Rayleigh Instability Research Articles

A genetic algorithm-based approach for numerical solution of droplet status after Coulomb fission using the energy

As a droplet moves, due to evaporation at the surface, the droplet size is gradually reduced. Due to decreasing the size of the droplets moving in the spray core, the surface charges become closer and the repulsive force between the charges increases. When the Coulombic force overcomes the surface tension force (Rayleigh instability) the droplet breaks into smaller droplets (Coulomb fission). The present study predicts droplet Coulomb fission and droplets trajectories of steady spray plume in a monodisperse Electrohydrodynamics (EHD) spray within a Lagrangian framework. Droplet fission is simulated based on the principle of minimum free energy using the Genetic Algorithm (GA) and droplet trajectories are predicted using the Lagrangian single-droplet dynamic tracking method. The numerical model is validated by comparing the model predictions with the experimental and previous modeling results. In the current method, an optimization method for minimizing the energy in the minimum energy principle is utilized to avoid any simplifying assumptions, such as number of sibling droplets and charge distribution on their surfaces which may affect the physics of the problem. According to the process of the present solutions and results, it is clearly seen that the developed method has sufficient accuracy and precision.

Necking, beading, and bulging in soft elastic cylinders

Due to surface tension, a beading instability takes place in a long enough fluid column that results in the breakup of the column and the formation of smaller packets with the same overall volume but a smaller surface area. Similarly, a soft elastic cylinder under axial stretching can develop an instability if the surface tension is large enough. This instability occurs when the axial force reaches a maximum with fixed surface tension or the surface tension reaches a maximum with fixed axial force. However, unlike the situation in fluids where the instability develops with a finite wavelength, for a hyperelastic solid cylinder that is subjected to the combined action of surface tension and axial stretching, a linear bifurcation analysis predicts that the critical wavelength is infinite. We show, both theoretically and numerically, that a localized solution can bifurcate sub-critically from the uniform solution, but the character of the resulting bifurcation depends on the loading path. For fixed axial stretch and variable surface tension, the localized solution corresponds to a bulge or a depression, beading or necking, depending on whether the axial stretch is greater than a certain threshold value that is dependent on the material model and is equal to 23 when the material is neo-Hookean. At this single threshold value, localized solutions cease to exist and the bifurcation becomes exceptionally supercritical. For either fixed surface tension and variable axial force, or fixed axial force and variable surface tension, the localized solution corresponds to a depression or a bulge, respectively. We explain why the bifurcation diagrams in previous numerical and experimental studies look as if the bifurcation were supercritical although it was not meant to. Our analysis shows that beading in fluids and solids are fundamentally different. Fluid beading resulting from the Plateau–Rayleigh instability follows a supercritical linear instability whereas solid beading in general is a subcritical localized instability akin to phase transition.

Instability of a swirling bubble ring

A toroidal bubble or a cylindrical gas jet are known to be subjected to the Rayleigh-Plateau instability. Air bubble rings produced by beluga whales and dolphins however are observed that remain stable for long times. In the present work, we analyse the generation of such toroidal bubbles via numerical simulations , in particular how the process depends on surface tension. Their stability properties are then briefly analysed. For the estimated Reynolds and Weber numbers relative to the bubbles produced by these animals, the presence of a vortex inside and around the bubble is found to strongly stabilize the Rayleigh-Plateau instability .

Simulation of Powder Packing and Thermo-Fluid Dynamic of 316L Stainless Steel by Selective Laser Melting

A mesoscopic model was established to investigate thermo-fluid dynamic behavior in selective laser melting of 316L stainless steel. A powder packing model, including particle size distribution based on the discrete element method, was developed to describe the relative density variation of the powder bed with different layer thicknesses. A finite element method model with Gaussian laser beam was established to predict the dynamic thermal behavior and flow mechanism of the particles for a single-line scanning. The level-set method was used to trace the free surface of the molten metal with temperature-dependent surface tension. A function to describe the relative density of the powder bed with its thickness was obtained. An evaporation model considering the influence of mass, energy loss, and evaporation on the surface morphology of the molten pool was established. According to the temperature and velocity field in the molten pool, a vortex formed by the Marangoni effect might decrease the depth and increase the width of the molten pool. The molten pool was not disconnected by Plateau–Rayleigh instability due to the small length/diameter ratio at low scanning speeds. The model assuming regularly arranged powder bed underestimates the maximum temperature as compared to the model considering a randomly packed powder bed because a higher relative density of the former facilitates heat conduction. The simulated results are consistent with experimental results, including porosity, material loss, and surface defects.

