Abstract Liquid atomization is a multiscale gas–liquid breakup process in which a continuous interface evolves into droplets through the growth of interfacial waves, three-dimensional deformation, local thinning, topological rupture, and capillary breakup. Classical Kelvin–Helmholtz (KH), Rayleigh–Taylor (RT), Tollmien–Schlichting (TS), and Rayleigh–Plateau (RP) mechanisms have provided essential interpretations for disturbance amplification and stage-dependent breakup; however, no single instability framework can fully account for the strongly unsteady, three-dimensional, and multiscale transition from surface-wave development to droplet formation. This review summarizes progress in turbulent atomization from a vorticity perspective, with emphasis on vorticity generation at gas–liquid interfaces, vorticity transport in turbulent shear layers, coherent vortical structures, and the interfacial topology cascade from lobes and liquid sheets to holes, bridges, ligaments, and droplets. Rather than formulating a closed predictive model, the review synthesizes an interpretive framework that relates near-interface vorticity, coherent-vortex evolution, local strain, curvature, and capillary effects to interfacial thinning and breakup. It further highlights the need to move beyond spatial correspondence between vortical structures and breakup events toward time-resolved, verifiable causal links among vorticity evolution, interfacial topology change, and droplet formation.

This study presents a numerical investigation of impinging-jet atomization across various Weber numbers (We) under high backpressure conditions. Using the volume-of-fluid method, adaptive mesh refinement, and the isoAdvector interface reconstruction technique, atomization characteristics are simulated and analyzed for different values of We. The results indicate that the geometry induces turbulent jets, which drive turbulent atomization through the shear interactions at the gas-liquid interface. The key observed phenomena include the interaction of impact waves with liquid sheet perforation and the breakup of web of ligaments, both of which are prominent under high backpressure conditions. A novel method, based on the threshold velocity of spray droplet groups, is employed to quantitatively measure the spreading angle, showing that the angle increases with We in both front and side views. Additionally, the Sauter mean diameter of droplets follows power-law scaling with exponents of -1/3 in the upstream region and -1/2 in the downstream region, while the droplet size distribution conforms to a log-normal profile. This research provides valuable insights into interface evolution and droplet characteristics during impinging-jet atomization under high backpressure, offering essential guidance for optimizing industrial atomization processes.

Despite decades of studies on symmetric impinging-jet atomization, the combined role of controlled pre-impingement asymmetry and viscosity in setting the instability pathways and droplet statistics of laminar microjets remains insufficiently quantified. The effects of pre-impingement jet-length difference and liquid viscosity on the flow morphologies, instability dynamics, and atomization behavior of laminar impinging microjets are investigated experimentally using high-speed imaging. By systematically varying the jet-length asymmetry and viscosity over a range of Weber numbers, the evolution of liquid-sheet motion and breakup is resolved from synchronized front- and side-view observations. Specifically, the scientific objective of this work is to elucidate how pre-impingement jet-length asymmetry and liquid viscosity jointly regulate the dynamical behavior of laminar impinging microjets, with particular emphasis on regime transitions of liquid-sheet morphologies, the coupling between upper-sheet oscillations and rim instabilities revealed by synchronized multi-view imaging and POD-based frequency analysis and the resulting droplet-size statistics. These aspects address physical questions that have not been systematically resolved in classical impinging-jet studies, which predominantly focus on symmetric configurations or performance-oriented atomization. With increasing Weber number, the flow undergoes a sequence of regime transitions, including merged-jet, liquid-chain, wavy-rim, fishbone, closed-rim, open-rim, and arc-shaped atomization states. The presence and extent of the closed-rim regime depend sensitively on both jet-length asymmetry and liquid viscosity. Increasing jet-length difference accelerates transitions between these regimes, whereas increasing liquid viscosity stabilizes the liquid sheet and shifts the onset of unsteady breakup to higher Weber numbers. Proper orthogonal decomposition is applied to time-resolved image sequences to extract dominant oscillatory modes and their characteristic frequencies. Within the fishbone regime, the oscillation frequency of rim deformation either coincides with that of the upper region of the liquid sheet or appears as its subharmonic, indicating period-doubling behavior under specific combinations of Weber number and jet-length asymmetry. These frequency characteristics govern the spatiotemporal organization of ligament formation and detachment along the sheet rim. In the arc-shaped atomization regime, droplet-size distributions follow a log-normal form, and at sufficiently high Weber numbers, the mean droplet diameter shows only a weak dependence on jet-length asymmetry. These findings provide microscale-regime guidance for tunable droplet formation in open microfluidic jetting and related small-scale multiphase flows. The innovation of this study lies in the systematic use of synchronized multi-view imaging combined with POD-based frequency analysis and droplet statistics to directly connect liquid-sheet oscillations, rim instability dynamics, and breakup organization under controlled geometric asymmetry and viscosity variations. This approach enables a unified physical interpretation of regime transitions and instability mechanisms that cannot be resolved from single-view observations or morphology-based classification alone.

