Breakup Frequency Research Articles

Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Accurate detection of successive breakup and coalescence events requires that the snapshot interval be an order of magnitude smaller than the characteristic breakup and coalescence times to capture these successive events while minimizing the identification of repeated confounding events. Together, these algorithms serve as a toolbox for detailed analysis of two-phase simulations, and enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

Modelling neutron star mountains

ABSTRACT As the era of gravitational-wave astronomy has well and truly begun, gravitational radiation from rotating neutron stars remains elusive. Rapidly spinning neutron stars are the main targets for continuous-wave searches since, according to general relativity, provided they are asymmetrically deformed, they will emit gravitational waves. It is believed that detecting such radiation will unlock the answer to why no pulsars have been observed to spin close to the break-up frequency. We review existing studies on the maximum mountain that a neutron star crust can support, critique the key assumptions and identify issues relating to boundary conditions that need to be resolved. In light of this discussion, we present a new scheme for modelling neutron star mountains. The crucial ingredient for this scheme is a description of the fiducial force which takes the star away from sphericity. We consider three examples: a source potential which is a solution to Laplace’s equation, another solution which does not act in the core of the star and a thermal pressure perturbation. For all the cases, we find that the largest quadrupoles are between a factor of a few to two orders of magnitude below previous estimates of the maximum-mountain size.

Experimental Methods for Measuring the Breakup Frequency in Turbulent Emulsification: A Critical Review

The growing interest in using population balance modeling to describe emulsification processes has spurred an interest in experimentally measuring the breakup frequency. This contribution classifies, compares, and critically reviews the different methods that have been suggested for measuring the breakup frequency, applicable to emulsification devices. Two major approaches can be seen in previous studies. The first is ‘single drop breakup experiment’-based studies, which estimate the breakup frequency by observing the fate of individual drops. The second approach involves ‘emulsification experiment’-based studies, which combine measured drop-size distributions with assumptions to allow for estimations of the breakup frequency. This second approach can be further subdivided in three types: Parametric determination, inverse self-similarity-based methods, and direct back-calculation methods. Each of these methods are reviewed in terms of their implementation, reliability, and validity. Suggestions of methodological considerations for future studies are given for each class, together with more general suggestions for further investigations. The overall objective is to provide emulsification researchers with background information when choosing which method to use for measuring the breakup frequency and with support when setting up experiments and data evaluation procedures.

Towards a model of bubble breakup in turbulence through experimental constraints

Complex bubble breakup in turbulence has been studied and modeled extensively by employing the population balance equation. This equation hinges on two quantities, i.e. daughter bubble size distribution and breakup frequency. Since there is no first-principle equation that can be solved to calculate these two quantities, many phenomenological models based on different physical mechanisms have been proposed. A large number of possible mechanisms at play leads to models with drastically different, and even contradictory, predictions. In contrast, experimental measurements of these two quantities, including several previous works and our own results collected in a vertical water tunnel that features a large homogeneous and isotropic region, seem to be consistent with one another. To resolve the difference between models and experiments, rather than following another physical argument, we approach the problem from a different direction by asking how to constrain a model based on experimental results. The specific constraints extracted from eight experimental results include: (i) direct measurements of daughter bubble size distribution; (ii) Super-Hinze-scale bubble size spectrum for constraining breakup frequency; (iii) Sub-Hinze-scale bubble size spectrum for modeling daughter bubble size distribution; (iv) Convergence time to an equilibrium state. Finally, based on these experimental constraints, a new breakup model that incorporates a corrected formulation for breakup frequency as well as a simplified function for daughter bubble distribution is developed to meet all constraints. Although the new model is deliberately not connected to any specific physical arguments for simplification, it appears to be robust and consistent with all experimental constraints mentioned.

On the validity of different methods to estimate breakup frequency from single drop experiments

Single drop breakup visualizations are the golden standard for experimentally measuring breakup frequency, g, in turbulent flows. There is a growing demand for empirically obtained breakup frequencies, for population balance equation (PBE) based predictive modelling and for comparing to theoretical suggestions. However, five different methods to estimate g from a breakup visualization can be found in previous investigations, many of them contradictory. This study uses analytical and numerical methods to show that only two of the five suggestions result in estimates that are valid (where ‘valid’ means that the breakup frequencies are meaningful in a PBE setting). This case is also used to discuss the difference between the stochastic one drop deformation/breakup view of turbulent fragmentation and the deterministic number density based PBE description, arguing that some aspects of the breakup process will be challenging to describe within the PBE framework, regardless of the choice of breakup frequency model.