The role of the “monopole” instability in the evolution of two-dimensional turbulent free shear layers

The role of instability in the growth of a two-dimensional, temporally evolving, “turbulent” free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot–Savart relation. The initial evolution of perturbations in a constant vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman–Rubach–Lamb linear instability of monopoles, until the neighboring coherent structures merge. After several mergers, the layer evolves eventually to a self-preserving reverse cascade, characterized by a universal spread rate found by Suryanarayanan, Narasimha, and Hari Dass [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)] and a universal value of the ratio of dominant spacing of structures (Λf) to the layer thickness (δω). In this universal, self-preserving state, the local amplification of perturbation amplitudes is accurately predicted by Rayleigh theory for the locally existing “base” flow. The model of Morris, Giridharan, and Lilley [“On the turbulent mixing of compressible free shear layers,” Proc. R. Soc. London, Ser. A 431, 219–243 (1990)], which computes the growth of the layer by balancing the energy lost by the mean flow with the energy gain of the perturbation modes (computed from an application of Rayleigh theory), is shown, however, to provide a non-universal asymptotic state with initial condition dependent spread rate and spectra. The reason is that the predictions of the Rayleigh instability, for a flow regime with coherent structures, are valid only at the special value of Λf/δω achieved in the universal self-preserving state.

Instability of the abstract Rayleigh–Taylor problem and applications

Based on a bootstrap instability method, we prove the existence of unstable strong solutions in the sense of [Formula: see text]-norm to an abstract Rayleigh–Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates. In the proof we develop a method to modify the initial data of the linearized abstract RT problem by exploiting the existence theory of a unique solution to the stratified (steady) Stokes problem and an iterative technique, such that the obtained modified initial data satisfy the necessary compatibility conditions on boundary of the original (nonlinear) abstract RT problem. Applying an inverse transform of Lagrangian coordinates to the obtained unstable solutions and taking then proper values of the parameters, we can further obtain unstable solutions of the RT problem in viscoelastic, magnetohydrodynamics (MHD) flows with zero resistivity and pure viscous flows (with/without interface intension) in Eulerian coordinates.

Influence of the trap potential waveform on surface oscillation and breakup of a levitated charged drop

A charged droplet can be electrodynamically levitated in air using a quadrupole trap by typically applying a sinusoidal electric field. When a charged drop is levitated, it exhibits surface oscillations simultaneously building charge density due to continuous evaporation and subsequently undergoes breakup due to Rayleigh instability. In this work, we examined large-amplitude surface oscillations of a sub-Rayleigh charged drop and its subsequent breakup, levitated by various applied signals such as sine, square, and ramp waveforms at various imposed frequencies, using high-speed imaging (recorded at 100 000–130 000 frames per second). It is observed that the drop surface oscillates in a sphere–prolate–sphere–oblate mode and seldom in a sphere–prolate-sphere mode depending on the intricate interplay of various forces due to charge(q), the intensity of the applied field (Λ), and the shift of the droplet from the geometric center of the trap (zshift). The Fast Fourier Transformation analysis shows that the droplet oscillates with the forced frequency irrespective of the type of the applied waveform. While in the sinusoidal case, the nonlinearities are significant, in the square and ramp potentials, there is an admittance of all the harmonic frequencies of the applied potential. Interestingly, the breakup characteristics of a critically charged droplet are found to be unaffected by the type of the applied waveform. The experimental observations are validated with an analytical theory as well as with the Boundary Integral simulations in the potential flow limit, and the results are found to be in a reasonable agreement.

Bioinspired Anti-Plateau-Rayleigh-Instability on Dual Parallel Fibers.