This study experimentally examines the breakup dynamics and droplet statistics of laminar impinging microjets with asymmetric pre-impingement lengths. Dual-view high-speed imaging, combined with proper orthogonal decomposition (POD) and droplet size measurements, is applied over a wide range of jet Weber numbers ( We(j)). Two distinct atomization modes are identified. Under low-asymmetry conditions, breakup is governed by the aerodynamic-wave mode, in which aerodynamic waves developing at the trailing-edge drive ligament formation and droplet shedding. Under high-asymmetry conditions, a new upper-sheet-perforation-induced mode emerges, characterized by periodic perforations in the upper sheet and rim-jet interactions that establish a self-sustained breakup cycle and periodic atomization. Breakup length increases with Wej, but the scaling differs: nonlinear under low asymmetry and nearly linear under high asymmetry. POD analysis confirms the separation of modal responses and shows that geometric asymmetry intensifies oscillations and accelerates sheet destabilization. Droplet sizes follow lognormal distributions in all cases. For low asymmetry, the distribution width is largely insensitive to Wej and the median droplet size remains nearly constant. For high asymmetry, the distribution width decreases as Wej increases, while the median size changes little, resulting in narrower spectra and more uniform sprays. These findings clarify the distinct modal pathways of asymmetry-regulated atomization and provide guidance for the design and optimization of impinging-jet atomizers.

This study investigates the dynamic atomization characteristics of kerosene impinging jets under high-pressure conditions using a coupled Eulerian-Eulerian and Eulerian-Lagrangian framework. By systematically analyzing the effects of injector pressure differences and inlet/outlet pressure oscillations, the research provides critical insights into spray dynamics and combustion stability. Results indicate that increasing the pressure difference shortens liquid sheet breakup length and suppresses droplet mass flow rate fluctuations. Pressure oscillations induce periodic deformations in the liquid sheet, altering the spray’s overall structure. Voronoi tessellation analysis reveals distinct droplet clustering patterns in the impinging-jet spray, suggesting vortex-driven modulation of the spray field. Detailed visualization and analysis of the temporospatial distribution of mass flow rate density and droplet size during primary atomization show that mass flow rate density peaks in the central region and diminishes toward the periphery, while droplet size distribution follows an inverse trend. The Sauter mean diameter (SMD) exhibits non-monotonic axial variation with pressure differences. Under inlet/outlet pressure oscillations, SMD decreases rapidly downstream, with the reduction rate positively correlated to oscillation amplitude. Notably, SMD fluctuations under pressure oscillations significantly exceed those induced by pressure differences. Furthermore, inlet/outlet pressure oscillations generally reduce SMD, though SMD variability increases with oscillation amplitude. Time-lag analysis reveals substantial phase delays between pressure oscillation and atomization parameters: the mass flow rate oscillations of injectors and generated droplets exhibit a half-period delay, while the delay between injector mass flow rate and droplet SMD oscillations extends to a full period. These findings advance injector design optimization and stability prediction in liquid rocket engines by elucidating the atomization process’s dependence on operational parameters under realistic combustion chamber conditions.

