Critical Weber Number Research Articles

Absolute instability of power law liquid jets

Non-Newtonian fluid threads are common in many natural and synthetic processes. An appreciation of how such threads break into droplets has been a subject of study for a long time. In this paper, we investigate the absolute instability of a cylindrical thread, modeled as a power law fluid, falling under gravity surrounded by an inviscid medium. Particular attention is paid to investigating the effects of the gas-to-liquid density ratio and the Reynolds number as well as the influence of the flow index number on critical Weber numbers (which mark the transition between convective and absolute instability). Our results determine the convective to absolute instability boundary for a number of different parameter values.

Bouncing dynamics of binary equal-sized high-viscosity molten glass droplets in head-on collisions

Despite extensive research on head-on droplet collisions over the past decades, detailed investigations into the bouncing behavior of high-viscosity droplets, such as molten glass droplets, are still scarce. In this study, a volume-of-fluid method coupled with dual marker functions is employed to simulate the collision dynamics of molten glass droplets. The results show good agreement with experimental observations in both spatial and temporal dimensions. Theoretical analysis reveals a critical Weber number of 22 for bouncing and coalescence of molten glass droplets with a diameter of 100 μm. Below this threshold, we examine the bouncing behavior across various Weber numbers, categorizing the process into four distinct stages: mutual proximity, radial expansion, suction separation, and reverse separation, and providing a detailed analysis of velocity, pressure, and energy at each stage. As the Weber number increases, vortices sequentially emerge at 4, 8, 12, and 16, suggesting a strong correlation between droplet deformation and vortex generation. At lower Weber numbers, the air film pressure between droplets transitions smoothly between radial expansion and suction separation. However, between Weber numbers 9 and 22, a distinct concave pressure phenomenon is observed during suction separation. Pressure chattering occurs at the beginning of radial expansion and the end of suction separation. Furthermore, the results indicate that the cumulative viscous dissipation energy consistently approaches half of the initial kinetic energy, irrespective of the Weber and Ohnesorge numbers.

Characterization of the oil water two phase flow in a novel microchannel contactor equipped with helical wire static mixer

This study investigates an oil/water two-phase system to assess the potential efficacy of a novel passive mixer in enhancing the liquid-liquid interfacial area within a micro-channel contactor. In this system, two fluids are introduced into a microchannel with a diameter of 800 μm and a length of 20 cm, which is equipped with a stainless-steel helical wire measuring 250 μm in diameter. Throughout the experiments, both fluids are supplied at equal flow rates, and the dominant forces, including attachment and detachment forces, are examined. The results reveal a critical Weber number of 3.8 × 10−³, at which the first detachment occurs. A comparison between microchannels with and without the passive micromixer demonstrates that greater slug breakup occurs in the system incorporating the helical wire micromixer. This innovative configuration results in a significant reduction in slug/droplet size compared to a microchannel without a barrier, decreasing from approximately 600 μm to 390 μm at a flow rate of 0.8 mL/min. Additionally, a flow map is presented, illustrating three distinct flow regimes: flow contains long slug, Slug-droplet flow, and droplet flow regimes, with the droplet flow regime covering the largest area. The findings indicate that the implementation of this innovative passive mixer substantially increases the interfacial area, providing significant advantages for mass transfer applications.

Feasibility of Using Polymers to Improve Foam Flow Performance in Vertical Pipes: Application to Liquid Unloading in Gas Wells

