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Circulating tumor cell (CTC) clusters represent formidable precursors of cancer metastasis due to their heightened immune resistance against natural killer (NK) cells. Despite this, the cytotoxicity of NK cells against CTC clusters, particularly their interaction with other immune cells such as neutrophils, remains inadequately examined. This study introduces a dual‐nozzle integrated droplet microfluidic chip (dual‐nozzle chip) designed to facilitate the deterministic encapsulation of three distinct cell types—CTCs, NK cells, and neutrophils—to monitor the dynamic cytotoxicity between immune cells and target cells. The dual‐nozzle chip comprises double‐spiral channels and a serpentine channel for inertial cell focusing, alongside dual‐nozzle oil phases employed to generate monodisperse droplets at high flow rates. Utilizing Rayleigh–Plateau instability, the focused cell streams, characterized by high inertia, undergo pinching off into monodisperse droplets at the flow‐focusing junction, where dual‐nozzle oil phases are introduced. Consequently, triple cells are paired at the desired ratios, overcoming the intrinsic challenge posed by the Poisson distribution. A droplet‐based assay demonstrates that NK cell‐mediated cytotoxicity varies depending on the type of cancer cells and the presence of suppressor cells. The design strategy of the dual‐nozzle chip exhibits promises for broader applications, emphasizing its potential for analyzing diverse cell‐to‐cell interactions. [ABSTRACT FROM AUTHOR]

The breakup of a jet consisting of two coaxial jets of immiscible liquids has been studied experimental with varying phase flow rates. Distilled water and a mixture of polymethylsiloxanes were used as working liquids. Jet breakup regimes, the types of capsules formed, and the sizes of single-core capsules formed under the influence of capillary instability were determined. The natural frequencies of surface instability were measured. [ABSTRACT FROM AUTHOR]

The Rayleigh-Plateau instability, a phenomenon of paramount significance in fluid dynamics, finds widespread application in the Continuous InkJet (CIJ) printing process. This study presents a comprehensive dataset comprising experimental investigations of fluid jet breakup phenomena under large-amplitude stimulation conditions using an industrial CIJ print-head from Markem-Imaje. Unlike previous studies, this dataset encompasses a diverse range of experimental conditions, including nine different Newtonian fluids with meticulously measured rheological properties (viscosities, surface tensions and densities). The applied stimulation amplitudes vary from 5V to 45V, representing a substantial span of excitation levels.The experimental setup captures the intricate dynamics of fluid jets subjected to these varying conditions, producing a rich collection of over 5,000 high-resolution images depicting the breakup phenomena. Each amplitude of stimulation and fluid type yields more than 55 distinct images, providing detailed insights into the evolving jet morphologies.To ensure the accuracy and relevance of the dataset, all ejection parameters are rigorously documented and included. The dataset thus serves as a valuable resource for researchers seeking to explore the dynamics of large-amplitude Rayleigh-Plateau instability in CIJ printing. Its comprehensiveness and diversity make it particularly suitable for the application of novel machine learning and deep-learning approaches, enabling the study of jet morphological evolution beyond the confines of classical Rayleigh's theory. This dataset holds promise for advancing our understanding of fluid jet dynamics and enhancing the efficiency and quality of CIJ printing processes.

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh– Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena. [ABSTRACT FROM AUTHOR]

Liquid-crystal columns were prepared and observed under microgravity aboard suborbital TEXUS rocket flights. The microgravity phase of each flight lasted for approximately six minutes. We tested structures in different liquid-crystalline mesophases. In the isotropic and nematic phases, the Rayleigh-Plateau instability led to the collapse of the columns. However, in the smectic A and C mesophases, it was found that the columns survived the extension to slenderness ratios (length/diameter) of over 4.5 (and in one case, more than 6). The liquid-crystalline material in the millimeter-sized columns was macroscopically disordered. Thus, regular shell-like internal layer structures that stabilized the columns can be excluded. Instead, the reason for their persistence was the yield stress of the material, which is quite different for the different mesophases. In the columnar mesophase, the cylindrical bridge even survived the strong deceleration when the rocket re-entered the atmosphere. During the breakup of the filaments, the neck thinning dynamics were determined. [ABSTRACT FROM AUTHOR]

Direct contact heat exchangers based on wetted string columns offer an intriguing alternative to packed beds and spray columns. We experimentally examine the flow and heat transfer characteristics of thin liquid films flowing down strings of a diameter approximately 1 mm against a counterflowing air stream. Numerical simulations are also performed to help interpret and validate our experimental results. The Rayleigh-Plateau instability caused by interplay among surface tension, gravity, and viscous forces leads to the formation of uniformly spaced drop-like liquid beads traveling down a string. The liquid mass flow rate and also the nozzle radius influence the radius and spatial/temporal frequency of liquid beads. Aerodynamic drag exerted by the counterflowing air stream deforms liquid beads. The relationship between flow characteristics and heat transfer effectiveness are examined experimentally for different combinations of the air velocities, liquid mass flow rates, and nozzle radii. We show that the liquid mass flow rate and the air velocity are two primary factors influencing heat transfer effectiveness whereas details of the liquid flow instability affect local bead-to-air heat transfer coefficients. We also compare the heat transfer effectiveness and the pressure drop between a wetted string column that consists of an array of vertical strings and a well-established structured packing that consists of vertical plates. The wetted string column is shown to deliver comparable heat transfer performance but at a lower air pressure drop than the structured packing. The present work helps improve our understanding of the flow and heat transfer performance of string-based direct-contact heat exchangers and helps build a foundation for their systematic design and optimization.

