Breakup Frequency Research Articles

On the breakup frequency of bubbles and droplets in turbulence: A compilation and evaluation of experimental data

The dispersed phase in liquid–liquid emulsions and air–liquid mixtures can often be fragmented into smaller sizes by the surrounding turbulent carrier phase. The critical parameter that controls this process is the breakup frequency, which is defined from the breakup kernel in the population balance equation. The breakup frequency controls how long it takes for the dispersed phase to reach the terminal size distribution for given turbulence. In this article, we try to summarize the key experimental results and compile the existing datasets under a consistent framework to find out what is the characteristic timescale of the problem and how to account for the inner density and viscosity of the dispersed phase. Furthermore, by pointing out the inconsistency of existing experimental data, the key important unsolved questions and related problems on the breakup frequency of bubbles and droplets are discussed.

Interfacial relaxation of droplets caused by mass transfer in a pulsed column

AbstractThe method developed in our previous work (Wang et al., AIChE J. 2020; 66(8): e16257), was used to study the influence of the mass‐transfer direction and flux on the dynamic interfacial tension (DIFT) in a pulsed column. The breakup frequency was the highest near the entrance of the dispersed droplet, corresponding to the lowest interfacial tension and highest mass transfer flux. The decrease in the interfacial tension was proportional to the square root of mass‐transfer flux, and this difference is defined as a new parameter, named interfacial relaxation. When the mass‐transfer direction was changed from the dispersed phase to continuous phase to the opposite direction, the proportion of binary breakage was decreased from ~80% to ~40% and the interfacial relaxation was more sensitive to the mass‐transfer flux. A DIFT model was finally established based on the interfacial relaxation parameter, which predicted the experimental results with an error of ±10%.

Experimental study on droplet breakup in an orifice jet mixer

AbstractThe droplet breakups in an orifice jet mixer are studied to gain a deeper understanding of the breakup mechanism and establish breakup models used as population balance model source terms for accurate predictions. The breakup process and details are captured in situ using a high‐speed photomicrography system. Experiments are performed with different levels of pressure drop and mother droplet size. A complete breakup process consists of several different sub‐breakup events, hence the cascade breakup definition is adopted to determine statistical results. High breakup frequency is achieved under high pressure drop and small mother droplet size. The average number of daughter droplets is 102–105 and is positively correlated with the pressure drop and mother droplet size. The daughter droplet size distribution has a tailing phenomenon and is mainly affected by the pressure drop. New breakup models based on the above features are established and predict well with the experimental results.

Modulation of coaxial cone-jet instability in active co-flow focusing

The breakup of coaxial cone-jet interfaces to compound droplets in axisymmetric co-flow focusing (CFF) upon actuation is studied through numerical simulations. Due to the coupling effect of double interfaces, the response behaviours of coaxial cone-jet flow to actuation are more complex than those of a single-layered interface structure. Particularly, the coaxial jet presents totally different response modes between weak and strong interface coupling situations. In this work, the phase diagrams of response modes for coaxial jet breakup are depicted, considering the effect of perturbation frequency, amplitude and liquid flow rates. In particular, the breakup of a coaxial jet can be synchronized with actuation within a frequency range containing the natural breakup frequency, resulting in uniform compound droplets with a single core inside the shell, and the size of droplets can be adjusted by frequency. As the perturbation frequency exceeds the upper critical value, the external perturbation is unable to dominate the jet breakup, while below the lower critical frequency, the jet breaks up with multiple droplets generated in one period. The perturbation amplitude mainly affects the jet breakup length and also leads to the transition between different response modes. The coaxial cone upstream of the orifice can act as a buffer layer, regulating the perturbation amplitude of the coaxial jet downstream. The degree of buffering effect is affected by the perturbation frequency and amplitude. As the perturbation amplitude approaches unity, the decrease of perturbation frequency leads to the intermittent jet behaviour from the cone tip with a vibrating manner of the coaxial cone. Based on the linear instability analysis on the simplified single jet models for weak-coupled and strong-coupled jets, scaling analyses are carried out, which predict the jet breakup length and the natural frequency and critical frequency for the synchronized breakup. Finally, a strong pulse is added on the perturbation to produce compound droplets with a controllable number of cores. The present work provides valuable guidance for the practical application of on-demand compound droplet generation through active CFF.