The Plateau-Rayleigh instability (PRI) is a well-known phenomenon where a liquid column always breaks up into droplets to achieve the minimization of surface energy. It normally leads to the non-uniformity of a liquid film, which, however, is unfavorable for the fluid coating process. So far, strategies to overcome this instability rely on either the surfactants, UV/high-temp curing treatments, or specific chemical reactions, which suffer from both limited liquid composition and complicated experimental conditions. Natural mulberry silk, a typical composite fiber, is produced by silkworms through a similar fluidic coating process, but exhibits a remarkably uniform and smooth surface. Drawing inspiration, it is revealed that the unique dual parallel fibers are capable of overcoming the PRI during the fluid coating process. Such anti-PRI ability is attributable to the changes in the Laplace pressure difference caused by the alternative asymmetry of the liquid film, as has been demonstrated by both a force analysis on the irregular liquid film and theoretical simulation according to the stability of the liquid on parallel fibers in the fluid coating process. The strategy is applicable for preparing various smooth functional coatings on fibers, which offers new perspectives for fluid coating and microfluidic technologies.

Integrated three-dimensional characterization of reactive phase formation and coarsening during isothermal annealing of metastable Zn–3Mg–4Al eutectic

Microstructural instabilities associated with a metastable lamellar eutectic when exposed to an elevated temperature were analyzed in a Zn−3Mg−4Al alloy as a model system. X-ray diffraction and scanning electron microscopy showed that annealing at a temperature 43 K below the equilibrium eutectic temperature converted the metastable ternary MgZn2/η-Zn/β-ZnAl eutectic to a stable mixture of Mg2Zn11/η-Zn/α-Al. 3D EBSD suggested that supersaturation of η-Zn with Mg and Al eased difficulties in nucleation of Mg2Zn11 and α-Al at the MgZn2/η-Zn phase interfaces. Quasi-in-situ X-ray nanotomography revealed that a reactive diffusion process prevailed in an early stage of annealing leading to rapid consumption of MgZn2 for growth of Mg2Zn11 and concomitant thinning and pinch-off of η-Zn lamellae. The reactive diffusion process also brought about significant and quantifiable changes in the topological characteristics of the η-Zn phase at remarkably shorter time scales compared to Rayleigh instability and Ostwald ripening mechanisms. The present results provide fresh insights on the short-term annealing effects on metastable eutectics, with relevance to structural evolution in additive manufacturing.

Optically Programmable Plateau-Rayleigh Instability for High-Resolution and Scalable Morphology Manipulation of Silver Nanowires for Flexible Optoelectronics.

The ability to engineer microscale and nanoscale morphology upon metal nanowires (NWs) has been essential to achieve new electronic and photonic functions. Here, this study reports an optically programmable Plateau-Rayleigh instability (PRI) to demonstrate a facile, scalable, and high-resolution morphology engineering of silver NWs (AgNWs) at temperatures <150 °C within 10 min. This has been accomplished by conjugating a photosensitive diphenyliodonium nitrate with AgNWs to modulate surface-atom diffusion. The conjugation is UV-decomposable and able to form a cladding of molten salt-like compounds, so that the PRI of the AgNWs can be optically programmed and triggered at a much lower temperature than the melting point of AgNWs. This PRI self-assembly technique can yield both various novel nanostructures from single NW and large-area microelectrodes from the NW network on various substrates, such as a nanoscale dot-dash chain and the microelectrode down to 5 μm in line width that is the highest resolution ever fabricated for the AgNW-based electrode. Finally, the patterned AgNWs as flexible transparent electrodes were demonstrated for a wearable CdS NW photodetector. This study provides a new paradigm for engineering metal micro-/nanostructures, which holds great potential in fabrication of various sophisticated devices.

Breakup morphology of expelled respiratory liquid: From the perspective of hydrodynamic instabilities.