Foam unloading is a cost-effective technique for removing liquid from low-energy gas wells, but it faces challenges due to the instability of foam at the wellbore. Surfactants alone struggle to create and maintain durable foam films under wellbore conditions. Polymers are known to enhance foam stability by increasing lamella thickness and viscosity, but their impact on foam unloading has not been well explored. This study investigates the effects of Xanthan Gum (XG) and Polyvinylpyrrolidone (PVP) polymers on stability and unloading efficiency of the foams made by Alkyl Polyglycoside surfactant. The research evaluates foam stability and examines the bubble size and lamella thickness under varying salinity conditions. Additionally, the study evaluates foam unloading efficiency by determining unloaded mass rate, critical gas velocity and Weber number. Results show that polymer concentration, type and molecular weight significantly affect foam morphology and stability. Xanthan Gum at 1000 ppm demonstrated the smallest bubble size and greatest foam stability. This concentration also achieved the highest unloaded mass, 30% more than the surfactant-only case. Regarding the molecular weight of the polymers, HPVP demonstrated an ability to generate smaller bubbles in comparison with LPVP. Consequently, HPVP exhibited superior performance in liquid unloading, surpassing LPVP by a margin of 8.5%. The addition of polymers reduced critical gas velocity, with 1000 ppm of XG yielding the lowest value. Initially, the Weber numbers for polymer-stabilised foams were higher than the surfactant-only case (XG: 208.01, LPVP: 17.70, HPVP: 26.38 vs. APG: 2.25) due to the Marangoni effect but decreased during the unloading process (XG: 788.58, LPVP: 1850.26, HPVP: 1702.01 vs. base case: 4046.42), indicating improved stability and performance. Overall, the study demonstrates that polymers can significantly improve foam stability and performance, maintaining foam integrity throughout the unloading process if engineered properly prior to their application.

Dynamic Behavior of Impacting Droplet on the Edges of Different Wettability Surface.

The dynamic behavior of impacting droplet shearing by the surface edge with different wettabilities is complicated and has great significance for engineering application. The morphological evolution of droplet with various Weber numbers (We) and wettability impacting on the edge of square substrate is investigated by high-speed photography. Moreover, the effects of the contact angle (α) and Weber numbers (We) on the shear breaking process of droplets are obtained. There are three types morphological evolution of impacting droplet are observed experimentally, including unbroken, tensile breakup, and shear breakup. Contact angle and Weber number have been proved to be the significant factors affecting the type of droplet morphological evolution. Meanwhile, the critical Weber number of different types are obtained quantitatively. Moreover, as α increases, the critical Weber numbers for breakup increase. In the shear breakup process, the mass ratio between the droplets remaining on the substrate and the initial droplets is maintained at 50%. Particularly, a reliable prediction model for the spreading of droplet impacting the side wall is proposed and compared with the experimental data. Overall, this study provides new direction and guidance for exploring droplet breakup kinetics.

A New Criterion for the Splashing of a Droplet on Dry Surface from High-Fidelity Simulations

In this study, a new criterion for the splashing of a droplet on a dry smooth surface is established from high-fidelity numerical simulations. The new criterion involves the Weber number, Reynolds number and contact angle. A new splashing mode, termed spreading splashing, is proposed, which predominates for contact angles below 120 degrees. For contact angles above 120 degrees, prompt splashing dominates. For contact angles above 90 degrees, there exists a critical Weber number of around 60, below which splashing does not occur.

Investigation in the bag breakup of water droplet in airflow with different temperatures and densities

This paper tries to clarify the respective significance of thermal effects and airflow density on the influence of bag breakup of water droplets in hot airflow. The bag breakup processes of water droplets in the airflow temperature range of 293 K (ρg=1.205 kg/m3) to 493 K (ρg=0.716 kg/m3) were investigated. Meanwhile, room-temperature gas mixtures with corresponding densities were prepared using room-temperature helium blended with room-temperature air to explore the bag breakup processes of water droplets. The results show that although the critical conventional Weber number (Wecon) of spherical droplets for bag breakup varies significantly in both streams, the critical initiation Weber number (Weini) of disk-shaped droplets for bag breakup remains almost consistent. Different deformation processes from Wecon to Weini result in different Wecon. In the gas mixtures with room temperature, the critical Wecon for bag breakup increases from 9.47 to 12.12 as the stream density decreases from 1.205 to 0.716 kg/m3. However, the critical Wecon for bag breakup decreases from 9.47 to 7.80 in the hot airflow at identical airflow density variations.