Calibrating angular momentum transport in intermediate-mass stars from gravity-mode asteroseismology

Context. The physical mechanisms driving the transport of angular momentum in stars are not fully understood, as current models cannot explain the observed stellar rotation profiles across all stages of evolution. Aims. By making use of pulsating F-type dwarfs, we aim to (i) observationally calibrate the efficiency of angular momentum transport, assuming a constant uniform viscosity, and (ii) test how well state-of-the-art rotating stellar models with angular momentum (AM) transport by rotationally induced processes can explain observed rotation profiles. In both cases, the aim is to simultaneously reproduce the measured near-core rotation and core-to-surface rotation ratio. Methods. Asteroseismic modelling is applied to a sample of seven slowly rotating pulsators in order to derive (core) masses and ages from their gravity-mode oscillations. This work focuses on the main sequence (MS), using models that start with an initial uniform rotation frequency at the start of core-hydrogen burning, which is a free parameter. Two treatments of AM transport are considered: (i) a constant uniform viscosity, and (ii) rotationally induced processes (including the Spruit-Tayler dynamo). Next, the initial rotation frequency of each star is derived from the observed present-day near-core rotation frequency for both treatments. Results. Asteroseismic modelling of gravity mode periods reveals that all seven slowly rotating stars (one of which is not further modelled) in the sample are near the end of core-hydrogen burning. To explain the near-core rotation rate at the inferred age, initial rotation frequencies at the zero-age main sequence need to be below 10% of the initial critical break-up frequency. The derived initial rotation frequencies are consistent with previous works. Conclusions. A diffusive approximation of angular momentum transport can in general explain the observed rotation profiles of the six slowly rotating F-type dwarfs for average values of the viscosity of between 2 × 105 and 5 × 107 cm2 s−1 or when the viscosity is computed from rotationally induced mechanisms. Yet, for three stars in the sample, the core-to-surface rotation fraction from rotationally induced mechanisms is predicted to be higher than observed.

Breakup mode of continuous-type liquid-liquid pintle injector

A pintle injector is necessary for the reuse of a launch vehicle. Significant studies have been conducted on the breakup process in impinging or swirl type injectors. However, the breakup process in liquid-liquid pintle injectors from injection to the atomization of liquid films has rarely been investigated. Therefore, in this study, the breakup mode and process quantified characteristics of the pintle injector were investigated. The backlight imaging technique was applied to capture the spontaneous phenomenon, and a longitudinal section view of the spray on the pintle injector was obtained using the 2P-SLIPI technique. The breakup modes were classified into three categories based on the spray shape (hollow cone, fishbone, and branch). The atomization process was investigated with high-speed and SLIPI images in chronologicalorder. Schematics of the process were also prepared to understand the breakup mechanism. The dynamic characteristics, such as breakup frequency and peak amplitude, and static characteristic (breakup length) were investigated using the flow Weber number. Furthermore, the dynamic characteristics are dependent on the radial flow, and the static characteristics are influenced by the annular jet flow. This study will serve as a reference for the breakup mechanism and characteristics of a liquid-liquid pintle injector design.

Bubble breakup criteria for the population balance model of gas–liquid flow simulations

This work presented a critical review of various literature models with focus on the bubble breakup criteria. A general formulation of critical energy for breakup criteria was derived. Based on the framework of Luo and Svendsen (1996), effects of breakup criteria and effective eddy scale on model outputs were examined. Results showed that a joint criterion consisting of surface energy criterion and force criterion (Cf + Wed', Wec = 2) exhibited both reasonable breakup frequency and daughter size distribution (M-shape), and an optimized kernel function was proposed. A correlation between fragmentation ratio and eddy scale was introduced, and a new breakup model with a simplified kernel function was obtained based on the model of Qi et al. (2022). Both kernel functions were implemented in CFD-PBM simulations, and the results agreed with bubble size distributions. The confusions about literature bubble breakup criteria were cleared and two bubble breakup models were suggested.