Understanding the breakup morphology of an expelled respiratory liquid is an emerging interest in diverse fields to enhance the efficacious strategies to attenuate disease transmission. In this paper, we present the possible hydrodynamic instabilities associated with expelling the respiratory liquid by a human. For this purpose, we have performed experiments with a cylindrical soap film and air. The sequence of the chain of events was captured with high-speed imaging. We have identified three mechanisms, namely, Kelvin–Helmholtz (K–H) instability, Rayleigh–Taylor (R–T) instability, and Plateau–Rayleigh (P–R) instability, which are likely to occur in sequence. Furthermore, we discuss the multiple processes responsible for drop fragmentation. The processes such as breakup length, rupture, ligament, and drop formation are documented with a scaling factor. The breakup length scales with We−0.17, and the number of ligaments scales as . In addition, the thickness of the ligaments scales as We−0.5. Here, We and Bo represent the Weber and Bond numbers, respectively. It was also demonstrated that the flapping of the liquid sheet is the result of the K–H mechanism, and the ligaments formed on the edge of the rim appear due to the R–T mechanism, and finally, the hanging drop fragmentation is the result of the P–R instability. Our study highlights that the multiple instabilities play a significant role in determining the size of the droplets while expelling a respiratory liquid. This understanding is crucial to combat disease transmission through droplets.

Parameter space mapping of the Princeton magnetorotational instability experiment.

Extensive simulations of the Princeton Magnetorotational Instability (MRI) Experiment with the Spectral/Finite Element code for Maxwell and Navier-Stokes Equations (SFEMaNS) have been performed to map the MRI-unstable region as a function of inner cylinder angular velocity and applied vertical magnetic field. The angular velocities of the outer cylinder and the end-cap rings follow the inner cylinder in fixed ratios optimized for MRI. We first confirm the exponential growth of the MRI linear phase using idealized conducting vertical boundaries (end caps) rotating differentially with a Taylor-Couette profile. Subsequently, we run a multitude of simulations to scan the experimental parameter space and find that the normalized volume-averaged mean-square radial magnetic field, our main instability indicator, rises significantly where MRI is expected. At various locations, the local radial components of fluid velocity and generated magnetic field are well correlated with the volume-averaged indicator. Based on this correlation, a diagnostic system that will measure the radial magnetic field at several locations on the inner cylinder is proposed as the main comparison between simulation and experiment. A detailed analysis of poloidal mode structures in the SFEMaNS code indicates that MRI, rather than Ekman circulation or Rayleigh instability, dominates the fluid behavior in the region where MRI is expected.

Stability of surfactant-laden liquid film flow over a cylindrical rod

The stability of surfactant-laden liquid film flow over a cylindrical rod is examined in creeping flow limit using standard temporal linear stability analysis. The clean film flow configuration (i.e., in absence of surfactant) is well-known to become unstable owing to Rayleigh-Plateau instability of cylindrical liquid interfaces. Previous studies demonstrated that for a static liquid film (i.e., zero basic flow) coating a rod, the presence of interfacial surfactant decrease the growth of Rayleigh-Plateau instability, but is unable to suppress it completely. Further, the presence of interfacial surfactant is known to introduce an additional mode, referred to as surfactant mode in the present work. To the best of our knowledge, the stability of surfactant mode has not been analyzed in the context of cylindrical film flows. Thus, we reexamined the stability of surfactant-laden cylindrical liquid film flow to analyze the stability behavior of the above said two modes when the basic flow is turned on. The present study reveals that the incorporation of basic flow in stability analysis leads to the complete suppression of Rayleigh-Plateau instability due to the presence of interfacial surfactants as compared to the partial suppression obtained for a stationary liquid film. Three nondimensional parameters appear for this problem: Bond number (denoted as Bo) which characterizes the strength of basic flow, Marangoni number (denoted as Ma) which signifies the presence of surfactant, and ratio of rod radius to film thickness denoted as S. In creeping flow limit, the characteristic equation is quadratic with one root belonging to Rayleigh-Plateau mode and the other to surfactant mode. We first carried out an asymptotic analysis to independently capture the eigenvalues corresponding to both the modes in limit of long-wave disturbances. The long-wave results show that the Rayleigh-Plateau instability is completely suppressed on increasing the Marangoni number above a critical value while the surfactant mode always remains stable in low wave-number limit. The continuation of long-wave results to arbitrary wavelength disturbances show that the suppression of Rayleigh-Plateau instability mode still holds, however, the surfactant mode becomes unstable at sufficiently high values of Marangoni number. Further, this surfactant mode instability shifts toward low wave numbers with critical Marangoni number for instability scaling with wave number in a particular fashion. We used this scaling and carried out an asymptotic analysis to capture this instability in low wave-number limit. Depending on S and Bo, we observed the existence of a stable gap in terms of Ma where both the eigen-modes remain stable. Our results indicate that for a given Bond number, the width of stable gap in terms of Ma decreases with decrease in S and the stable gap vanishes when S is sufficiently small. The effect of increasing Bond number (or equivalently, the strength of basic flow) is found to be stabilizing for the film flow configuration.