This study experimentally investigates the spatiotemporal dynamics and droplet statistics of impinging jet atomization under varying Weber numbers (We) and impact angles (2a), focusing on unstable rim regime and impact wave regime. High-speed imaging, combined with Proper Orthogonal Decomposition (POD), is employed to characterize the dynamic evolution and breakup behavior of the liquid sheet. Two distinct atomization mechanisms are identified: an unstable rim regime at low We (81.53-226.47), and an impact wave regime at higher We (326.12-579.77). POD spatial modes and their associated power spectral densities reveal that the rim breakup corresponds to low-frequency large-scale structures, whereas impact-wave-driven fragmentation exhibits high-frequency fluctuations. Droplet statistics show that diameters follow a log-normal distribution under the impact wave regime, while velocities exhibit a normal distribution across all regimes. The 2a significantly influences droplet velocity dispersion but has a limited effect on droplet size for impact wave. The droplet Reynolds number demonstrates a consistent scaling relationship with normalized diameter. An empirical model is developed to predict droplet sizes in the impact-wave-dominated regime, incorporating POD-derived disturbance wavelengths, breakup length, and ligament-to-droplet correlation. The model enables reliable estimation of mean droplet diameters based on injector geometry and flow parameters. These findings offer critical insights for the design and optimization of impinging jet atomizers in engineering applications such as aerospace propulsion, micro-reactors, and pharmaceutical sprays. (c) 2026 The Author(s). Published by Elsevier Ltd on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

This study combines experimental observations and numerical simulations to comprehensively analyse the interface evolution of confined droplets in microfluidic devices with flow-focusing junctions under different aspect ratios. Microchannels with aspect ratios of 1, 1/2 and 1/3 are designed, where droplets are generated at the first flow-focusing junction, and three distinct flow patterns – no breakup, single breakup and multiple breakups – are observed at the second flow-focusing junction. The relationship between droplet length and flow parameters is established, investigating the effects of capillary number and channel aspect ratio on droplet breakup behaviour. It is found that the scaling exponent of the minimum neck thickness increases with the continuous phase flow rate. Numerical simulations are carried out to illustrate the shape evolution of a droplet in three-dimensional space, allowing the calculation of the curvature distribution of the interface. The scaling exponent of the mean radius of curvature in a channel with an aspect ratio of 1 differs from that in a channel with an aspect ratio of less than 1. These findings provide theoretical support for understanding droplet breakup dynamics and lay a foundation for optimising microfluidic device design and structural innovation.

This study numerically investigates the spray dynamics and time-lag effects in high-pressure liquid oxygen (LOX) impinging jet atomization under three scenarios: varying pressure differences without oscillations, upstream pressure oscillations with different amplitudes, and downstream pressure oscillations. By coupling the Volume of Fluid method with the Lagrangian Particle Tracking model, the atomization process—encompassing liquid sheet breakup, fragment formation, and droplet generation—is analyzed through high-fidelity simulations. The results show that, in the absence of pressure oscillations, increasing the pressure difference influences jet velocity and droplet mass flow rate but has minimal effect on the Sauter Mean Diameter (SMD) within the considered range. Even without oscillations, the droplet mass flow rate exhibits large, nonperiodic fluctuations, reflecting the intrinsic instability of the atomization process, which may contribute to combustion instability. When external pressure oscillations are applied, either at the injector inlet or combustion chamber outlet, periodic variations are induced in both mass flow rate and SMD of the generated droplets. The amplitude of oscillation is positively correlated with the intensity of pressure fluctuations. Additionally, time-lag phenomena are observed: there is a negligible time lag between pressure oscillations and LOX mass flow rate fluctuations, while significant delays are seen between LOX mass flow rate and droplet mass flow rate oscillations. The time lag between LOX mass flow rate and SMD oscillations is comparatively shorter. These findings provide insights into transient spray behavior and temporal correlations in high-pressure impinging jet atomization, aiding the optimization of injector designs and improving combustion stability in rocket engines.