Combining level-set method and population balance model to simulate liquid–liquid two-phase flows in pulsed columns

The level-set method and population balance model (PBM) were combined to develop a numerical framework for the simulation of liquid–liquid two-phase flows in a pulsed disc and doughnut column (PDDC). First, breakup behavior in droplet swarms in a local area of the PDDC was elucidated under a low holdup condition using a modified level-set method with multi-levels. The droplet breakup frequency function and the daughter droplet size distribution function were determined via statistical analysis on the breakup behavior in droplet swarms. The determined droplet breakup kernel functions were then plugged into the PBM to simulate liquid–liquid two-phase flows in the full-scale PDDC. The calculated droplet size distribution agreed well with the experimental results. The developed numerical framework provides a strategy to simulate two-phase flows avoiding the use of adjustable parameters which are dependent on experiments.

Determination of dynamic interfacial tension in a pulsed column under mass transfer condition

AbstractInterfacial tension is an essential physical property in two‐phase flow, and it changes due to the mass transfer. The measurement of dynamic interfacial tension (DIFT) in such a condition is a difficult problem. In the previous study (Zhou et al., Chem Eng Sci. 2019; 197:172–183), we presented the quantitative relation between the droplet breakup frequency function (DBFF) and interfacial tension. It is found that the DBFF is highly depended on interfacial tension. Therefore, the DBFF is a suitable parameter to quantitatively characterize the interfacial tension. Based on this concept, the DIFT in the column is determined by regression method after the DBFF under mass transfer condition is measured. It is found that the DIFT is smaller than the static interfacial tension. This result indicates that interphase mass transfer leads to decreasing of the interfacial tension. The decreasing extent of the DIFT has a positive correlation with the mass transfer flux.

Retracted: “Symmetric and Asymmetric Disturbances in the Rayleigh Zone of an Air-Assisted Liquid Sheet: Theoretical and Experimental Analysis,” [ASME Journal of Fluids Engineering, 2020, 142(7), p. 071302; DOI: 10.1115/1.4045998

AbstractThe temporal analysis of symmetric (dilatational) and asymmetric (sinusoidal) perturbations at the interface of a water sheet in a coflowing air stream focuses on low gas Weber number region (Weg < 0.4), namely, Rayleigh breakup zone. The motive for this investigation is to acquire a better insight of breakup phenomena involved, rather than technical relevance, by utilizing Kelvin–Helmholtz instability. Accordingly, perturbations are introduced on the basic flow whose stability is to be examined by the method of normal (Fourier) modes. The temporal growth-rate of perturbations is traced to extract the wavenumber associated with maximum growth-rate. Thus, the critical wavelength, in conjunction with the phase velocity of the disturbance will facilitate to obtain the corresponding breakup frequency of the liquid sheet. The analytical findings on liquid sheet breakup frequency with increasing Weber number ratio exhibit the dominance of symmetric wave over asymmetric wave. It also shows independent evolution of breakup frequency with respect to Weber number ratio for the respective perturbation modes, which appears to be a pointed profile. That is, the frequency contour for dilatational mode dips, whereas it rises for the sinusoidal mode and at the Weber number ratio of 0.518 the crossover occur. The theoretical results were substantiated by high-speed flow visualization studies that discern the coexistence of low-frequency (primary) and high-frequency (intermediate) breakup events. Furthermore, the empirical average frequency data track reasonably well with the dilatational instability.

Nonparametric inference of neutron star composition, equation of state, and maximum mass with GW170817