Direct contact heat exchangers based on wetted string columns offer an intriguing alternative to packed beds and spray columns. We experimentally examine the flow and heat transfer characteristics of thin liquid films flowing down strings of a diameter approximately 1 mm against a counterflowing air stream. Numerical simulations are also performed to help interpret and validate our experimental results. The Rayleigh-Plateau instability caused by interplay among surface tension, gravity, and viscous forces leads to the formation of uniformly spaced drop-like liquid beads traveling down a string. The liquid mass flow rate and also the nozzle radius influence the radius and spatial/temporal frequency of liquid beads. Aerodynamic drag exerted by the counterflowing air stream deforms liquid beads. The relationship between flow characteristics and heat transfer effectiveness are examined experimentally for different combinations of the air velocities, liquid mass flow rates, and nozzle radii. We show that the liquid mass flow rate and the air velocity are two primary factors influencing heat transfer effectiveness whereas details of the liquid flow instability affect local bead-to-air heat transfer coefficients. We also compare the heat transfer effectiveness and the pressure drop between a wetted string column that consists of an array of vertical strings and a well-established structured packing that consists of vertical plates. The wetted string column is shown to deliver comparable heat transfer performance but at a lower air pressure drop than the structured packing. The present work helps improve our understanding of the flow and heat transfer performance of string-based direct-contact heat exchangers and helps build a foundation for their systematic design and optimization.

The so-called Rayleigh-Plateau instability of fluid jets has been widely studied and is extensively used in the Continuous InkJet (CIJ) printing process. The present dataset contains the numerically-generated interfaces of Newtonian fluids jets in CIJ jetting conditions for low to moderately high stimulation amplitudes. We used Basilisk, an open-source Computational Fluid Dynamics (CFD) software specialized in multiphase flow to compute thousands of jets of fluids for Reynolds numbers ranging from 100 to 1000. The dataset gives raw data of CFD simulations liquid-air interfaces, for each Reynolds – stimulation amplitude pair. The present 10 GB dataset contains ≈110000 interfaces which allows to use novel machine learning and deep-learning approaches to explore jet morphologies evolution that can’t be addressed with the classical Rayleigh’s theory.

The evolution of the capillary breakup of a liquid jet under large excitation amplitudes in a parameter regime relevant to inkjet printing is analysed using three-dimensional numerical simulations. The results exhibit a reversal of the breakup length of the jet occurring when the velocity scales associated with the excitation of the jet and surface tension are comparable, and an inversion of the breakup from front-pinching to back-pinching at sufficiently large excitation amplitudes. Both phenomena are shown to be associated with the formation of vortex rings and a local flow obstruction inside the jet, which modify the evolution of the jet by locally reducing or even reversing the growth of the capillary instability. Hence, this study provides a mechanism for the well-known breakup reversal and breakup inversion, which are both prominent phenomena in inkjet printing. An empirical similarity model for the reversal breakup length is proposed, which is shown to be valid throughout the considered range of characteristic parameters. Hence, even though the fluid dynamics observed in capillary jet breakup with large excitation amplitudes are complex, the presented findings allow an accurate prediction of the behaviour of jets in many practically relevant situations, especially continuous inkjet printing. [ABSTRACT FROM AUTHOR]

The instability of a freely falling jet of liquid in air taking into account the viscosity of the contacting media is considered. In neglecting the viscosities of both media, instability was studied by Rayleigh and Plateau. They showed that instability develops as a result of the action of surface forces, and is expressed in a change in the cylindrical shape of the boundary of a freely falling jet of liquid with air into a sequence of spherical drops. In subsequent works, by phenomenological consideration of viscosity by means of the Ohnesorge number, it is shown that the viscosity of each of the contacting media affects the nature of the instability. However, this method of taking viscosity into account is not entirely correct, because does not take into account the specificity of the boundary conditions existing at the interface. It is proposed to use percolation boundary conditions, the validity of which is proved by the example of the exact determination of the threshold velocity of occurrence of Kelvin-Helmholtz instability. A dispersion equation of the Rayleigh-Plateau problem with percolation boundary conditions that describes the instability taking into account the viscosity of both media is obtained. The dissipative nature of the development of such instabilities is substantiated. The growth rates of instabilities are determined in cases when: the jet and medium have a low viscosity (ideal fluids); the jet is characterized by high viscosity, and the environment is small; the jet and the environment are highly viscous. It is shown that the theoretical model of droplet decay of the jet in the absence of viscosity of both media is quite good, in quantitative terms, consistent with experimental results. The maximum increment is equal γmaxKGγ≈0.32, against the Rayleigh-Plateau increment γmaxKGγ≈0.34, for disturbances with the same wave number XMAX≈0.37. It was also shown that for viscous jets and a weakly viscous environment, the instability increment describes the experimental results with a rather high degree of accuracy. Numerical calculations show that for jets of comparable viscosity, the instability increment decreases with increasing viscosity of the environment. If the viscosity of the environment is constant, then the increment of instability will be greater where the viscosity of the stream is higher. It is shown that the results of theoretical calculations are in good agreement with the available experimental data.