In-situ analysis on formation of micropores by Rayleigh instability in solidification of Sn-Ni alloy

A new formation mechanism of micropores whose radii are approximately 1 μm is investigated during solidification of Sn-Ni alloy through the in-situ observation by confocal laser scanning microscope. A series of liquid lines which are closely related to the stability of the growing L/Ni3Sn2 interface were formed during solidification, then, these liquid lines decomposed into different rows of liquid droplets by Rayleigh instability in solid Ni3Sn2 phase. The relationship between the formation of the micropores and the liquid droplets is confirmed. In addition, the distribution of the radii of the micropores agrees with the prediction of the Rayleigh instability theory.

Tuning the Splitting Behavior of Droplet in a Bifurcating Channel through Wettability-Capillarity Interaction.

We present a comprehensive computational physics-based study of the influence of surface wettability on the displacement behavior of a droplet in a three-dimensional bifurcating channel. Various surface wettability configurations for the daughter branches are considered to gain insight into the wettability-capillarity interaction. Also, the influence of initial droplet size on the splitting dynamics for different wettability configurations is investigated. Time evolution of the droplet displacement behavior in the bifurcating channel is discussed for different physicochemical parameters including capillary number and wettability. Three distinct flow regimes are identified as the droplet interacts with the bifurcating tip of the channel, namely, splitting, nonsplitting, and oscillating regimes. Furthermore, the occurrence of Rayleigh-Plateau instability in different wettability scenarios is discussed. Additionally, the intricacies associated with the droplet dynamics are elucidated through the temporal evolution of the droplet surface area and mass outflow of the continuous phase. A flow regime map based on the capillary number and wettability contrast of the daughter branches is proposed for a comprehensive description of the droplet dynamics.

Tracking the Effects of Ligands on Oxidative Etching of Gold Nanorods in Graphene Liquid Cell Electron Microscopy.

Surface ligands impact the properties and chemistry of nanocrystals, but observing ligand binding locations and their effect on nanocrystal shape transformations is challenging. Using graphene liquid cell electron microscopy and the controllable, oxidative etching of gold nanocrystals, the effect of different ligands on nanocrystal etching can be tracked with nanometer spatial resolution. The chemical environment of liquids irradiated with high-energy electrons is complex and potentially harsh, yet it is possible to observe clear evidence for differential binding properties of specific ligands to the nanorods' surface. Exchanging CTAB ligands for PEG-alkanethiol ligands causes the nanorods to etch at a different, constant rate while still maintaining their aspect ratio. Adding cysteine ligands that bind preferentially to nanorod tips induces etching predominantly on the sides of the rods. This etching at the sides leads to Rayleigh instabilities and eventually breaks apart the nanorod into two separate nanoparticles. The shape transformation is controlled by the interplay between atom removal and diffusion of surface atoms and ligands. These in situ observations are confirmed with ex situ colloidal etching reactions of gold nanorods in solution. The ability to monitor the effect of ligands on nanocrystal shape transformations will enable future in situ studies of nanocrystals surfaces and ligand binding positions.