The detection of GW170817 in gravitational waves provides unprecedented constraints on the equation of state (EOS) of the ultra-dense matter within the cores of neutron stars (NSs). We extend the nonparametric analysis first introduced in Landry & Essick (2019), and confirm that GW170817 favors soft EOSs. We infer macroscopic observables for a canonical 1.4 $M_{\odot}$ NS, including the tidal deformability $\Lambda_{1.4} = 211^{+312}_{-137}$ ($491^{+216}_{-181}$) and radius $R_{1.4}= 10.86^{+2.04}_{-1.42}$ ($12.51^{+1.00}_{-0.88}$) km, as well as the maximum mass for nonrotating NSs, $M_{max} = 2.064^{+0.260}_{-1.34}$ ($2.017^{0.238}_{-0.087}$) $M_\odot$, with nonparametric priors loosely (tightly) constrained to resemble candidate EOSs from the literature. Furthermore, we find weak evidence that GW170817 involved at least one NS based on gravitational-wave data alone ($B^{NS}_{BBH}= 3.3 \pm 1.4$), consistent with the observation of electromagnetic counterparts. We also investigate GW170817's implications for the maximum spin frequency of millisecond pulsars, and find that the fastest known pulsar is spinning at more than 50% of its breakup frequency at 90% confidence. We additionally find modest evidence in favor of quark matter within NSs, and GW170817 favors the presence of at least one disconnected hybrid star branch in the mass--radius relation over a single stable branch by a factor of 2. Assuming there are multiple stable branches, we find a suggestive posterior preference for a sharp softening around nuclear density followed by stiffening around twice nuclear density, consistent with a strong first-order phase transition. While the statistical evidence in favor of new physics within NS cores remains tenuous with GW170817 alone, these tantalizing hints reemphasize the promise of gravitational waves for constraining the supranuclear EOS.

Experimental Characterization of a Liquid Jet Emanating From An Effervescent Atomizer

Abstract The study focuses on experimental characterization of the primary atomization associated with an effervescent atomizer. Unlike the existing designs available in the literature that inject air perpendicular to the liquid flow direction, the present atomizer design utilizes coflowing air configuration. In doing so, the aerodynamic shear at the liquid–gas interface create instability and enhance the subsequent jet breakup. Both integrated and intrinsic properties of the liquid jet were extracted by utilizing high-speed flow visualization techniques. The integrated property consists of breakup length, while the intrinsic property involves primary and intermediate breakup frequencies. The primary instability is characterized by low-frequency sinusoidal mode, whereas the intermediate instability consists of high-frequency dilatational mode. Dimensionless plots of these parameters with Weber number ratio leads to a better collapse of data, thereby generating appropriate universal functions. The combined diagram of frequencies converge with increasing relative velocity. This may be due to the dominance of energy consuming sinusoidal wave as the aerodynamic shear increases.

Influence of the ambient pressure on the liquid accumulation and on the primary spray in prefilming airblast atomization

The influence of the ambient pressure on the breakup process is investigated by means of PIV and shadowgraphy in the configuration of a planar prefilming airblast atomizer. The ambient pressure is varied from 1 to 8 bar. Other investigated parameters are the gas velocity and the film loading. From single-phase PIV measurements, it is found that the gas velocity in the vicinity of the prefilmer partly matches the analytical profile from the near-wake theory. As done in previous publications, the characteristics of the liquid accumulation are extracted from the shadowgraphy images of the liquid phase directly downstream of the prefilmer. Two different characteristic lengths, as well as the ligament velocity and a breakup frequency are determined. In addition, the droplets generated directly downstream of the liquid accumulation are captured. Hence, the spray Sauter Mean Diameter (SMD) and the mean droplet velocity are given for each operating point. The novelty of this study is that a scaling law of these quantities with regard to ambient pressure is derived. A correlation is observed between the characteristic length of the accumulation and the SMD, thus reinforcing the idea that the liquid accumulation determines the primary spray characteristics. In this paper, a threshold to distinguish the zones between primary and secondary breakup is proposed based on an objective criterion. It is also shown that taking non-spherical droplets into account significantly modifies the shape of the dropsize distribution, thus stressing the need to use shadowgraphy when investigating primary breakup. Additionally, the ambient pressure and the velocity are varied accordingly to keep the aerodynamic stress ρgUg2 constant. This leads to almost identical liquid accumulation and spray characteristics. Hence, it is confirmed that the aerodynamic stress is a more appropriate parameter than the gas velocity or the ambient pressure to characterize prefilming airblast breakup. Finally, SMD correlations from the literature are compared to the present experiment. Most of the correlations calibrated with LDA/LDT measurement underestimate the SMD. This highlights the need to use shadrowgraphy for calibrating primary breakup models.

Numerically simulating droplet breakup in droplet swarm using modified level set method with multi-levels

A modified level set method with multi-levels was developed to simulate the breakup behavior of multi-droplets in the turbulent flow of a pulsed disc and doughnut column. This free interface capturing method uncovered the mechanisms of three droplet breakup patterns that were observed in experiments: (1) breakup owing to shearing effect, (2) breakup because of collision with plate surfaces, and (3) breakup due to interface instability. The simulation results also indicated that the breakup frequency of 2-mm droplets increased from 0.1 to 0.6 s−1 and the breakup duration decreased from 0.025 to 0.015 s when the pulsation intensity increased from 8 to 14 mm/s. Multiple breakage occurred when the droplet size increased to 3 mm. The simulation results agreed well with our previous experimental results.