Pinch-off of a regular bubble during the impact of droplets on a liquid pool

A droplet impacting a liquid pool can result in the pinch-off of a regular bubble. In this study, the cavity deformation and regular bubble pinch-off after droplets impacting a liquid pool were experimentally investigated. The results indicate that the phenomenon of regular bubble pinch-off results from the combined effects of cavity expansion and capillary wave propagation. The inertial force, viscous force, and droplet diameter are all crucial to the cavity evolution and the process of regular bubble pinch-off. The cavity depth increases with the droplet's inertial force but does not change with the droplet's viscous force. As the droplet's inertial force increases, the diameter of the regular bubble first increases and then decreases. The diameter of the regular bubble at We = 165 is almost four times that at We = 193. In addition, the peak size of the regular bubble decreases as the liquid viscosity increases, but increases as the droplet diameter increases. These variations in the regular bubble size are explained using a theoretical analysis. Finally, the effects of the inertial and viscous forces on the thresholds between no-bubble and regular-bubble pinch-off regimes are studied. As the Ohnesorge number increases from 1.37 × 10−2 to 2.03 × 10−2, the upper and lower critical Weber numbers for the occurrence of the regular bubble pinch-off can increase by 30 and 25, respectively. The theoretical boundaries of regular bubble pinch-off agree well with the boundaries observed in the experiments.

Impact regimes of a single water droplet impacting a hot immiscible liquid surface

This paper studied the dynamic interaction process of a single water droplet impinging onto an immiscible target liquid, which was a follow-up study on a single water droplet impacting a miscible target liquid i.e. ethanol. Heptane was chosen as the impacted liquid, and the water droplet with a fixed diameter of 1.98 mm was used in the experiments. The droplet Weber number ranged from 30 to 762 by changing the height between the droplet and the impacted liquid surface. A high-speed digital camera at a speed of 2000 fps was used to capture the dynamic process. A comprehensive map We∼θ of typical impact phenomena including penetration, splashing, and bubble was plotted, considering both the cases of immiscible and miscible liquids. The critical Weber numbers of forming the typical phenomena were deduced. The critical Weber numbers for the transition from penetration to splashing and the transition from splashing to bubble could be approximately predicted by We=824.3−140.9e1.5θ and We=62.1+61.5θ, respectively. To clarify the formation mechanisms of typical phenomena, the energy conversions during the dynamic process were analyzed. The influences of pool temperature on energy conversion rates of the crater and jet formation could be predicted by χ=0.437θ+0.156 and φ=0.245θ+0.072, respectively.

Reconfigurability-Encoded Hierarchical Rectifiers for Versatile 3D Liquid Manipulation.

Manipulating small-volume liquids is crucial in natural processes and industrial applications. However, most liquid manipulation technologies involve complex energy inputs or non-adjustable wetting gradient surfaces. Here, a simple and adjustable 3D liquid manipulation paradigm is reported to control liquid behaviors by coupling liquid-air-solid interfacial energy with programmable magnetic fields. This paradigm centers around a hierarchical rectifier with magnetized microratchets, using Laplace pressure asymmetry to enable multimodal directional steering of various surface tension liquids (23-72 mN m-1). The scale-dependent effect in microratchet design shows its superiority in handling small-volume liquids across three orders of magnitude (100-103 µL). Under programmed magnetic fields, the rectifier can reconfigure its morphology to harness interfacial energy to exhibit richer liquid behaviors without dynamic real-time control. Reconfigured rectifiers show improved rectification performance in the inertia-dominant fluid regime, i.e., a remarkable 2000-fold increase in the critical Weber number for pure ethanol. Moreover, the rectifier's switchable reconfigurations offer flexible control over liquid transport directions and spatiotemporally controllable 3D liquid manipulation reminiscent of inchworm motions. This scalable liquid manipulation paradigm promotes versatile engineering and biochemistry applications, e.g., portable liquid purity testing (screening resolution <1 mN m-1), logical open-channel microfluidics, and automated chemical reactionplatforms.