Liquid-crystal columns were prepared and observed under microgravity aboard suborbital TEXUS rocket flights. The microgravity phase of each flight lasted for approximately six minutes. We tested structures in different liquid-crystalline mesophases. In the isotropic and nematic phases, the Rayleigh-Plateau instability led to the collapse of the columns. However, in the smectic A and C mesophases, it was found that the columns survived the extension to slenderness ratios (length/diameter) of over 4.5 (and in one case, more than 6). The liquid-crystalline material in the millimeter-sized columns was macroscopically disordered. Thus, regular shell-like internal layer structures that stabilized the columns can be excluded. Instead, the reason for their persistence was the yield stress of the material, which is quite different for the different mesophases. In the columnar mesophase, the cylindrical bridge even survived the strong deceleration when the rocket re-entered the atmosphere. During the breakup of the filaments, the neck thinning dynamics were determined.

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. [ABSTRACT FROM AUTHOR]

Elastic tubes can experience surface instabilities when compressed beyond a critical strain, referred to as Wilkes instability herein. Soft materials may undergo the Rayleigh–plateau instability which is driven by surface tension. However, the surface instability of soft elastic tubes can be impeded by the coexistence of axial compression and surface tension. In this paper, we adopted an analytical framework for predicting the surface instability of an incompressible tube accounting for both axial loading and surface tension. A general solution in a mixed cylindrical coordinate is derived for determining isochoric transformations based on energy variational method. A linear perturbation analysis was performed to find out the critical elasto-capillary number and axial stretch for the onset of the instability. Cylindrical tubes with different thickness, i.e., the ratio of outer to inner radii, are investigated. We find that thinner tubes are more likely to experience surface instability than thicker ones, as validated by finite element simulations. We conclude that a compressive strain could prevent the Rayleigh–plateau instability induced by surface tension, while stretching will favor it. Similarly, the surface tension behaves as a barrier to the formation of compression-induced Wilkes instability. [ABSTRACT FROM AUTHOR]

The Rayleigh-Plateau instability, a phenomenon of paramount significance in fluid dynamics, finds widespread application in the Continuous InkJet (CIJ) printing process. This study presents a comprehensive dataset comprising experimental investigations of fluid jet breakup phenomena under large-amplitude stimulation conditions using an industrial CIJ print-head from Markem-Imaje. Unlike previous studies, this dataset encompasses a diverse range of experimental conditions, including nine different Newtonian fluids with meticulously measured rheological properties (viscosities, surface tensions and densities). The applied stimulation amplitudes vary from 5V to 45V, representing a substantial span of excitation levels. The experimental setup captures the intricate dynamics of fluid jets subjected to these varying conditions, producing a rich collection of over 5,000 high-resolution images depicting the breakup phenomena. Each amplitude of stimulation and fluid type yields more than 55 distinct images, providing detailed insights into the evolving jet morphologies. To ensure the accuracy and relevance of the dataset, all ejection parameters are rigorously documented and included. The dataset thus serves as a valuable resource for researchers seeking to explore the dynamics of large-amplitude Rayleigh-Plateau instability in CIJ printing. Its comprehensiveness and diversity make it particularly suitable for the application of novel machine learning and deep-learning approaches, enabling the study of jet morphological evolution beyond the confines of classical Rayleigh's theory. This dataset holds promise for advancing our understanding of fluid jet dynamics and enhancing the efficiency and quality of CIJ printing processes., (© 2024 The Authors. Published by Elsevier Inc.)

Highlights • The instability is enhanced by the van der Waals attractions and Marangoni effect. • The Marangoni effect does not cause the breakup and the film thins as t −1 without van der Waals attractions. • The film thins as Δ t 1/5 due the van der Waals attractions, which ruptures in finite time. Abstract An ultra-thin liquid film flowing down a vertical uniformly heated cylinder under the influence of gravity is investigated. A thin liquid film model is derived, assuming that the film thickness h is much smaller than the fiber radius a. To predict the breakup of film, the van der Waals attraction, proportional to h - 3 , is taken into account. Linear stability analysis shows that the Rayleigh-Plateau instability is enhanced by the long-range attractions and Marangoni effect. The spatial-temporal stability analysis shows that the instability is absolute when A + M > 0.17 (A is a composite Hamaker number accounting for the strength of van der Waals attractions and M is the Marangoni number). A self-similarity analysis shows that the film thins as h ∼ (t r - t) 1 / 5 ( t r is the breakup time), which is supported by the numerical simulations of the thin film model. Although the scaling is independent on the Marangoni effect, nonlinear simulations demonstrate that the breakup time t r decreases as the Marangoni effect becomes stronger, demonstrating that the breakup process is accelerated by the Marangoni effect. Nonlinear simulation also shows that the thin heated or non-heated film mainly breaks up in the absolutely unstable regime. [ABSTRACT FROM AUTHOR]