This study investigates the formation and evolution of fishbone patterns in oblique impinging liquid microjets through high-speed imaging experiments and numerical simulations. The results identify periodic oscillations in the upper region of the liquid sheet as the primary mechanism driving fishbone instabilities, which induce rim disturbances and lead to bifurcations into diverse fishbone morphologies. Transitions between stable and unstable flow patterns are systematically mapped across varying Weber numbers and impingement angles, providing a comprehensive framework for understanding this interfacial dynamics. Two critical transitions – marking the onset and disappearance of fishbone patterns – are characterised, offering insights into the underlying physics governing the stability and instability of these flow structures.

Ultra-thin liquid sheets generated by impinging two liquid jets are crucial high-repetition-rate targets for laser ion acceleration and ultra-fast physics, and serve widely as barrier-free samples for structural biochemistry. The impact of liquid viscosity on sheet thickness should be comprehended fully to exploit its potential. Here, we demonstrate experimentally that viscosity significantly influences thickness distribution, while surface tension primarily governs shape. We propose a thickness model based on momentum exchange and mass transport within the radial flow, which agrees well with the experiments. These results provide deeper insights into the behaviour of liquid sheets and enable accurate thickness control for various applications, including atomization nozzles and laser-driven particle sources.

This review summarizes recent progress in the study of impinging-jet dynamics and atomization,with a focus on liquid sheet formation,instability mechanisms,and the influence of key parameters such as fluid properties,Weber number,and Reynolds number.Special attention is given to atomization behaviors under high pressure and external perturbations.Representative ex-perimental and numerical approaches are introduced,and critical findings under complex conditions are highlighted.In addition,practical applications of impinging-jet technology in aerospace propulsion,biomedical devices,and energy science are discussed.This review aims to serve as a concise reference for researchers interested in multiphase flow dynamics and engineering applica-tions of impinging jets.

This paper first analyzes the reasons for low combustion efficiency in the afterburner and proposes a solution utilizing aerodynamic effects. The accuracy of the numerical method is verified by a ground direct-connected experiment. Through analyses of combustion efficiency, particle mixing degree, and flow field characteristic, the study compares the excitation effects of single-side and double-side aerodynamic effects and investigates the optimal application position. Further comparisons are conducted between array and non-array aerodynamic effects under various flow rates. The results show that the momentum transfer between aerodynamic airflow and gas has a significant impact on the flow field. Single-side excitation outperforms double-side excitation in promoting particle-air mixing and combustion. Initiating aerodynamic intervention as early as possible after the gas passes through the air intake outlets is more effective. At the optimal position, aerodynamic excitation improves combustion efficiency by 83.5 %. The excitation effect improves with larger aerodynamic flow rates. A threshold for aerodynamic flow rate is identified. When it is below the threshold, the non-array scheme can achieve efficient energy conversion, allowing a small aerodynamic flow rate to result in a significant improvement in mixing and combustion. When it exceeds the threshold, the array scheme performs better.

Combustion dynamics are a critical factor in determining the performance and reliability of a chemical propulsion engine. The underlying processes include liquid atomization, evaporation, mixing, and chemical reactions. This paper presents a high-fidelity numerical study of liquid atomization and spray combustion under high-pressure conditions, emphasizing the effects of pressure oscillations on the flow evolution and combustion dynamics. The theoretical framework is based on the three-dimensional conservation equations for multiphase flows and turbulent combustion. The numerical solution is achieved using a coupling method of volume-of-fluid and Lagrangian particle tracking. The Zhuang-Kadota-Sutton (ZKS) high-pressure evaporation model and the eddy breakup-Arrhenius combustion model are employed. Simulations are conducted for a model combustion chamber with impinging-jet injectors using liquid oxygen and kerosene as propellants. Both conditions with and without inlet and outlet pressure oscillations are considered. The findings reveal that pressure oscillations amplify flow fluctuations and can be characterized using key physical parameters such as droplet evaporation, chemical reaction, and chamber pressure. The spectral analysis uncovers the axial variations of the dominant and secondary frequencies and their amplitudes in terms of the characteristic physical quantities. This research helps establish a methodology for exploring the coupling effect of liquid atomization and spray combustion. It also provides practical insights into their responses to pressure oscillations during the occurrence of combustion instability. This information can be used to enhance the design and operation of liquid-fueled propulsion engines.