Overcoming Rayleigh–Plateau instabilities: Stabilizing and destabilizing liquid-metal streams via electrochemical oxidation

Liquids typically form droplets when exiting a nozzle. Jets--cylindrical streams of fluid-can form transiently at higher fluid velocities, yet interfacial tension rapidly drives jet breakup into droplets via the Rayleigh-Plateau instability. Liquid metal is an unlikely candidate to form stable jets since it has enormous interfacial tension and low viscosity. We report that electrochemical anodization significantly lowers the effective tension of a stream of metal, transitioning it from droplets to long (long lifetime and length) wires with 100-μm diameters without the need for high velocities. Whereas surface minimization drives Rayleigh-Plateau instabilities, these streams of metal increase in surface area when laid flat upon a surface due to the low tension. The ability to tune interfacial tension over at least three orders of magnitude using modest potential (<1 V) enables new approaches for production of metallic structures at room temperature, on-demand fluid-in-fluid structuring, and new tools for studying and controlling fluid behavior.

Flow-accelerated platelet biogenesis is due to an elasto-hydrodynamic instability

Blood platelets are formed by fragmentation of long membrane extensions from bone marrow megakaryocytes in the blood flow. Using lattice-Boltzmann/immersed boundary simulations we propose a biological Rayleigh-Plateau instability as the biophysical mechanism behind this fragmentation process. This instability is akin to the surface tension-induced breakup of a liquid jet but is driven by active cortical processes including actomyosin contractility and microtubule sliding. Our fully three-dimensional simulations highlight the crucial role of actomyosin contractility, which is required to trigger the instability, and illustrate how the wavelength of the instability determines the size of the final platelets. The elasto-hydrodynamic origin of the fragmentation explains the strong acceleration of platelet biogenesis in the presence of an external flow, which we observe in agreement with experiments. Our simulations then allow us to disentangle the influence of specific flow conditions: While a homogeneous flow with uniform velocity leads to the strongest acceleration, a shear flow with a linear velocity gradient can cause fusion events of two developing platelet-sized swellings during fragmentation. A fusion event may lead to the release of larger structures which are observable as preplatelets in experiments. Together, our findings strongly indicate a mainly physical origin of fragmentation and regulation of platelet size in flow-accelerated platelet biogenesis.

Numerical analysis of the influence of molten pool instability on the weld formation during the high speed fiber laser welding

The dynamic behaviors of the molten pool play a critical role in determining the weld bead formation process and the welded joints quality. A numerical simulation modeling method is proposed to investigate the instability of the molten pool and understand its influence on the formation process of the weld and the related welding defects during the high speed fiber laser welding. In the modeling, the molten metal flowing dynamic behaviors and free surface evolution of molten pool are coupling taken into account. The instable phenomena including the profiles variation of the molten pool surface in the vertical direction and edges oscillation in the horizontal direction are demonstrated and discussed in the simulation results in details. The Rayleigh instability of the molten pool is numerically approved and the relationship between the molten pool profile and Rayleigh instability is revealed, which is kept consistent with the experiment and literature results. It is found that the welding defects formation process in the weld is greatly affected by the instable phenomena in the molten pool. The oscillation and fluctuation of the molten pool surface in the horizontal direction and vertical direction during the cooling process can directly result in the defects formation in the weld.

Top-down Approach for Fabrication of Polymer Microspheres by Interfacial Engineering

Polymer microspheres with uniform size, composition, and surface property have gained extensive researches in past decades. Conventional bottom-up approaches are using monomers or oligomers to build up desired polymer microspheres. However, directly shaping high-molecular-weight polymers into well-ordered polymer microspheres remains a great challenge. Herein, we reported a facile and efficient top-down approach to fabricate microspheres with high-molecular-weight polymer microfibers. By harnessing interfacial engineering-control during the polymer microspheres formation, uniformly sized microspheres could be produced with widely ranged diameters (from 10 µm to the capillary length of each polymer melt). The size limitation of this approach could be further extended by a controllable Plateau-Rayleigh instability phenomenon. Principally, the top-down approach allows fabrication of microspheres by various polymer melts with surface energy higher than 25 mN/m. Our work paves a way for green, cost-effective, and customizable production of a variety of functional polymer microspheres without any chemical reaction assistant.