Highlights • An experimental apparatus is set up to investigate melt jet breakup in water. • Drop-shaped leading edges are formed in the air before penetration into water. • Rayleigh-Plateau instability appears and even pinches jet column into segments. • Rayleigh-Plateau instability has the dominant effect on melt jet column breakup. Abstract In the present study, an experimental apparatus is set up to investigate the characteristics and mechanism of melt jet breakup in water in the premixing phase of fuel-coolant interaction during nuclear reactor severe accident. Wood's metal is used as the simulant material. The melt jet breakup experiments are conducted under different jet diameters, melt temperatures, water temperatures and penetration velocities. The breakup process is recorded by a high speed video camera. The characteristics of the breakup of the leading edge and the jet column are analyzed in detail. It is concluded that Rayleigh-Plateau instability has the dominant effect on the melt jet column breakup in water. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the capillarity-driven evolution of a solid toroidal island on a flat rigid substrate, where mass transport is controlled by surface diffusion. This problem is representative of the geometrical complexity associated with the solid-state dewetting of thin films on substrates. We apply Onsager's variational principle to develop a general approach for describing surface diffusion-controlled problems. Based on this approach, we derive a simple, reduced-order model and obtain an analytical expression for the rate of island shrinking and validate this prediction by numerical simulations based on a full, sharp-interface model. We find that the rate of island shrinking is proportional to the material constants B and the surface energy density γ 0 , and is inversely proportional to the island volume V 0 . This approach represents a general tool for modeling interface diffusion-controlled morphology evolution. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

Abstract 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. Graphical abstract Image 1 Highlights • Drawing process induces various morphologies of nanoparticles in fibers. • Particles as long as 300 μm detected by X-ray nanotomography. • The composition changes the morphology of the elongated particles. • Rayleigh-Plateau instability threshold depends on the composition. • Higher drawing tensions favor particle break-up. [ABSTRACT FROM AUTHOR]

Silver nanomaterials (AgNMs) have been applied as antibacterial agents to combat bacterial infections that can cause disease and death. The antibacterial activity of AgNMs can be improved by increasing the specific surface area, so significant efforts have been devoted to developing various bottom-up synthesis methods to control the size and shape of the particles. Herein, we report on a facile heat-treatment method that can improve the antibacterial activity of transparent silver nanowire (AgNW) films in a size-controllable, top-down manner. AgNW films were fabricated via spin-coating and were then heated at different temperatures (230 and 280 °C) for 30 min. The morphology and the degree of oxidation of the as-fabricated AgNW film were remarkably sensitive to the heat-treatment temperature, while the transparency was insensitive. As the heat-treatment temperature increased, the AgNWs spontaneously broke into more discrete wires and droplets, and oxidation proceeded faster. The increase in the heat-treatment temperature further increased the antibacterial activity of the AgNW film, and the heat treatment at 280 °C improved the antibacterial activity from 31.7% to 94.7% for Staphylococcus aureus, and from 57.0% to 98.7% for Escherichia coli. Following commonly accepted antibacterial mechanisms of AgNMs, we present a correlation between the antibacterial activity and surface observations of the AgNW film.

We report the observation of a crown-like sheet expansion and its subsequent atomization in burning multi-component fuel droplets. The droplets consisting of constituents with significant volatility differential are chosen in this study. Through homogeneous nucleation, the breakup of high-pressure vapor bubble results in the formation of radially expanding crown-like hemispherical sheet. The expansion of liquid sheet and the development of radial ligaments on its destabilized rim results in the creation of several secondary droplets. This pattern of breakup bears a close resemblance to the universally recognized Worthington-Edgerton crown configuration, which forms when a liquid droplet impact on a deep pool/thin film of same liquid or another liquid. Two distinct modes of liquid sheet fragmentation are identified during the experiments: (i) unstable sheet fragmentation and (ii) stable sheet fragmentation. In particular, the breakup characteristics of stable sheet mode is comparable to the commonly observed crown breakup by drop impingements. The modes of sheet breakup are primarily influenced by the proportion of volatile component in the mixture, which in turn dictates the onset of fragmentation and the intensity of breakup. [ABSTRACT FROM AUTHOR]

The effect of the operating pressure on the droplet formation dynamics of a molten laminar jet was studied using a high-speed camera. A melt was formed in a platinum alloy crucible at 1380 °C, after which a pressure was applied to the system to form a jet through a 300 μm nozzle. The molten jet breaks up into droplets as described by the Plateau-Rayleigh theory, which are then solidified using liquid nitrogen to form small ceramic spheres. A high-speed camera was positioned directly below the nozzle to obtain footage for a full range of operating pressures at 3500 frames per second, which was then analysed using image processing methods. An optimum operating pressure was found at which the desired instabilities grow the fastest and the variance between the droplet spacing is at a minimum. This resulted in an increased yield and a narrower size distribution of the final product. [ABSTRACT FROM AUTHOR]

Fingering of an inviscid liquid droplet upon impact on a super-hydrophobic surface is revisited. Generation of coronal fingers is investigated here using a transverse rim instability analysis based on the toroidal curvature of rim, instead of the linear front assumption in the classical Rayleigh-Plateau (R-P) model. The governing equations are formulated from the first principles and solved numerically. For a droplet with a known volume and impact velocity, the model predicts the number of spires upon impact, k. Here k is found to be the largest wave number with a positive growth rate on the droplet rim and is shown to be in the order of (Weber)3/5. The theoretical model is consistent with our water droplet experiments for 60 < We < 160, superseding the R-P prediction. [ABSTRACT FROM AUTHOR]

The dynamics of a viscous film flowing down a vertical fibre under the action of gravity and the thermocapillarity induced by an axial temperature gradient is investigated theoretically. The instability of this exterior coating flow is driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity. We derived an evolution equation for the interface in the framework of the long wave approximation. A linear stability analysis and a nonlinear simulation are performed to investigate the influence of the thermocapillarity on the dynamics of axisymmetric disturbances. The results of linear stability showed that the thermocapillarity does not influence the growth rate of the disturbance and only affects its frequency. For the nonlinear evolution, the thermocapillarity plays an important role in influencing the profile of the interface in different flow regimes. We also examined the effect of thermocapillarity on the wave speed and the characteristics of the structures of travelling wave solutions. [ABSTRACT FROM AUTHOR]

In this series of articles, the author discusses various phenomena in fluid dynamics, which may be investigated via tabletop experiments using low-cost or home-made instruments. The fifteenth article in this series demonstrates some fluid instabilities. [ABSTRACT FROM AUTHOR]

The article discusses the linear stability analysis study undertaken with regard to investigating the influence of insoluble surfactant on the Rayleigh-Plateau (RP) instability and the Rayleigh-Taylor (RT) instability, as part of analyzing the flow of thin liquid films on rotating cylinders.

