Breakup Criterion Research Articles

Critical criterion for droplet breakup in a contractive microchannel

Predicting the critical transition condition for different behaviors of droplet flowing through a micro contraction is a classic academic issue, and there is currently a lack of a simple and universally applicable prediction formula. This article aims to construct critical transition conditions for different droplet behaviors through their characteristic time. In present work, the droplet behavior, including deformation and breakup, are observed in a locally contractive microchannel by a high-speed camera. By tracing the dynamic evolution of droplet interface, it is found that the essential differences between droplet deformation and breakup is whether the minimum neck width will be less than the critical value for the appearance of the irreversible collapse. Based on this, two characteristic times are proposed to describe the deformation and breakup processes, which well explain the trend of flow pattern transition lines. Two mathematical models are established for the two characteristic times, and the critical conditions for the transformation from deformation to breakup is derived from these models. The predicted results are in good agreement with the experimental results, indicating the applicability of the proposed method in this paper.

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.

Breakup mechanism of the electrically induced conical liquid bridge

The breakup mechanism of a conical liquid bridge is reported based on the previously proposed electrostatic liquid loading method. The breakup criterion in terms of interface feature size is derived. Based on the criterion, the breakup mechanism can be categorized as either spontaneous breakup or stretching breakup. The evolution of interface and velocity for two breakup behaviors is subsequently investigated. For the spontaneous breakup, the remnant volume Vd depends primarily on the top radius Rt and is proportional to the square of Rt. For the stretching breakup, the remnant volume depends on the early stage of the stretching, and Vd is proportional to the cube of Rt. In addition, the influence of the stretching velocity U is examined. Results show that U has a weaker effect on the change of remnant volume than the top radius Rt for large capillary numbers. This study is helpful in understanding the liquid bridge breakup mechanism and improving the transfer printing process.

Theoretical deformation modeling and drop size prediction in the multimode breakup regime

A theoretical model has been proposed to incorporate internal flow mechanics to better predict the deformation and the resulting breakup of a liquid drop in a continuous uniform air jet in the multimode breakup regime. A Weber-number-dependent breakup criterion predicts the deformation of the drop at the time of the breakup, which occurs at the time the internal pressure at the drop equator exceeds internal pressure at the pole. This breakup criterion is used to determine an improved coefficient used in the Taylor Analogy Breakup (TAB) model. The TAB model is also extended to include the effects of turbulence within the drop. Hill vortices form within the drop as a result of viscous forces and flow around the drop. It is proposed that these vortices contribute to the deformation that eventually leads to the outer ring and smaller drop within the ring that is classic to multimode breakup. Instability analysis is used to model the breakup of the outer ring and predict the resultant droplet sizes. The model-predicted breakup times and ring breakup droplet diameter are compared with experimental results collected using digital in-line holography.

Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons.

Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.

A systematic evaluation of criteria for river ice breakup initiation using River1D model and field data

Mechanical breakup of river ice cover is often associated with ice runs, ice jams, and fast-rising water levels. It not only poses great flood threats to riverside communities, but also has great implications to environment and river ecosystems. Our current ability to model the onset of mechanical breakup is limited. Existing river ice models either require the user to manually specify the breakup times and locations or they employ empirical criteria to simulate ice cover breakup. This paper presents a systematic evaluation of existing empirical and semi-empirical/physics-based breakup criteria using the University of Alberta's River1D model. Each criterion was evaluated according to its ability to capture the breaking front propagation observed on the Athabasca River and Peace River during three breakup seasons, as well as the transferability of the calibrated parameter(s). The storage release from broken ice cover has been postulated to lead to the formation of a non-attenuating, i.e. self-sustaining wave, which in turn maintains fast ice cover breaking over very long distance. This study shows that the characteristics of self-sustaining wave under natural river conditions are greatly affected by the varying resistance to ice breaking along a river, which is different than previous findings based on numerical studies in prismatic channels.