Population synthesis of accreting neutron stars emitting gravitational waves

ABSTRACT The fastest-spinning neutron stars in low-mass X-ray binaries, despite having undergone millions of years of accretion, have been observed to spin well below the Keplerian break-up frequency. We simulate the spin evolution of synthetic populations of accreting neutron stars in order to assess whether gravitational waves can explain this behaviour and provide the distribution of spins that is observed. We model both persistent and transient accretion and consider two gravitational-wave-production mechanisms that could be present in these systems: thermal mountains and unstable rmodes. We consider the case of no gravitational-wave emission and observe that this does not match well with observation. We find evidence for gravitational waves being able to provide the observed spin distribution; the most promising mechanisms being a permanent quadrupole, thermal mountains, and unstable r modes. However, based on the resultant distributions alone, it is difficult to distinguish between the competing mechanisms.

Description of the Droplet Size Evolution in Flowing Immiscible Polymer Blends.

Control of the phase structure evolution in flowing immiscible polymer blends during their mixing and processing is fundamental for tailoring of their performance. This review summarizes present state of understanding and predictability of the phase structure evolution in flowing immiscible polymer blends with dispersed structure. Results of the studies of the droplet breakup in flow, important for determination of the droplet breakup frequency and of the size distribution of the daughter droplets, are reviewed. Theories of the flow-induced coalescence providing equations for collision efficiency are discussed. Approximate analytic expressions reliably describing dependence of the collision efficiency on system parameters are presented. Available theories describing the competition between the droplet breakup and coalescence in flow are summarized and approximations used in their derivation are discussed. Problems with applicability of available theories on prediction of the droplet size evolution during mixing and processing of immiscible polymer blends, which have not been broadly discussed so far, are addressed.

Experimental investigation of bubble breakup in bubble chains rising in a liquid metal

The process of bubble breakup in a liquid metal was studied by X-ray radiography and high-speed video imaging. Argon gas bubbles were injected through a single orifice at the bottom of a rectangular vessel filled with the eutectic GaInSn alloy. Moderate gas flow rates were applied at isothermal conditions resulting in the formation of bubble chains. The bubble breakup events observed in the chosen experimental geometry were mainly initiated by bubble collisions or by the effect of local shear flow. We present experimental results accompanied by statistical analysis of the bubble breakup frequency, number of daughter bubbles and their size distribution, bubble velocities before and after the breakup process for a broad range of Argon gas flow rates.

Parametric Study of the Frequency of Bubble Formation at a Single Orifice With Liquid Cross-Flow

The bubble formation frequency from a single-orifice nozzle subjected to the effects of a crossflowing liquid was investigated using high-speed shadowgraphy, combined with image analysis and signal processing techniques. The effects of the nozzle dimensions, orientation within the conduit, liquid cross-flow velocity, and gas mass flow rate were evaluated. Water and air were the working fluids. Existing expressions in the literature were compared to the experimental values obtained. The expressions showed modest agreement with the experimental mean average frequency magnitude. It was found that increasing the gas injection diameter could decrease the bubbling frequency approximately 12% until reaching a certain value (0.52 mm). Further increasing the nozzle dimensions increase the frequency by around 20%. Bubbling frequency is more sensitive to the liquid velocity where changes up to 63% occurred when the velocity was raised from 3.1 to 4.3 m/s. Increasing gas mass flow rates decreased the gas jet breakup frequency in all cases. This phenomenon was primarily attributed to changes in the bubbling mode from discrete bubbling to pulsating and jetting modes. The nozzle orientation plays a role in modifying the bubbling frequency, having a higher magnitude when oriented against gravity.