The linear stability analysis is carried out for the straight jet of a polymer melt in an electrospinning process. The stability of axisymmetric disturbances is examined in order to comprehend the onset of fiber morphology with diametric variations or bead formation along the fiber under non-isothermal electrospinning conditions. As the polymeric fluid (polylactic acid melt) is a low conductivity fluid with unentangled polymer molecules, the viscoelasticity is described using the non-linear rheological Giesekus constitutive model assuming very small axial conduction current. The non-periodic axisymmetric disturbances are imposed on the non-uniform radius jet, obtained as the solution of the 1-D slender filament governing equations and the eigenspectrum for the disturbance growth rate is constructed under the realistic melt electrospinning conditions. The growth rate corresponding to the leading mode in the eigenspectrum is found to increase with increasing surface tension forces and decrease with the enhanced external electric field. Thus, the leading growth rate behavior suggests that the classical Rayleigh–Plateau instability dominates over the conducting mode of instability for melt electrospinning. Further, the role of non-isothermal conditions in the stability behavior is examined. The convective heat transfer from electrified jet to the cooling ambiance leads to thicker fibers with greater stability to axisymmetric disturbances. The stabilizing effect of heat transfer is attributed mainly to the temperature sensitive fluid rheology. In particular, the enhancement in polymer viscosity in the jet propagation direction is responsible for the build up of stabilizing viscoelastic stress. The fluid elasticity, denoted by the flow Deborah number, also tends to stabilize the electrified jet as temperature drop along the flow increases the relaxation time of the polymer chains leading to high polymeric stress associated with the stretched chains. As crystallization of polymeric chains under non-isothermal condition is not considered, the analysis holds for either amorphous polymers or polymers with slow crystallization kinetics compared to the short residence time during the spinning flow. [ABSTRACT FROM AUTHOR]

Atomic multipole moments associated with a spherical volume fully residing within a topological atom (i.e., the β sphere) can be obtained analytically. Such an integration is thus free of quadrature grids. A general formula for an arbitrary rank spherical harmonic multipole moment is derived, for an electron density comprising Gaussian primitives of arbitrary angular momentum. The closed expressions derived here are also sufficient to calculate the electrostatic potential, the two types of kinetic energy, as well as the potential energy between atoms. Some integrals have not been solved explicitly before but through recursion and substitution are broken down to more elementary listed integrals. The proposed method is based on a central formula that shifts Gaussian primitives from one center to another, which can be derived from the well‐known plane‐wave expansion (or Rayleigh equation). © 2018 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Toroidal droplets in a viscous liquid are unstable and transform into single or multiple spherical droplets. For thin tori, this can happen via the Rayleigh-Plateau instability causing the breakup of cylindrical jets. In contrast, for thick tori, this can happpen via the shrinking of the "hole". In this work, we use the thin-torus limit to directly measure the growth rate associated with capillary disturbances. In the case of toroidal droplets inside a much more viscous liquid, we even obtain the full dispersion relation, which is in agreement with theoretical results for cylindrical jets. For thick tori, we employ particle image velocimetry to determine the flow field of a sinking toroidal drop inside another viscous liquid. We find that the presence of the "hole" greatly suppresses one of the circulation loops expected for sinking cylinders. Finally, using the flow field of a shrinking toroidal droplet and the time-reversal symmetry of the Stokes equations, we theoretically predict the expected shape deformation of an expanding torus and confirm the result experimentally using charged toroidal droplets. [ABSTRACT FROM AUTHOR]

By imposing vibration to a core-annular flow of an aqueous two-phase system (ATPS) with ultralow interfacial tension, we observe a liquid finger protruding from the interface of an expanding jet. We find that the protruded finger breaks up only when its length-to-width ratio exceeds a threshold value. The breakup follows a constant wavelength-to-width ratio that is consistent with that of breakup under Rayleigh-Plateau instability. The mechanism is applicable to aqueous two-phase systems with a large range of viscosity ratios. The protruded finger can break up into small droplets that are monodisperse in size, controllable in generation frequency under a wide range of flow rates. This work suggests a way to generate small water-water droplets with high monodispersity and production rate from a single nozzle. [ABSTRACT FROM AUTHOR]