On the minimum spin period of accreting pulsars

ABSTRACT The distribution of the spin frequencies of neutron stars in low-mass X-ray binaries exhibits a cut-off at 730 Hz, below the break-up frequency (mass-shedding limit) of neutron stars. The absence of submillisecond pulsars presents a problem, given that these systems are older than the spin-up time-scale. We examine models of the disc–magnetosphere interaction near torque equilibrium balanced by the torque due to gravitational wave emission. We note that field lines penetrating the disc beyond the inner radius reduce the maximum rotation frequency of the star, a result well known since the seminal work of Ghosh & Lamb. We show that the polar cap area corresponds to about half the neutron star surface area at the cut-off frequency if the inner radius is slightly smaller than the corotation radius. We then include the change in the moment of inertia of the star due to the accretion of mass and find that this effect further reduces the maximum rotation frequency of the star. Finally, we include the torque due to gravitational wave emission and calculate its contribution to the torque equilibrium. Our results suggest that all three processes are significant at the cut-off frequency, and that all of them must be considered in addressing the absence of submillisecond pulsars.

Experimental investigations on dynamic wave structures of a prefilming atomizer

An experimental study was performed on a planar prefilming airblast atomizer to investigate the dynamic wave behavior on a prefilmer. Using a high-speed camera, backlighting visualization and reflection imaging were applied to record the breakup process of the liquid film and the temporary evolution of wave structures. Image post-processing methods were used to obtain the film thickness, surface wave frequency, breakup length, and ligament breakup frequency. Depending on non-dimensional aerodynamic numbers, surface waves on the prefilmer were classified into three mechanisms. In addition, correlations were derived from experimental data and used to predict atomization characteristics. The deviations of surface wave frequency and breakup length were limited to ±10%. These predictive correlations can assist in resolving engineering issues regarding prefilming atomizers.

Experimental Study on Breakup Characteristics of Hollow Cone Spray in Gas Crossflow

Hollow cone spray with a medium spray half-cone angle (in the range of 36°–45°) exposed to a gaseous crossflow is a situation that has been extensively investigated experimentally. In this experiment, flow visualization techniques are employed to examine the initial liquid sheet thickness at the nozzle orifice exit and the sheet breakup process. The dynamics of the primary breakup of the sheet is analyzed based on the observations of the sheet breakup in the near-nozzle region. The experimental results show that the breakup mechanism of the liquid sheet varies greatly depending on liquid centrifugal momentum and aerodynamic force. Four distinct breakup modes are observed, and the breakup regimes are mapped in the parametric space based on the liquid Weber number (84–2175) and the liquid-to-air momentum ratio (22–8455). It is observed that the leeward side of the sheet is dominated by shear oscillation breakup within the range of the liquid-to-air momentum ratio less than 600. The influences of the aerodynamic Weber number on breakup frequency and the number of surface waves observed on the leeward side sheet are discussed by analyzing the spray images. The breakup-regime transition criteria for hollow cone spray in crossflow and the trajectory of spray in crossflow are proposed by employing a multivariable regression method.

Rectifying jet breakup by electric forcing

AbstractThe high‐throughput production of monodisperse droplets is paramount in most of the applications in droplet microfluidics. In a flow‐focusing junction, a straightforward way to increase droplet production rate is to increase the flow rates. However, at a critical flow velocity, the droplet monodispersity breaks down due to a transition from the dripping to the jetting regime. As a result, a much more polydisperse droplet population is generated. The change from monodisperse to polydisperse droplet production emerges from the intrinsic properties of the instabilities of jets. In the jetting regime, droplet pinch‐off is governed by a convective instability which amplifies random noise when traveling down the jet leading to an irregular breakup. We show that with the use of an amplitude‐modulated electric signal, we select the breakup frequency of the jet. Matching the perturbation frequency close to the natural breakup frequency of the jet, we increase the monodispersity of the droplet population. This method is applicable to droplet production at a high throughput, that is, beyond the dripping to jetting threshold, including an active control since the frequency, and hence droplet sizes, are determined by the forcing frequency.