An analysis of the contact time of nanodroplets impacting superhydrophobic surfaces with square ridges

Reducing the contact time between liquid droplets and solid surfaces is important in numerous engineering applications. Mechanisms for reducing the contact time have been extensively studied. However, there is still a lack of systematic research on the mechanisms governing the changes in the contact time of nanodroplets impacting superhydrophobic surfaces with square ridges. Additionally, there has been relatively little examination of the differences between nanodroplets and macroscopic droplets in this scenario. In this work, we investigate the impact of nanodroplets on both superhydrophobic planes and superhydrophobic surfaces with square ridges. When nanodroplets impact a superhydrophobic plane, we find that the droplet contraction time determines the total contact time. When nanodroplets impact superhydrophobic surfaces with square ridges, we find for the first time that the critical factor determining its contact time is the detachment time of the droplet from the square ridges as it lifts off. Compared to millimeter-sized droplets, nanodroplets exhibit stronger adhesion to solid surfaces. Additionally, we propose for the first time that nanodroplets are more resistant to deformation and splitting. We define the Weber number (We) at which the droplet rebounds as the critical rebound Weber number (We), and use this to evaluate the effect of square ridges on improving droplet rebound. We observe that a moderate increase in the square ridge height is beneficial to reducing the contact time. By altering the square ridge width, we find that a narrower ridge is more favorable for reducing the contact time and for facilitating droplet splitting.

Transition from dripping mode to jetting mode under passive control with a drainage device

Traditional Chinese medicine is a pivotal industry in China, and the technology for manufacturing high-quality pills is of great interest to numerous sectors. Among various methodologies, the liquid drip method has gained significant attention from the pharmaceutical industry due to its advantages such as high drug content uniformity, low cost, ease of operation, high production efficiency, and extensive adjustment range. However, the occurrence of undesirable satellite droplets during the drip production process remains a persistent issue. These satellite droplets are challenging to collect and their prolonged presence can disrupt the normal functioning of the system. Previous studies have identified two primary modes of droplet formation: dripping mode and jetting mode. Given that droplet formation in dripping mode is more stable and satellite droplets can be effectively suppressed, studying the transition between dripping and jetting modes and improving the uniformity of the generated droplets become crucial. Achieving this transition can be accomplished through both active and passive methods. In view of the limitations of the active methods in actual productions, we explored a passive method of adding a drainage device, which can effectively inhibit satellite droplets.In this experimental and numerical simulation investigation, we successfully induced the dripping-to-jetting transition by incorporating a drainage device into the dropper. Additionally, we examined how modifications to the dropper's structure influenced droplet formation. Results indicated that increasing the length and diameter of the drainage device resulted in higher critical Weber numbers required for the dripping-to-jetting transition. Contrarily, the effect of the Kapitza number on the critical Weber numbers exhibited an opposite trend. The critical Kapitza number without complex droplets was also discussed.

Dynamic Drop Penetration of Horizontally Oriented Fiber Arrays.

In this experimental study, we combine drop impact into porous media and onto a single fiber to study drop impact into fiber arrays inspired by mammalian fur coats. In our 3D-printed arrays, we vary the packing density, fiber alignment, strand cross-section, and wettability. Drops impact fibers fixed at both ends, penetrating over short periods of time by momentum and laterally spreading throughout the array. Using image analysis, we measure penetration depth and wetted width into the array. Impact Weber number and intrinsic porosity define penetration, retraction, and rebound regimes. On average, at an impact Weber number of ≈80, staggered fibers reduce penetration by 24% in hydrophilic fibers and 34% in hydrophobic fibers, and the penetration reduction percentage is expected to increase with increasing Weber number. Our results indicate that as density grows toward the density of mammalian pelts, penetration will reach a maximum value independent of drop impact velocity, thereby providing an effective rain barrier. Hydrophilicity at the densities we test, 50-150 strands/cm2, aids fiber array resistance to dynamic penetration by impacting drops through the promotion of lateral drop spreading and inhibition of drop fragmentation. Conversely, hydrophobic fibers best resist low-speed wicking. The fraction of a drop that infiltrates hydrophilic and hydrophobic fibers is nearly identical for a fixed Weber number because lateral spreading restricts the penetration depth into hydrophilic fibers but does not restrict mass infiltration. Above a critical Weber number, the entire drop mass penetrates fiber arrays regardless of strand wettability.