Two-layer thermally driven turbulence: mechanisms for interface breakup

Abstract

Analytical modelling of laminar drag and freestream turbulence eddies on droplet breakup criterion for internal combustion engines

The paper presents novel analytical droplet breakup criteria, on Weber number (We)-relative turbulence intensity and We-Ohnesorge (Oh) representations, based on the critical Weber number. The We-Oh analytical criterion stressed the importance of turbulence effects on We-Oh breakup criterion at high We-Oh applications. In developing the analytical models the energy criterion for a disturbed parent droplet to disintegrate and the dual-timescale for turbulent shear in droplet dispersion were considered. The present model has an advantage over to two popular droplet breakup criterion models (Pilch-Erdman and Kolev) because the present model has the ability to support a parametric investigation of droplet breakup characteristics in turbulent flow fields. The Weber-relative turbulence intensity and We-Oh analytical breakup criteria are in good agreement with published experimental data. It is envisaged that the analytical model will be incorporated into larger CFD codes for spray simulation. The continuous research in this important area will present the next generation fuel injectors for improved fuel economy of internal combustion engines, especially high-pressure direct injection engines. The model has the potential to be applied in other natural and engineering systems.

Droplet breakup and rebound during impact on small cylindrical superhydrophobic targets

The impact behavior of a water droplet on small cylindrical superhydrophobic targets is studied numerically and theoretically. A numerical model using the volume of fluid method is developed to simulate the droplet impact process on small cylindrical superhydrophobic targets. The model is verified by comparing the calculated results with the experimental observations in our previous work and reference. The influences of the Weber number and the target-to-droplet diameter ratio (less than one) on the droplet impact behaviors, including the droplet profile and the deformation factor, are investigated. The results indicate that a larger Weber number accelerates the spreading and falling of the droplet and promotes the droplet breakup. An increase in the diameter ratio delays the spreading and falling of the droplet on the side of the target, thus enhancing the deformation and rebound of the droplet. Both the increases in the Weber number and the diameter ratio contribute to a larger maximum deformation factor. Furthermore, the droplet breakup criterion is analyzed theoretically based on the energy conservation. A formula describing the relationship between the critical Weber number and the diameter ratio for the droplet breakup is proposed, which shows high prediction accuracy compared with the numerical values. The critical Weber number for the droplet breakup becomes larger with the increase in the diameter ratio. The findings in this research deepen our understanding of the mechanism of droplet impact on small targets.

Numerical investigation on the standard catastrophic breakup criteria

Hypervelocity collisions are predicted to be the dominant space debris source in the mid-term future, when a critical spatial density of satellites is reached. The NASA Standard Satellite Breakup Model (SSBM) has been adopted by major space agencies for characterizing hypervelocity spacecraft breakups for debris environment modeling. The SSBM is an empirical model based on data from ground tests and observations of on-orbit events. We propose to enhance this database by numerical simulations including a wide range of collision conditions and complex spacecraft models. We established the software tool PHILOS-SOPHIA for systematically studying the effects of on-orbit hypervelocity collisions. A particular focus was laid on the breakup criteria of the SSBM, which defines an energy-to-mass-ratio of 40 J/g being the collision condition for catastrophic fragmentations. We simulated six different scenarios of a complex spacecraft colliding with a small satellite. In the detailed fragmentation analysis, we find both good agreements and clear deviations between the hydrocode results and the SSBM predictions. Particularly, the collision geometry strongly influences the fragmentation damage and the area-to-mass distributions. Depending on the collision vector, impacts on the outer parts of a spacecraft may result in both higher and lower fragmentation in comparison with impacts on the center of mass. The simple breakup criteria does not reflect this complexity and we recommend performing more research. Numerical simulations, thoroughly backed by advanced experiments, can make a significant contribution to improve the accuracy of breakup models.

Velocity scaling and breakup criteria for jets formed due to acceleration and deceleration process

A study of velocity scaling and breakup criteria for jets formed as a result of an acceleration and deceleration process is presented. The process is characterized by five dimensionless numbers: Weber number, Ohnesorge number, Bond number, and dimensionless acceleration and deceleration times.

Physical and mathematical models for space objects breakup and fragmentation in hypervelocity collisions

The paper presents results of analysis of existing mathematical models for orbital debris fragments breakup in high velocity collisions. The breakup models are modified and updated taking into account the latest breakup criteria, experimental data and basic conservation laws. The model examples are analyzed, the criterion is developed for distinguishing fragments, which will stay in orbit after collision event.