A computational methodology to account for the liquid film thickness evolution in Direct Numerical Simulation of prefilming airblast atomization

Prefilming airblast atomization is becoming widely used in current aero engines. Fundamental studies on the actual annular configuration of airblast atomizers are difficult to realize. For this reason, researchers have also focused on planar configurations. In this regard, the Karlsruhe Institute of Technology (KIT) developed a test rig to conduct experimental activities, conforming a large database with results for different working fluids and operating conditions. Such data allow two-phase flow modelers to validate their calculations concerning primary atomization on these devices. The present investigation proposes a Direct Numerical Simulation (DNS) study on the KIT planar configuration through the Volume of Fluid (VOF) method within the PARIS Simulator code. The novelty compared to DNS works reported in the literature resides in the use of a boundary condition that allows accounting not only for the gas inflow turbulence but also for the spatio-temporal evolution of the liquid film thickness at the DNS inlet and its related effect on turbulence. The proposed methodology requires computing precursor single-phase and two-phase flow Large-Eddy Simulations on the prefilmer flow, with the assumption that the flow between computational domains is one-way coupled. Results are compared to DNS that only account for a constant (both timewise and spanwise) liquid film thickness at the domain inlet, validating the full methodology workflow. The proposed methodology is shown to improve the qualitative description of the atomization mechanism, as the different stages of breakup (liquid accumulation behind the prefilmer edge, bag formation, bag breakup, ligament formation and ligament breakup) coexist spanwise for a given temporal snapshot. This implies a more continuous atomization than the one predicted by the constant film thickness case, which showed the same breakup stage to be present along the prefilmer span for a given instant and led to a more discretized set of atomization events. The proposed workflow allows quantifying the influence of the liquid film flow evolution above the prefilmer surface on primary breakup frequency and relevant atomization features.

Frequency Specificity of Liquid-Fountain Swinging with Mist Generation: Effects of Ultrasonic Irradiation Angle

Atomization of liquid into the air attained through submerged ultrasound irradiation will involve the formation of liquid fountain, which exhibits a sequence of oscillating and/or intermittent characteristics/events: its vertical/axial growth and breakup; its lateral “compound swinging”; and its associated dynamics of mist formation and spreading. This study attempts to provide a mechanistic view of ultrasonic atomization (UsA) process in terms of the swinging periodicity of water fountain and to specifically examine the influence of ultrasonic irradiation (i.e., transducer installation) angle on the liquid-fountain oscillations with mist generated intermittently. Through high-speed visualization, it was qualitatively found that as the extent of tilt (from the vertical direction) in the irradiation angle was increased, the degree of occurrence of mist generation and the amount of identifiable mist being generated tended to decrease. This trend was associated with reductions in both the growth rate and breakup frequency of the fountain on the tilt. It was further found, through the analysis of time variation in the resulting angle of liquid-fountain inclination, that the swinging fountain fluctuated periodically in an asymmetric manner and its periodicity could be fairly predicted based on a proposed simple “pendulum” model. An optimum value of the transducer installation angle was observed and judged to be 2° from the viewpoint of effective mist generation as well as fluid dynamic stability of the UsA liquid fountain.

(Invited) Graphene Oxide-Based Membranes: Viscoelastic Properties and Application to Broadband Microspeakers

Graphene and graphene derivatives have attracted attention as materials for acoustic transduction [1-3]. Graphene oxide (GO) membranes and borate cross-linked graphene oxide (X-GO) membranes combine high stiffness, low mass density, and high loss coefficient. We show [4] that these mechanical properties are ideal for efficient, broadband, electro-acoustic transduction, where the acoustic diaphragm should be light, stiff, and internally damped. We present a quantitative comparison of the figure of merit, (E/ρ 3)1/2, where E is Young's modulus and ρ is the mass density, and the material performance index, tan δ (E/ρ 3)1/2, where tan δ is the loss coefficient. GO and X-GO exhibit high figures of merit, comparable to that of wood and exceeding that of aluminum and thermoplastics. The material performance indices of GO and X-GO exceed that of wood, thermoplastics, and aluminum. The latter are common diaphragm materials in acoustic transducers.For acoustic applications, it is important to understand the frequency dependent viscoelastic response. The complex modulus G = G' + iG'' of GO and X-GO membranes was measured by dynamic mechanical analysis and analyzed by the application of the time-temperature superposition (TTS) principle of polymer rheology. We find that X-GO shows a more than 30% increase in storage modulus G’ over the frequency range of 1 to 10 kHz, exceeding 55 GPa at 10 kHz. There is a reduction in loss coefficient tan δ = G''/G' for X-GO of ≈30% over the same frequency range, reaching tan δ = 0.04 at 10 kHz, which is approximately one order of magnitude larger than that of aluminum.A quantitative comparison of microspeaker performance was conducted at a fixed diaphragm mass m = 15-20 g and 14 mm x 8 mm size, including GO, X-GO, oak wood, polyethylene terephthalate (PET), aluminum, and titanium. Scanning laser measurements confirm pistonic operation of X-GO membranes. Microspeaker sound pressure level response was measured in both time and frequency domains. X-GO diaphragms exhibit 45% higher damping than aluminum membranes in microspeaker assemblies. Consequently, X-GO membranes enable the upshift of loudspeaker breakup frequency by 1/6 to 1/2 octave above speakers assembled with oak wood, PET, aluminum and titanium membranes. GO based materials are thus found to be an exceptional material for electro-acoustic transduction.