This study employs direct numerical simulations to examine the effects of varying backpressure conditions on the turbulent atomisation of impinging liquid jets. Using the incompressible Navier–Stokes equations, and a volume-of-fluid approach enhanced by adaptive mesh refinement and an isoface-based interface reconstruction algorithm, we analyse spray characteristics in the environments with ambient gas densities ranging from 1 to 40 times the atmospheric pressure under five different backpressure scenarios. We investigate the behaviour of turbulent jets, incorporate realistic orifice geometries and identify significant variations in the atomisation patterns depending on backpressure. Two distinct atomisation types emerge, namely jet-sheet-ligament-droplet at lower backpressures and jet-sheet-fragment-droplet at higher ones, alongside a transition from dilute to dense spray patterns. This variation affects the droplet size distribution and spray dynamics, with increased backpressure reducing the spray's spreading angle and breakup length, while increasing the droplet size variation. Furthermore, these conditions promote distributions that induce rapid, nonlinear wavy motion in liquid sheets. Topological analysis of the atomisation field using velocity-gradient tensor invariants reveals significant variations in topology volume fractions across different regions. Downstream, the droplet Sauter mean diameter increases and then stabilises, reflecting the continuous breakup and coalescence processes, notably under higher backpressures. This research underscores the substantial impact of backpressure on impinging-jet atomisation and provides essential insights for nozzle design to optimise droplet distributions.

This research focuses on developing high-fidelity experimental and numerical models to analyze microscale underfill dynamics and void formation in high-density flip-chip packaging. Three underfilling scenarios are investigated, namely, point type, I-shaped line type, and L-type line type. The point-type underfilling validates the numerical model against experimental results, while the I-shaped and L-type line-type underfilling explore grid independence, void formation, and critical parameters such as filling position, contact angle, and liquid viscosity. Results indicate that contact angle and viscosity significantly influence filling efficiency and interface evolution. A smaller contact angle accelerates the process, reducing interface jumping motions. Viscous effects are quantified, revealing dimensionless filling time convergence. The use of low-viscosity surrogate fluids enhances numerical simulation efficiency. Sub-bump-sized, bump-sized, and sup-bump-sized voids are observed, identifying three void formation scenarios representing different underfilling flow mechanisms. This study provides insight into microscale flip-chip underfill physics and establishes validated models for next-generation high-density flip-chip products. These models can be further refined and integrated into optimization tools for automated process design, contributing to improved assembly yield and reliability of emerging electronic packages through physics-based understanding and modeling.

The combustion efficiency of the afterburner has an important effect on the overall performance of the ducted rocket. In some difficult working conditions with low incoming air temperature or high flight altitude, it is more difficult to achieve efficient combustion in the afterburner. Therefore, this paper mainly solves the problem of low primary gas combustion efficiency in the afterburner of boron-based ducted rockets when the incoming air temperature is low. The flow field can be improved by optimizing the gas injection mode, so as to improve the combustion efficiency. In this paper, a synergistic impact gas injection device associated with angles of two directions is designed. By controlling the self -impact angle alpha of gas/gas, and the mutual -impact angle beta of gas/air, efficient mixing and combustion is realized. Through numerical simulation, the mixing degree and combustion efficiency, as well as the contours of B2O3 mass fraction are obtained, and the influence regularities and flow field characteristics are analyzed. The selection scheme of the optimal injection device is verified by a ground directconnected experiment. Finally, through the jet observation experiments, the gas ejection form from the synergistic impact gas injection device is observed. The research of this paper shows that when the mutual -impact angle beta is small, the larger the self -impact angle alpha is, the higher the mixing degree and combustion efficiency will be. When the mutual -impact angle beta is large, each self -impact angle alpha has a high mixing degree and combustion efficiency. When the self -impact angle alpha is 40 degrees or the mutual -impact angle beta is 35 degrees, the mixing can be completed in advance before the gas reaches the afterburner outlet. The higher the average mixing degree, the higher the combustion efficiency. This paper provides an innovative and efficient method for promoting combustion in the afterburner.

