rayleigh’s writing is difficult and his dispersion equation is quite complex. Then, in 1961, S. Chandrasekhar, in his monograph, also considered the stability of a viscous cylindrical jet and obtained his dispersion equation which is also quite complex and differs from the one obtained by Rayleigh. As in the case of Rayleigh’s dispersion equation, other works use only the asymptotic solution of Chandrasekhar’s equation that corresponds to the case where the viscosity is very large in comparison to inertia. In this article, the author demonstrates that Chandrasekhar’s dispersion equation is equivalent to Rayleigh’s and then simplifies their dispersion equations to a form which can be easily solved numerically for arbitrary values of viscosity. He also presents a Mathematica code to calculate the maximum increment of the Plateau‐Rayleigh instability for given parameters of the jet. To illustrate how the code works, he applies it to a cylindrical jet to estimate its breakup.

The influence of the entry region on the instability of a coflowing injector device

The occurrence of dripping and jetting regimes in a microfluidic coflowing injector device has been related recently to the spatio-temporal stability properties of the developed velocity profile. Dripping corresponds to an absolutely unstable flow while jetting is observed when the Rayleigh–Plateau instability of the core-annular jet is convective. In this work we take into account the effect of the entry region on the dripping to jetting transition by carrying out a global stability analysis of the steady two-phase base flow. We show that, depending on the flow parameters, the entry region can affect significantly the transition between the two regimes.

Where does the droplet size distribution come from?

This study employs DNS of two-phase flows to enhance primary atomization understanding and modeling to be used in numerical simulation in RANS or LES framework. In particular, the work has been aimed at improving the information on the liquid-gas interface evolution for modeling approaches, such as the Eulerian–Lagrangian Spray Atomization (ELSA) framework. Even though this approach has been already successfully employed to describe the complete liquid atomization process from the primary region to the dilute spray, improvements are still expected on the derivation of the drop size distribution (DSD). The main aim of the present work is the introduction of a new framework to achieve a continuous description of the DSD formation during the atomization process. The attention is here focused on the extraction from DNS data of the behavior of geometrical variable of the liquid-gas interface, such as the mean (H) and Gauss (G) surface curvatures. The use of a Surface Curvature Distribution is also proposed and studied.A Rayleigh–Plateau instability along a column of liquid and a droplet collision case are first of all considered to analyze and to verify the capabilities of the code to correctly predicting the curvature distributions. A statistical analysis based on the curvatures data, in terms of probability density function, is presented in order to determine the physical parameters that control the curvatures on this test case. Then, the same formulation is applied in the analysis of the two phase Homogeneous Isotropic Turbulence (HIT) configuration to study how the curvatures evolve all along the atomization process. Joint PDFs are used to illustrate the topological changes of the interface when increasing the liquid volume fraction.

Coulomb explosion and ultra-fast hypergolic ignition of borohydride-rich ionic liquids with WFNA

In this work, the hypergolic ignition process of 8 recently synthesized ionic liquids (I.L.s) with [BH3(CN)BH2(CN)]− anions with white fuming nitric acid is experimentally investigated by using droplet test method and long distance microscope-high speed photography techniques. Results show that the hypergolic ignition process of the present I.L.s is of a completely different three stage nature and ultra-fast hypergolic ignition is observed for this family of I.L.s (< 5 ms). Specifically, at the very first stage upon contact (within a fraction of millisecond), ‘coulomb explosion’ like behavior in terms of fast and vigorous ejection of liquid spikes that protrude from mixing layer is observed, and this phenomenon has never been reported in previous hypergolic test for I.L.s or conventional hydrazine based fuels. The ‘coulomb explosion’ delay time (CEDT) is found to be correlated with the side alkyl functional group, which indicates the I.L. structure (characterized by the side alkyl functional group and the heterocyclic core) effects on shifting the Rayleigh instability limit (Ecoulomb/2Esurface > 1). Subsequently in the second stage, liquid spikes that are ejected into the oxidizer pool during CEDT significantly increase the reactive surface area underneath the liquid surface. As a consequence, local temperature increases, gas phase intermediate product and oxidizer/fuel vapor accumulate due to the continuous liquid phase reaction underneath the surface. When the local pressure overcomes the surface tension, disintegration of the surface in terms of larger ligaments and secondary droplets ejection was observed, together with shooting out of the vapor/smoke. Finally, in the third stage when the local temperature and the vapor concentration increase sufficiently, further gas phase reaction leads to ignition. Fine and stable flame with strong bright and green luminescence continuously evolve from the initial mixing layer. Some red and dark smokes are gradually generated above the burning bright and green flame until finally the flame dies out. The ignition delay time (IDT) decreases with the increase of unsaturation index of the heterocyclic core in the cation, and also the decrease of CEDT. The enthalpy of formation of the I.L.s for different cation structures are correlated with IDT, which represents both the fuel structure chemistry and the ‘coulomb explosion’ enhances mixing effect on the overall reactivity of this diffusive system.

On the morphologies of oxides particles in optical fibers: Effect of the drawing tension and composition

Rare-earth-doped oxide nanoparticles in the core of silica optical fibers are becoming well studied as they yield enhanced and tailorable spectroscopic and optical properties. In this paper, the evolution of particle morphology, induced by the drawing step, is studied. Indeed, during the fiber draw process, the glass flows and particles can elongate and even break-up into smaller particles through Rayleigh-Plateau instabilities. The shape of elongated particles is related to the composition as it depends on the viscosity ratio between the particle and the matrix. Moreover, a lower drawing temperature enhances the break-up phenomenon. These observations offer new possibilities for the control of the size and the shape of particles, hence performance of active optical fibers.