Lattice Boltzmann modeling of primary liquid film breakup at the prefilmer edge: Effects of surface wettability

In this paper, numerical predictions are performed for a planar prefilming atomizer using the lattice Boltzmann (LB) method. The main target is to inspect the effects of surface wettability on the primary liquid film breakup at the prefilmer edge. To this end, a phase-field-based multiple-relaxation-time LB model for two-phase flow is derived and verified for the present study, as well as the wetting boundary scheme. After that, the effects of surface wettability are assessed by specifying different contact angles during the simulations. Numerical results indicate that the whole primary breakup process of the liquid film can be roughly divided into three interactive stages: (i) liquid accumulation at the trailing edge; (ii) ligament formation and its flapping movements; (iii) ligament breakup and droplet formation. It is visible that the liquid accumulation and the following ligament breakup show similar periodic patterns with quite consistent frequencies. Besides, when the contact angle is increased, the volume of liquid accumulated at the prefilmer edge declines, the maximum flapping region of ligaments shrinks, the ligament breakup length reduces, but the ligament breakup frequency increases. Based on the above-mentioned results, it can be concluded that the prefilmer with hydrophobic surfaces benefits the primary liquid film breakup in the close vicinity of the prefilmer edge.

Evaporation, break-up, and pyrolysis of multi-component Arabian Light crude oil droplets at various temperatures

Crude oil sprays are often used in direct combustion applications and refinery catalytic cracking units. Droplet evaporation, break-up, and pyrolysis are important aspects prior to gas-phase chemical reactions. This paper reports an experimental suspended droplet study of Arabian Light (AL) crude oil to assess the effect of ambiance temperature on dynamic events. Experiments were conducted at three different temperatures of 620 K, 710 K, and 840 K, to examine different regimes (devolatilization, transition stage, and complete pyrolysis) for several repetitions. Break-up events involved during the evaporation were successfully identified and classified into break-up modes depending on their break-up intensity (β). Additionally, the effect of the temperature on the break-up events was assessed, showing that the number of break-up events increases exponentially with temperature. Finally, the density distribution of each break-up mode, as well as their final probability distribution were assessed. Intermediate and high-intensity break-ups (2-mode and 3-mode) break-ups were favored at lower temperatures, as well as micro-explosion (4-mode), in comparison with pyrolysis regime. However, break-up frequency increased exponentially with temperature. Additionally, based on the individual break-up modes density distributions characteristic times were identified successfully for pyrolysis regime, were the gasification dynamics changed. The global droplet behavior was examined by following the time evolution of the normalized droplet diameter. Two successive stages were identified at all temperature conditions: the swelling and the regression stage. In the devolatilization and the transition regimes, evaporation was controlled purely by the diffusive processes, whereas in the pyrolysis stage, the pure diffusion stage was not observed. Instead, a second swelling was registered, where an amorphous carbonaceous structure was formed. This was attributed to the pyrolysis of the heavy hydrocarbons in the droplet.

