Significance A cylindrical stream of water from a faucet breaks up into droplets due to the action of surface tension, a phenomenon known as the Rayleigh–Plateau instability. At nanometer scales, the random motion of the fluid molecules alters the instability. In this paper, we present a numerical method for studying these microscopic effects. The algorithm uses fluctuating hydrodynamics, an extension of conventional fluid dynamics that includes thermal fluctuations. Our simulations show that these fluctuations affect the shape of the tapering cylinder and hasten the pinching into droplets. We also find that short cylinders, which are stable in the absence of fluctuations, eventually also break into a droplet.

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.

Abstract Numerous experiments and theoretical calculations have shown that cylindrical vesicles can undergo a pearling instability similar to the Rayleigh–Plateau instability of a liquid jet when they are subjected to external tension. In a living cell, a Rayleigh–Plateau-like instability could be triggered by internal tension generated in the cell cortex. This mechanism has been suggested to play an essential role in biological processes such as cell morphogenesis. In contrast to the simple, passive and isotropic membrane of vesicles, the cortical tensions generated by biological cells are often strongly anisotropic. Here, we theoretically investigate how this anisotropy affects the Rayleigh–Plateau instability mechanism. We do so in the limit of both low and high Reynolds numbers and accordingly cover cell behaviour under anisotropic cortical tension as well as fast liquid jets with anisotropic surface tension. Combining analytical linear stability analysis with numerical simulations we report a strong influence of the anisotropy on the dominant wavelength of the instability: increasing azimuthal with respect to axial tension leads to destabilisation and to a shorter break-up wavelength. In addition, compared to the classical isotropic Rayleigh–Plateau situation, the range of unstable modes grows or shrinks when the azimuthal tension is higher or lower than the axial tension, respectively. We explore nonlinear effects like an altered break-up time and formation of satellite droplets under anisotropic tension. In Part 2 (Bächer et al. J. Fluid Mech., vol. xxx, 2021, Ax) of this series we continue our analysis by analytically investigating the influence of bending and shear elasticity, usually present in vesicles and cells, on this anisotropic Rayleigh–Plateau instability.

understanding surface-tension-driven flows and the physics underlying the tendency of falling liquid streams to spontaneously break into droplets. This phenomenon Capillary breakup rheometry is an experimental technique used to assess the extensional rheological response of low viscous fluids. Unlike most shear and extensional rheometers, this technique does not involve active stretch or measurement of stress or strain but exploits only surface tension to create a uniaxial extensional flow. Hence, although it is common practice to use the name rheometer, ca Capillary thinning and breakup of complex fluids can be studied using different configurations. Historically, mainly three types of free-surface conformations have been employed in experiments: statically-unstable liquid bridges, dripping from a nozzle under gravity and continuous jets. Even though the initial evolution of the capillary instability is affected by the type of conformation used, each configurations capture the same phenomenon at the last stages close to breakup, where thinning dynamics is dominated by fluid properties exclusively. The different configurations can be best distinguished based on the Weber Number, hence on the relative magnitude between the imposed velocity and the intrinsic capillary speed of the considered material, defined as the ratio between the surface tension and shear viscosity ( γ / η {\displaystyle \gamma /\eta } ). In the first geometry, the imposed velocity is zero (We=0), after an unstable liquid bridge is generated by rapid motion of two coaxial cylindrical plate. The thinning of the capillary bridge is purely governed by the interplay of inertial, viscous, elastic and capillary forces. This configuration is employed in the CaBER device and it is at present the most used…

Abstract Several small modular nuclear reactors propose to use TRISO (TRistructural ISOtropic) fuel as part of their reactor design, due to their ability to withstand higher coolant temperatures. TRISO fuel particles require the fabrication of uranium oxycarbide kernels with a diameter of approximately 0.5 mm. One of the common production processes of the TRISO kernels involves generating droplets by using a vibrating needle to dispense a uranium nitrate solution into an ammonium hydroxide solution, leading to the formation of gelled microspheres. A cylindrical liquid jet is naturally unstable due primarily to the Plateau–Rayleigh instability. When an external mechanical vibration is applied to the jet flow, it disperses into a stream of uniformly sized droplets. The droplet size is determined by the frequency and amplitude of the mechanical vibration. The main aim of this study is to investigate the effect of applying transverse vibrations to a needle issuing a stream of liquid, to break up the stream and produce uniform-sized droplets. Resonating the needle tip can influence droplet formation by enhancing the instability of the liquid at the tip, promoting the formation of droplets. As the needle vibrates at resonant frequencies, it may create oscillations in the fluid that lead to the detachment of small, uniform droplets. A prototype vibrating needle test rig was designed and constructed to study the breakup behavior of water, a Newtonian fluid, and zirconia slurry, a non