Metal nanoparticle arrays are excellent candidates for a variety of applications due to the versatility of their morphology and structure at the nanoscale. Bottom-up self-assembly of metal nanoparticles provides an important complementary alternative to the traditional top-down lithography method and makes it possible to assemble structures with higher-order complexity, for example, nanospheres, nanocubes, and core–shell nanostructures. Here we present a mechanism study of the self-assembly process of 1-D noble metal nanoparticles arrays, composed of Au, Ag, and AuAg alloy nanoparticles. These are prepared within an encapsulated germanium nanowire, obtained by the oxidation of a metal–germanium nanowire hybrid structure. The resulting structure is a 1-D array of equidistant metal nanoparticles with the same diameter, the so-called nanobead (NB) array structure. Atom-probe tomography and transmission electron microscopy were utilized to investigate the details of the morphological and chemical evolution during the oxidation of the encapsulated metal–germanium nanowire hybrid-structures. The self-assembly of nanoparticles relies on the formation of a metal–germanium liquid alloy and the migration of the liquid alloy into the nanowire, followed by dewetting of the liquid during shape-confined oxidation where the liquid column breaks-up into nanoparticles due to the Plateau–Rayleigh instability. Our results demonstrate that the encapsulating oxide layer serves as a structural scaffold, retaining the overall shape during the eutectic liquid formation and demonstrates the relationship between the oxide mechanical properties and the final structural characteristics of the 1-D arrays. The mechanistic details revealed here provide a versatile tool-box for the bottom-up fabrication of 1-D arrays nanopatterning that can be modified for multiple applications according to the RedOx properties of the material system components. [ABSTRACT FROM AUTHOR]

• Revealing the Rayleigh-Plateau instability alters the flow regime of falling-films • Increasing the number of mesh cells across the jet depicts the Rayleigh instability • Additional falling satellite droplets enhance the film waviness of a liquid film • Contact angles more than 90° no longer display falling-film flow • Greater film thinning and mixing increases local heat transfer coefficient of film Falling-film heat exchangers are widely used to promote heat and mass transport within industrial environments. In contemporary condensers, for example, liquid films continuously form over a tube row and impact multiple tubes beneath, resulting in a rich variety of two-phase flow phenomena, including the classical Rayleigh-Plateau instability. It is widely known that altering the contact angle of the tubes influences the heat exchangers' heat and mass transfer characteristics by changing the falling films' flow behaviour (i.e. dropwise or jet). Therefore, resolving interfacial flow characteristics, such as the Rayleigh-Plateau instability, is crucial for falling film studies as this instability may change the state of the falling film from being jet flow to dropwise/jet flow or even just dropwise. To explore this aspect, three-dimensional direct numerical simulations are used in the present work to replicate the jet instability behaviour. By employing certain mesh refinement strategies demonstrated from various case studies, the interfacial flow behaviour and jet instability have been captured, showing good agreement with experimental and theoretical data previously published. This is determined from the increased jet bifurcation and a maximum error of 2.2% of the film thickness in comparison to Nusselt's result within the bulk region of the tube. In addition, the average and local heat transfer coefficients across the first tube were compared with numerical solutions to give an average error of 3.2 and 14 %. Jet instability is found to be directly related to the amplitude of the axial pressure variations which is augmented by the growth rate of the capillary wave that travels upstream. Specifically, for contact angles of 30 and 60°, the flow is in a dropwise and dropwise/jet state due to the emergence of the Rayleigh-Plateau instability. Notably, the additional satellite droplets that materialize from the unstable jet lead to an increase in the local heat transfer coefficient of the film compared to without the Rayleigh instability improvement. [ABSTRACT FROM AUTHOR]

We consider the motion of a gravity-driven flow down a uniformly heated vertical fibre. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity at the interface. A spatio-temporal stability analysis is performed to investigate the effect of thermocapillarity (Marangoni effect) on the convective/absolute instability (CI/AI) characteristics of the problem. We also performed a numerical simulation of Eq. (30) on the nonlinear evolution of the film to connect the breakup behaviours with the CI/AI characteristics. Our numerical results showed that for various Marangoni number ( Ma ), breakup of the film mainly occurs in the AI regime. With the increase of Ma , the film has a tendency to break up into droplets due to the enhancement of the absolute instability. [ABSTRACT FROM AUTHOR]

ABSTRACT Facile microscale patterning of ferroelectric P(VDF-TrFE) thin films are presented. Simple spin-coating of the polymer solution on a patterned stamp has led to a variety of features due to the topographic dewetting. The effects of important experimental parameters, such as polymer solution concentration, spin speed, and stamp geometry, are systematically examined and the results are presented as morphological phase diagrams. Further, the dewetted cylindrical lines on the stamp protrusions are found to undergo Rayleigh-Plateau instability, which leads to the break-up of lines into dots in a row. The various pattern features formed on structured stamp has then been successfully transfer-printed onto various substrates such as Si, glass, polymers. The P(VDF-TrFE) micropatterns have shown more uniform ferroelectric performances than those of unpatterned film, due likely to confinement effect. The proposed simple patterning and transfer-printing of ferroelectric polymer thin films can be found very useful in various emerging applications. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 45028. [ABSTRACT FROM AUTHOR]

Considerable recent research has focused on the ability of microstructured fibers to exhibit diverse optical functionalities. However, accurately preserving the structure imposed at the preform stage after drawing it down to fiber, while avoiding Rayleigh–Plateau style instabilities, has proven to be a major fabrication challenge. This modeling/analytical study was carried out in support of an experimental program into possible fabrication options for various microstructured optical fibers and considers the generic case of the nonisothermal drawing of a capillary preform to fiber. Model development was carried out in two stages. Initially, a fully conjugate multiphase model, which includes all heat transfer modes within an operational fiber drawing furnace, was validated against available experimental data. To evaluate the external radiative heat flux using the net-radiation method, a Monte Carlo ray-tracing (MC-RT) method was coupled to the commercial POLYFLOW package to obtain all view factors between the various furnace walls and the deforming preform/fiber. A simplified model was also developed (to shorten simulation run times) by explicitly calculating the convective heat transfer between the air within the furnace and the preform/fiber surface using a heat transfer coefficient determined by matching predicted results with those obtained from the multiphase model. [ABSTRACT FROM AUTHOR]