Rebound characteristics of a water droplet impacting on a superhydrophobic cone

Precise control of droplet rebound behavior on superhydrophobic surfaces is essential for various industrial applications like anti-icing and self-cleaning. However, current studies still lack a comprehensive understanding of this phenomenon. Herein, we conduct a numerical investigation on the rebound dynamics of water droplets impacting on superhydrophobic conical cones under various Weber numbers and cone angles. A phase diagram illustrating impact outcome transitions from non-impalement to impalement and ring bouncing is presented. A semi-empirical model is proposed to identify the impalement transition by correlating critical Weber number with cone angle. While ring bouncing reduces contact time by up to 47 % compared to flat surfaces, it is a transient regime due to low rebound velocity, causing the liquid ring to recontact the cone and eventually rebound from the cone tip in a conventional manner with a prolonged contact time. We also observe attractive phenomena upon ring bouncing, including periodically oscillating radial extension and rapid rotation. Shorter contact times in conventional bouncing are achieved at larger cone angles and lower Weber numbers by minimizing radial expansion and falling distance. Furthermore, a theoretical model that accurately predicts the contact time of ring bouncing is developed. It is demonstrated that rebound velocities in both conventional and ring bouncing rise as cone angle decreases, attributed to reduced viscous dissipation and surface energy. Notably, in conventional bouncing, rebound velocity increases by 63 % on average compared to flat surfaces when the cone angle is 60°.

Aerodynamic breakup of gel suspension droplets loaded with aluminum particles

The persistent and frequent space explorations are affected by the performance of propellants, among which the closely related gel propellants have been widely used due to their unique characteristics. Currently, research efforts primarily concentrate on the metallization and atomized combustion of gel propellants, emphasizing the combustion performance of metallized gel propellants. However, little attention has been given to the secondary breakup process that occurs just before combustion. By utilizing high-speed flow visualization technology, this study examines the key aerodynamic breakup process of gel suspension droplets loaded with micro aluminum particles, experimentally and theoretically investigating the droplet dynamics induced by particle volume fraction. The experimental confirmation of the three breakup behaviors exhibited by gel suspension droplets, namely oscillation mode, bag-stamen breakup, and hemline breakup, is presented along with the construction of a phase diagram. The impact of heterogeneous effects resulting from an increase in particle volume fraction on the critical breakup Weber number is revealed, with a concentration of 9 % as the turning point. Within the range of moderate Weber numbers, the tail flick deformation of suspension droplets in airflow is observed and reported for the first time. At different particle concentrations, there keeps a linear correlation between the dimensionless tail length and Weber number. Spherical suspension droplets will deform into thin disks in the airflow, with a nearly constant deformation rate regardless of changes in particle concentration. Additionally, the relationships between characteristic times and droplet parameters are discussed through statistical analysis of the results. As Ohnesorge number and particle volume fraction increase, the characteristic times both show a monotonically increasing trend. Moreover, a model of unstable growth rate associated with the particle volume fraction is established through linear instability analysis, accurately predicting the variation in critical Weber number for gel suspension droplet breakup. The congruence between our theoretical framework and experimental findings not only enhances comprehension of the impact of micro aluminum particles on the secondary breakup of gel suspension droplets but also provides valuable guidance for the aerospace applications of metallized gel propellants.

Numerical study of head-on collisions between two glass microsphere droplets

The collision of molten glass microsphere droplets represents a fundamental phenomenon in spheronization, yet a comprehensive understanding of this process remains elusive. A numerical simulation is conducted to investigate the head-on collision dynamics of two molten glass microsphere droplets at varying Weber numbers, by integrating the level set and volume of fluid methods. Three distinct collision regimes are identified: merging, separation into satellite-free droplets, and separation leading to the formation of satellite droplets. Furthermore, the critical Weber numbers delineating the different regimes are presented. Examination of axial and radial variations in the droplets reveals the existence of five distinct states spanning the three collision regimes. The distribution of external vortices around the droplets directly influences the outcomes of droplet collisions. High-pressure regions and high-pressure liquid bridges within droplets serve as key factors in determining the merging or separation of the droplets. Region of high pressure at the end of the liquid bridge acts as a critical indicator for distinguishing between collision separations with and without satellite droplet generation. Observations of velocity and pressure distributions in separations that produce satellite droplets are consistent with the end pinch-off mechanism. This study holds significant implications for controlling high sphericity during the spheronization of glass microsphere droplets.