This paper presents a numerical investigation to understand the transport and deposition of sprays emitted by an impinging-jet inhaler in the human respiratory tract under different inhalation flow rates. An injection model is used for the numerical simulations considering the spreading angles of the spray in the two directions, which are measured from experiments. The model parameter is adjusted to match the mean droplet size measured in the previous experiment. A time-varying sinusoidal inhalation flow rate is utilized as airflow conditions, which is closer to the actual situation when using an inhaler. The results demonstrate that the inhalation airflow rate significantly affects the spray's transport behavior and deposition results in the respiratory tract. Both excessively high and low inhalation flow rates lead to an increase in deposition in the mouth-throat. A moderate inhalation flow rate reduces throat deposition while maximizing lung deposition. Higher inhalation flow rates enable faster delivery of the droplets to the lungs, whereas lower inhalation flow rates achieve a more uniform deposition over time in the lungs. The amount of deposition in different parts of the lung lobes follows a fixed order. This study provides valuable insights for optimizing the inhalation flow rate conditions of the impinging-jet inhaler for clinical applications.

The noise level of gravity stations is an important indicator for measuring the operating status of a station and is a prerequisite for evaluating whether the station’s observations can be used to extract weak geodynamic signals. With the continuous expansion of areas of human activity, gravity stations originally located in the wild may become increasingly closer to cities. Whether their noise levels change is an important issue that is worthy of attention. Based on power spectrum analyses and probability density function methods, the noise level of the superconducting gravimeter (SG) at Jiufeng station in Wuhan in the seismic frequency band of 0.001–0.04 Hz was calculated, and its time-varying characteristics were analyzed. The noise level of Jiufeng station did not change significantly before and after the lockdown of Wuhan due to the COVID-19 epidemic in 2020. No significant changes in the noise level were found before and after the official operation of Wuhan Metro Line 19 at the end of 2023. From October 2016 to April 2017, the noise level showed an abnormal trend of suddenly rapidly rising and then slowly declining, which was found to be caused by a tilt problem in the gravity sensor. Overall, in the seismic frequency band of 0.001–0.04 Hz, the noise level at Jiufeng station showed seasonal variation characteristics, and the noise was stronger in winter than in summer, which is consistent with the characteristics of Earth’s hum. Since January 2022, the noise level has shown an increasing trend year by year. The results of this study can provide an important reference for the operation of gravity stations and the extraction of weak geodynamic signals.

Radial extracorporeal shockwave therapy (rESWT) is a noninvasive medical technique that treats a range of musculoskeletal conditions. To understand its biological effects and develop personalized treatment plans, it is crucial to fully characterize the acoustic field that rESWT generates. This study presents a quantitative assessment of rESWT's acoustic field, achieved through experiments and simulations. The study measures the acoustic fields using a needle-type hydrophone under different machine settings and establishes and calibrates a computational model based on the experimental measurements. The study also determines the spatial distributions of peak pressure and energy flux density for different driving pressures. High-speed photography is used to visualize cavitation bubbles, which correspond to the negative pressure distribution. The study finds that the axial pressure distribution is similar to the acoustic radiation from an oscillating circular piston, whereas the radial pressure distribution cannot be described by acoustic radiation. Furthermore, the study develops a machine learning model that predicts positive pressure distributions for continuous driving pressure. Overall, this study expands our understanding of the acoustic fields generated by rESWT and provides quantitative information to explore underlying biological mechanisms and determine personalized treatment approaches.