(as in water in a glass). Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled Surface tension is the energy per unit area due to having a surface in a liquid. It has the dimension of force per unit length, or energy per unit area. The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to solids. Surface tension is used for liquids, while surface stress In day-to-day life all of us observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability, which is entirely a consequence of the effects of surface tension. The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

A droplet of pure water placed on a clean glass surface will spread axisymmetrically, and a droplet of mercury will bead up into a spherical droplet. In both cases, the droplet is minimizing its surface energy – creating an object with a minimized surface area – and there is nothing to break the symmetry. Remarkably, droplets of the room-temperature liquid gallium-indium (EGaIn), which like all metals have an enormous surface tension, can nonetheless undergo fingering instabilities in the presence of an oxidizing voltage. I will describe how this oxide acts like a reversible surfactant, generating fingering instabilities, tip-splitting, and even fractals, through Marangoni instabilities. Remarkably, we find that EGaIn droplets placed in an electrolyte under an applied voltage can achieve near-zero surface tension. This effect can in turn be used to suppress the Rayleigh-Plateau instability in falling streams. Quantitative control of these effects provides a new route for the development of reconfigurable electronic, electromagnetic, and optical devices that take advantage of the metallic properties of liquid metals.

A comprehensive understanding of fluid dynamics and the identification of intricate rheological properties are essential for both academic research and industrial applications where fluid behavior is critical. Traditional methodologies for determining these properties have primarily relied on instruments known as rheometers. However, an innovative approach introduced in Maîtrejean et al. in 2022 shifts from direct measurement to the automated identification of rheological characteristics. This method utilizes the morphology of jets formed by the Rayleigh–Plateau instability as distinct signatures, enabling the identification of fluids based on their rheology through artificial intelligence (AI). While the original study, Maîtrejean et al. (2022), was based on a numerically generated dataset focusing solely on variations in viscosity for Newtonian fluids, the current research expands upon this by employing an experimentally generated dataset. This dataset encompasses Newtonian fluids with varying viscosities, densities, and surface tensions. Herein, we demonstrate the capability of our AI-driven model to accurately identify these three properties for Newtonian fluids. This study validates the applicability of the approach to this expanded set of properties for Newtonian fluids using experimental data and sets a new benchmark for precision in this context.

A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a Cahn-Hilliard free energy density combined with incompressible, isothermal fluctuating hydrodynamics where dissipative fluxes include both deterministic and stochastic terms. The intermolecular parameters in the free energy are chosen such that one species acts as a partially miscible surfactant. From Laplace pressure measurements, we show that in this model the surface tension decreases linearly with surfactant concentration, leading to Marangoni convection for interfaces with concentration gradients. In the capillary wave spectrum for interfaces with and without surfactant, we find that for the former, the spectrum deviates significantly from classical capillary wave theory, presumably due to Gibbs elasticity. In non-equilibrium simulations of the Rayleigh-Plateau instability, deterministic simulations showed that the surfactant delays pinching of a fluid cylinder into droplets. However, stochastic simulations indicate that thermal fluctuations disrupt the surfactant's stabilizing effect. Similarly, the spreading of a patch of surfactant, driven by Marangoni convection, was found to be partially suppressed by thermal fluctuations.

This work leverages an unsupervised machine learning and advanced image processing techniques to characterize the breakup of fuel sprays in a small-scale combustor under reacting conditions, providing valuable insights into near-nozzle flow phenomenology. The proposed methodology integrates an improved optical flow model on a convolutional neural network to extract flow vectors with a binarization technique to assess droplets’ size and shape across the region of interest. The velocimetry approach demonstrates superior performance compared to a state-of-the-art optical flow model when applied to high-speed X-ray phase contrast spray images, achieving more accurate and reliable flow predictions. Moreover, breakup processes are quantified by breakup length and sphericity in accordance with velocity estimations, allowing a more complete characterization of the flow. This study establishes a robust methodology for analyzing spray morphology and primary breakup in compact combustors, contributing valuable means of understanding and optimizing fuel spray behavior in advanced combustion systems.