In this paper, we present a dynamic microfluidic tensiometer able to perform measurements over more than four decades and which is suitable for high throughput experimentations. This tensiometer is able to withstand hard conditions such as high pressure, high temperature, high salinity, and crude oil. It is made of two coaxial capillaries in which two immiscible fluids are injected. Depending on the flow rate of each phase, either droplets or jetting will be obtained. The transition between these two regimes relies on the Rayleigh-Plateau instability. This transition can be theoretically computed thanks to a linear analysis based on the convective and absolute instabilities theory. From this model, the interfacial tension between the two phases can be calculated. [ABSTRACT FROM AUTHOR]

Electrospun core-shell fibers have great potentials in many areas, such as tissue engineering, drug delivery, and organic solar cells. Although many core-shell fibers have been prepared and studied, the morphology transformation of core-shell fibers have been rarely studied. In this work, the morphology evolution of electrospun core-shell polymer fibers driven by the Plateau-Rayleigh instability is investigated. Polystyrene/poly(methyl methacrylate) (PS/PMMA) core-shell fibers are first prepared by using blend solutions and a single axial electrospinning setup. After PS/PMMA core-shell fibers are annealed on a PS film, the fibers undulate and sink into the polymer film, forming core-shell hemispheres. The evolution process, which can be observed in situ by optical microscopy, is mainly driven by achieving lower surface and interfacial energies. The morphologies of the transformed structures can be confirmed by a selective removal technique, and polymer microbowls can be obtained. [ABSTRACT FROM AUTHOR]

Using a microfluidic multi-inlet coflow system, we show the Rayleigh-Plateau instability of adjacent, closely spaced fluid threads to be collective. Although droplet size distributions and breakup frequencies are unaffected by cooperativity when fluid threads are identical, breakup frequencies and wavelengths between mismatched fluid threads become locked due to this collective instability. Locking narrows the size distribution of drops that are produced from dissimilar threads, and thus the polydispersity of the emulsion. These observations motivate a hypothesized two-step mechanism for high internal phase emulsification, wherein coarse emulsion drops are elongated into close-packed fluid threads, which break into smaller droplets via a collective Rayleigh Plateau instability. Our results suggest that these elongated fluid threads break cooperatively, whereupon wavelength-locking reduces the ultimate droplet polydispersity of high-internal phase emulsions, consistent with experimental observations. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence of infinitely many non-singular subharmonic solutions, as well as the presence of complex dynamics, for the equation with singularity u ¨ + g 1 u β − g 2 u γ = h 0 ( t ) u δ , where h 0 ( t ) is a T -periodic stepwise function. Our result is stable with respect to small perturbations and can be applied to the Rayleigh–Plesset equation governing the dynamics of a bubble immersed in an infinite domain of liquid. [ABSTRACT FROM AUTHOR]

This paper reports an experimental and theoretical study of the dynamics of microbubbles flattened between the two walls of a microfluidic channel. Using a micropit, a single bubble is trapped by capillarity at a specific position in the channel and its oscillation under ultrasound is observed by stroboscopy. It is shown that the bubble dynamics can be described by a two-dimensional Rayleigh-Plesset equation including the deformation of the walls of the channel and that the bubble behaves as a secondary source of Rayleigh waves at the wall interface. Above a critical pressure threshold, the bubble exhibits a two-dimensional shape oscillation around its periphery with a period doubling characteristic of a parametric instability. We report how each shape mode appears, varying the bubble radius and the amplitude of excitation, and demonstrate that the wall deformation has no significant effect on their dynamics. [ABSTRACT FROM AUTHOR]

In the paper a novel system for drop-on-demand (DoD) generation from a metal wire is presented, whose main component is a newly developed laser droplet generation head, consisting of annular laser beam shaping optics and a wire feeding system. In the pendant droplet formation phase of the DoD generation, a laser pulse is used to melt the wire-end, which is fed into the focus of an annular laser beam. The formed pendant droplet is then detached by means of a detachment pulse, which induces Rayleigh–Plateau instability of the molten column of wire above the neck of the pendant droplet. The main process parameters, including the laser pulse and wire feeding parameters as well as the additional parameters which influence particular phases of the DoD generation process, have been identified. The empirical correlations between the influencing process parameters and the droplet characteristics, including droplet diameter and temperature, were determined, based on the analysis of high speed IR records of the process, images being acquired by an optical microscope and temperature data being acquired by pyrometers. As an example, DoD generation from a commercially pure 99.6% Ni wire (Nickel 200) of 0.6 mm diameter is considered. It is shown that droplets with diameters ranging from 0.85 to 1.25 mm can be generated, with a resolution of 50 μm and a standard deviation of 15 μm. The temperature of the detached droplet remains above the melting point of the Ni wire, and increases with the droplet diameter within the range from 1650 to 1750 °C. Some examples of Ni droplets deposited on a Ti sheet surface are presented, with the aim of demonstrating the capability of the proposed system, and motivating further applications in which drops on demand having a high temperature and a precisely defined diameter need to be generated, while limiting the thermal loading of the surroundings. [ABSTRACT FROM AUTHOR]