Bounce and contact mode regimes for drop impact on smooth surfaces: The influence of gas kinetics and electrostatics

When liquid drops impact on solid surfaces, an air layer forms in between the drop and the surface, acting as a cushion to mitigate the impact. In this work, we focus on delineating the bounce and contact mode regimes of impacting drops on smooth surfaces, specifically discerning whether drops rebound from the air layer or make contact with the solid surfaces, and pinpointing the precise contact modes between the drop and solid surfaces by resolving the gas film evolution and rupture. Our simulation model incorporates gas kinetics and electrostatics effects, both of which have been validated by experiments documented in the literature or theoretical models regarding thin film instabilities. We undertake a comprehensive review and categorization of the contact modes and elucidate how they change under different conditions of impact velocities, ambient pressures, and electric field intensities. We also provide some perspectives on the regime map for the lubricated surfaces, which contains an unresolved issue that the critical Weber number for bouncing-wetting transition is significantly reduced compared to the solid smooth surfaces like mica. These insights have noteworthy practical implications offering guidance for a wide range of scenarios, from normal-pressure environments to low-pressure conditions at high altitudes, encompassing high electric field conditions such as nanogenerators as well as low electric field conditions resembling glass surfaces with static electricity.

Breaking bubbles across multiple time scales in turbulence

The familiar process of bubbles generated via breaking waves in the ocean is foundational to many natural and industrial applications. In this process, large pockets of entrained gas are successively fragmented by the ambient turbulence into smaller and smaller bubbles. The key question is how long it takes for the bubbles to reach terminal sizes for a given system. Despite decades of effort, the reported breakup time from multiple experiments differs significantly. Here, to reconcile those results, rather than focusing on one scale, we measure multiple time scales associated with the process through a unique experiment that resolves bubbles’ local deformation and curvature. The results emphasize that the scale separation among various time scales is controlled by the Weber number, similar to how the Reynolds number determines the scale separation in single-phase turbulence, but shows a distinct transition at a critical Weber number.

Three-component volume of fluid method coupling with interface compression method and Eulerian–Lagrangian spray atomization surface density model for prediction of cavitating sprays

In this work, a new three phase cavitation model with Eulerian–Lagrangian Spray Atomization (ELSA) and Interface Capturing Method (ICM) coupling is presented to allow for, in a unified approach, physical insight of the surface evolution of cavitating sprays at the Sub-Grid Scale (SGS). Phase change is accounted for in the framework via mass transfer across a liquid and corresponding vapor phase. The surface density model was validated against direct numerical simulation data of an atomizing jet with a systematic variation of mesh resolutions. The sensitivity of the adjustable parameters such as the critical Weber number was also demonstrated. Then, experimental comparisons were made with a more realistic orthogonal spray geometry within a cavitating and turbulent non-cavitating system. These comparisons include both large scale visualizations and small scale SGS quantities such as the Sauter mean diameter. To our knowledge, this is the first study that presents the performance of a three phase cavitating framework with SGS ELSA-ICM coupling.

Suppressed Droplet Splashing on Positively Skewed Surfaces for High-Efficiency Evaporation Cooling.

Two types of functional surfaces with the same roughness but completely different surface topographies are prepared, namely positively skewed surfaces filled with micropillar arrays (Sa ≈4.4µm, Ssk >0) and negatively skewed surfaces filled with microcavity arrays (Sa ≈4.4µm, Ssk <0), demonstrating promoting droplet splashing. Remarkably, the critical Weber number for generating satellite droplets on the negatively skewed surfaces is significantly lower than that on the positively skewed surfaces, indicating that the negatively skewed surface with microcavity arrays is more likely to promote droplet splashing. It is mainly attributed to the fact that air on the negatively skewed surface can make the liquid film take on a Cassie-Baxter state on the surface so that the stabilizing capillary force of the liquid film exceeds the destabilizing stress of the air film. Moreover, the surface topography promoting droplet spreading and the mechanical properties of three-phase moving contact lines are analyzed from the perspective of microscopic interface mechanics. Finally, it is demonstrated the designed positively skewed surfaces can be employed for large-area heat dissipation by means of high-efficiency evaporation.