Viscoelastic Response of Graphene Oxide‐Based Membranes and Efficient Broadband Sound Transduction

AbstractFreestanding micrometer thick graphene oxide (GO) membranes combine high stiffness, low mass density, and high loss coefficient. This unique combination of properties is ideal for efficient and broadband electro‐acoustic transduction, relying on membrane lightness, stiffness, and internal damping. Here, the viscoelastic response of GO membranes is measured, and the application of ≈100 µm thick GO membranes is demonstrated in dynamic loudspeakers. Using dynamic mechanical analysis and the time‐temperature superposition principle of polymer rheology, it is found that the stiffness of GO membrane increases by more than 50% over 1–20 kHz while damping decreases by less than 20%. GO membranes exhibit 45% higher damping than aluminum membranes in loudspeakers assemblies. Consequently, GO membranes enable the upshift of loudspeaker breakup frequency by octave above speakers assembled with aluminum, polyethylene terephthalate, titanium, and oak wood membranes. GO is thus found to be an exceptional material for electro‐acoustic transduction.

Breakup model of oscillating drops in turbulent flow field

Following the drop oscillation breakup mechanism, a theoretical model for drop breakup probability is proposed based on the three-dimensional Maxwell velocity distribution. The model considers both the interfacial energy increase constraint and viscous energy increase constraint. The model shows that for low-viscous drops, the breakup probability is determined by the Weber number (WeL), and for intermediate or high viscous drops, the breakup probability is determined by the combined influence of the Weber number (WeL) and the Ohnesorge number (Oh). By combining the theoretical model of drop breakup time constructed in our previous work, the breakup frequency model is obtained based on the statistical description framework. The accuracy and generality of the model were then validated using the direct experimental data. Moreover, effects of the drop diameter, turbulent energy dissipation rate, and interfacial tension on the predicted drop breakup frequency were analyzed in detail.

Epiphora before and after upper eyelid functional blepharoplasty: A retrospective cohort study.

Epiphora and dermatochalasis are common presentations in the ophthalmology clinic. To evaluate the change of epiphora before and after functional blepharoplasty, this retrospective cohort study reviewed 39 medical records of epiphora patients who underwent upper blepharoplasty. Severity of epiphora using MUNK score was collected and compared between before and at 6 months after blepharoplasty. The analysis model was performed to measure tear breakup time (TBUT) and frequency of artificial tears use. Subgroups of subjects before blepharoplasty to short baseline TBUT (≤ 10 seconds) and long TBUT (≥ 10 seconds) were also evaluated for the MUNK score change. From the analysis of 39 patients, the results showed a statistically significant decrease in post blepharoplasty MUNK score compared to the baseline (all P < 0.001). There was no significant difference between baseline and post-operative TBUT (P > 0.05). Twenty patients were in the short TBUT group and 19 in the long TBUT group. The reduction of MUNK score after blepharoplasty in the short TBUT group was not different to the long TBUT group (P = 0.50, 95% CI -0.84 to 0.41). However, in short TBUT group, frequency of artificial tears use after surgery was less than pre-operation. From the study, upper eyelid blepharoplasty might be one technique reducing the bothersome epiphora in dermatochalasis patients.

Estimating Breakup Frequencies in Industrial Emulsification Devices: The Challenge of Inferring Local Frequencies from Global Methods

Experimental methods to study the breakup frequency in industrial devices are increasingly important. Since industrial production-scale devices are often inaccessible to single-drop experiments, breakup frequencies for these devices can only be studied with “global methods”; i.e., breakup frequency estimated from analyzing emulsification-experiment data. However, how much can be said about the local breakup frequencies (e.g., needed in modelling) from these global estimates? This question is discussed based on insights from a numerical validation procedure where set local frequencies are compared to global estimates. It is concluded that the global methods provide a valid estimate of local frequencies as long as the dissipation rate of turbulent kinetic energy is fairly homogenous throughout the device (although a residence-time-correction, suggested in this contribution, is needed as long as the flow is not uniform in the device). For the more realistic case of an inhomogeneous breakup frequency, the global estimate underestimates the local frequency (at the volume-averaged dissipation rate of turbulent kinetic energy). However, the relative error between local frequencies and global estimates is approximately constant when comparing between conditions. This suggest that the global methods are still valuable for studying how local breakup frequencies scale across operating conditions, geometries and fluid properties.