We carry out experimental and numerical studies to investigate the collapse and breakup of finite size, nano- and microscale, liquid metal filaments supported on a substrate. We find the critical dimensions below which filaments do not break up but rather collapse to a single droplet. The transition from collapse to breakup can be described as a competition between two fluid dynamic phenomena: the capillary driven end retraction and the Rayleigh-Plateau type instability mechanism that drives the breakup. We focus on the unique spatial and temporal transition region between these two phenomena using patterned metallic thin film strips and pulsed-laser-induced dewetting. The experimental results are compared to an analytical model proposed by Driessen et al. and modified to include substrate interactions. In addition, we report the results of numerical simulations based on a volume-of-fluid method to provide additional insight and highlight the importance of liquid metal resolidification, which reduces inertial effects. [ABSTRACT FROM AUTHOR]

The impact of droplets on a deep pool has applications in cleaning up oil spills, spray cooling, painting, inkjet printing, and forensic analysis, relying on the changes in properties such as viscosity, interfacial tension, and density. Despite the exhaustive research on different aspects of droplet impact, it is not clear how liquid properties can affect the instabilities leading to Rayleigh jet breakup and number of daughter drops formed after its pinch-off. In this article, through systematic experiments we investigate the droplet impact phenomena by varying viscosity and surface tension of liquids as well as impact speeds. Further, using numerical simulations, we show that Rayleigh-Plateau instability is influenced by these parameters, and capillary time scale is the appropriate scale to normalize the breakup time. Based on Ohnesorge number (Oh) and impact Weber number (We), a regime map for no breakup, Rayleigh jet breakup, and crown splash is suggested. Interestingly, crown splash is observed to occur at all Ohnesorge numbers; however, at high Oh, a large portion of kinetic energy is dissipated, and thus the Rayleigh jet is suppressed regardless of high impact velocity. The normalized required time for the Rayleigh jet to reach its peak varies linearly with the critical height of the jet. [ABSTRACT FROM AUTHOR]

The dispersion relation of a confined capillary jet with negligible inertia is measured by Fourier analysis of the jet radius. The real part of the dispersion relation, obtained through the spatiotemporal Fourier spectrum, demonstrates that the phase velocity is independent of the perturbation frequency, at least in the accessible range of frequencies. The imaginary part of the dispersion relation, i.e., the spatial growth rate, is frequency dependent. To measure this dependence, an external forcing is used to amplify modes with different frequencies. The spatial growth rate is then obtained from the exponential growth of the corresponding Fourier mode. The phase velocity and the spatial growth rate are found to increase and decrease, respectively, with the capillary number and to depend only weakly on the degree of confinement. These observations are consistent with a spatialinstability that convects the perturbations downstream with velocity proportional to the capillary number. The frequency of the dominant mode in the absence of forcing, on the contrary, depends mainly on the degree of confinement, i.e., on the jet diameter, and only weakly on the capillary number, which is consistent with the mode selection of the Rayleigh-Plateau instability. Experimental measurements are compared to predicted dispersion relations reported in the literature, and good qualitative agreement is observed. [ABSTRACT FROM AUTHOR]

A fundamental process of surface energy minimization is the decay of a wire into separate droplets initiated by the Rayleigh-Plateau instability. Here we study the linear stability of a wire deposited on a unidirectionally patterned substrate with the wire being aligned with the pattern. We show that the wire is stable when a criterion that involves its width and the local geometry of the substrate at the triple line is fulfilled. We present this criterion for an arbitrary shape of the substrate and then give explicit examples. Our result is rationalized using a correspondence between the Rayleigh-Plateau instability and the spinodal decomposition. This work provides a theoretical tool for an appropriate design of the substrate's pattern in order to achieve stable wires of, in principle, arbitrary widths. [ABSTRACT FROM AUTHOR]

In this work, the influence of the initial geometry on the evolution of a fluid filament deposited on a substrate is studied, with a particular focus on the thin fluid strips of nano-scale thickness. Based on the analogy to the classical Rayleigh-Plateau (R-P) instability of a free-standing fluid jet, an estimate of the minimal distance between the final states (sessile droplets) can be obtained. However, this numerical study shows that while the prediction based on the R-P instability mechanism is highly accurate for an initial perturbation of a sinusoidal shape, it does not hold for a rectangular waveform perturbation. The numerical results are obtained by directly solving fully three-dimensional Navier-Stokes equations, based on a Volume of Fluid interface tracking method. The results show that (i) rectangular-wave perturbations can lead to the formation of patterns characterized by spatial scales that are much smaller than what is expected based on the R-P instability mechanism; (ii) the nonlinear stages of the evolution and end states are not simply related, with a given end state resulting from possibly very different types of evolution; and (iii) a variety of end state shapes may result from a simple initial geometry, including one- and two-dimensional arrays of droplets, a filament with side droplets, and a one-dimensional array of droplets with side filaments. Some features of the numerical results are related to the recent experimental study by Roberts et al. ["Directed assembly of one- and two-dimensional nanoparticle arrays from pulsed laser induced dewetting of square waveforms," ACS Appl. Mater. Interfaces 5, 4450 (2013)]. [ABSTRACT FROM AUTHOR]