Flooding in the James Bay region of Northern Ontario, Canada: Learning from traditional knowledge of Kashechewan First Nation

Traditional Knowledge has the potential to increase our understanding of many kinds of ecological phenomenon including floods. This article offers insights into the nature of spring flooding and its impacts in the southwestern James Bay region of northern Ontario, Canada from the perspectives of residents of Kashechewan First Nation. This article highlights the important contribution of Kashechewan First Nation's traditional knowledge to understanding and reducing disaster risks in this flood-prone region. Through a collaboration with Kashechewan First Nation, traditional knowledge was documented in 2016 during 17 in-depth interviews, participatory flood mapping workshops, on-site walks, and photography. The results of this study show that spring flooding has occurred seasonally over many generations in the region and has not increased significantly over time. However, the timing and extent of spring flooding has changed in recent years with warming temperatures in the region (i.e., earlier spring, snowmelt, and rapid runoff) and impacts are exacerbated by landscape and resource developments (e.g., inadequate infrastructure, substandard ring-shaped dyke wall, and downriver winter ice road) which have increased the frequency and scale of spring ice breakup and ice jams. These ecological changes have created the increased risk of flooding for the community of Kashechewan. The methodological approach which used participatory techniques may be useful for ongoing flood monitoring and disaster risk reduction activities in southwestern James Bay and elsewhere among the Canadian Indigenous communities.

Experiments on Bubble Breakup Induced by Collision with a Vortex Ring

AbstractThe bubble breakup after collision with a vortex ring was validated as source of breakup parameters for population balance modeling. This system was chosen as a deterministic alternative to the stochastic nature of bubble breakup studies under turbulent flow. The vortex ring was characterized by combining experimental visualization and numerical simulations. Breakup frequency, mean number of daughter bubbles, and its size distribution were obtained by high‐speed camera recording of the collision process. The dependence of breakup parameters on the size of the mother bubble and Weber number was determined.

Study of droplet breakage in a pulsed disc and doughnut column-Part I: Experiments and correlations

We have developed a direct measurement method for the breakage of droplet swarm in our previous work. However, experimental data for droplet breakage is still extremely indispensable for the development and employment of population balance model (PBM). In this paper, the direct measurement of droplet breakage for a series of liquid-liquid systems has been carried out in a pulsed disc and doughnut column (PDDC) to meet the requirement. The data together with that in our previous work cover the main factors affecting the droplet breakage in the PDDC and are sufficient to support the establishment of useful empirical correlations for breakup frequency and daughter droplet size distribution. The experimental results and correlations all indicate that the breakup frequency function increases as the dispersed-phase viscosity or the interfacial tension decreases. The daughter droplet size distribution broadens considerably with decreasing interfacial tension.

Fundamental physics and the absence of sub-millisecond pulsars

Context. Rapidly rotating neutron stars are an ideal laboratory to test models of matter at high densities. In particular, the maximum rotation frequency of a neutron star depends on the equation of state and can be used to test models of the interior. However, observations of the spin distribution of rapidly rotating neutron stars show evidence for a lack of stars spinning at frequencies higher than f ≈ 700 Hz, well below the predictions of theoretical equations of state. This has generally been taken as evidence of an additional spin-down torque operating in these systems, and it has been suggested that gravitational wave torques may be operating and be linked to a potentially observable signal. Aims. We aim to determine whether additional spin-down torques (possibly due to gravitational wave emission) are necessary, or if the observed limit of f ≈ 700 Hz could correspond to the Keplerian (mass-shedding) break-up frequency for the observed systems, and is simply a consequence of the currently unknown state of matter at high densities. Methods. Given our ignorance with regard to the true equation of state of matter above nuclear saturation densities, we make a minimal physical assumption and only demand causality, that is, that the speed of sound in the interior of the neutron star should be lower than or equal to the speed of light c. We then connected our causally limited equation of state to a realistic microphysical crustal equation of state for densities below nuclear saturation density. This produced a limiting model that gave the lowest possible maximum frequency, which we compared to observational constraints on neutron star masses and frequencies. We also compared our findings with the constraints on the tidal deformability obtained in the observations of the GW170817 event. Results. We rule out centrifugal breakup as the mechanism preventing pulsars from spinning faster than f ≈ 700 Hz, as the lowest breakup frequency allowed by our causal equation of state is f ≈ 1200 Hz. A low-frequency cutoff, around f ≈ 800 Hz could only be possible when we assume that these systems do not contain neutron stars with masses above M ≈ 2 M⊙. This would have to be due either to selection effects, or possibly to a phase transition in the interior of the neutron star that leads to softening at high densities and a collapse to either a black hole or a hybrid star above M ≈ 2 M⊙. Such a scenario would, however, require a somewhat unrealistically stiff equation of state for hadronic matter, in tension with recent constraints obtained from gravitational wave observations of a neutron star merger.