Breakup criterion for droplets exposed to the unsteady flow generated by an incoming aerodynamic surface

An experimental and theoretical study is presented on the problem of droplet breakup exposed to a continuously accelerating flow generated by an incoming aerodynamics surface. Droplet breakup experiments were carried out in a rotating arm facility. Droplet diameters were of the order of 1 mm. The maximum velocity of the airfoils located at the end of the rotating arm was 90 m/s. Droplet deformation was computed using a phenomenological model developed previously by the authors. The dynamics of this deformation was coupled to an instability model based on the growth of Rayleigh-Taylor waves at the droplet surface. It was found that, within the experimental uncertainty, breakup occurs when the instability wavelength approaches the droplet hydraulic diameter assuming that it flattens and deforms as an oblate spheroid. This fact allowed for the generation of a theoretical closed-form droplet deformation and breakup model that predicts the onset of breakup with discrepancies of about ±10% when compared to the experimental results. Finally, as an application case, this closed-form model is used to simulate an actual situation in which the objective is to investigate whether a series of droplets that are approached by an airfoil either impact on its surface, or break prior to collision, or break without colliding, or pass through undamaged.

Deformation dynamics and breakup criteria of confined fluid threads in motion

Experiments are carried out to study the breakup of moving fluid threads tightly confined in circular microchannels. A configuration with two flow-focusing channel junctions is used to control lengths and deformations of fluid threads at the first and second junctions, respectively. As fluid threads move and deform simultaneously at the second junction, the final outcomes (nonbreakup, single breakup, and double breakup) depend on the combination of three flow rates. The regime diagram for different outcomes is obtained, and the critical geometrical condition for the transition between nonbreakup and breakup is then identified from the deformation dynamics of the neck section. A theoretical analysis is then carried out to predict critical values of characteristic geometries for the transition between nonbreakup and breakup. The predictions of the critical initial thread length and the length of the first thread after breakup show good agreement with experimental measurements.

Fluid dynamic induced break-up during volcanic eruptions

Determining whether magma fragments during eruption remains a seminal challenge in volcanology. There is a robust paradigm for fragmentation of high viscosity, silicic magmas, however little is known about the fragmentation behaviour of lower viscosity systems—the most abundant form of volcanism on Earth and on other planetary bodies and satellites. Here we provide a quantitative model, based on experiments, for the non-brittle, fluid dynamic induced fragmentation of low viscosity melts. We define the conditions under which extensional thinning or liquid break-up can be expected. We show that break-up, both in our experiments and natural eruptions, occurs by both viscous and capillary instabilities operating on contrasting timescales. These timescales are used to produce a universal break-up criterion valid for low viscosity melts such as basalt, kimberlite and carbonatite. Lastly, we relate these break-up instabilities to changes in eruptive behaviour, the associated natural hazard and ultimately the deposits formed.

On the breakup of Taylor length scale size bubbles and droplets in turbulent dispersions

This work explores the mechanism of bubble and droplet breakup caused by turbulence in turbulent dispersions. Considering the deformation properties of the particle during the particle-eddy interaction process, a breakup model for bubbles and droplets of the Taylor length scale size is developed. The particle-eddy interaction frequency is modeled based on bubbles/droplets interacting with both larger and smaller eddies, in contrast with the usual collision frequency. Breakup criteria are demonstrated to depend on the degree of surface deformation prior to breakup. The relationship between the local characteristics of surrounding flows, such as the turbulent eddies’ variance and dissipation rate and the breakage rate as well as the daughter size distribution is then established and quantified. In particular, the contribution of turbulent eddies to the total breakage rate is clarified. This work provides a further understanding of breakup observations in complex turbulent fields and offers a more fundamental breakup kernel for the population balance model.

Comparison of secondary breakup models for droplet-laden compressor flows

Different secondary breakup models are assessed to simulate gas-droplet flows that involve large velocity gradients and yield relative velocities between both phases (e.g. wet compression flows). For the simulation of such two-phase flows, the Euler-Lagrange approach is employed, using a commercial flow solver and an in-house FORTRAN source code. The droplet deformation models: Taylor Analogy Breakup (TAB) and a simplified implementation of the Non-linear TAB (NLTAB3) are each tested with two different breakup criteria to evaluate the adequacy for considered droplet-laden compressor flows. A detailed atomization model is applied to account for a temporal fragmentation process. By contrast with experimental results good agreements are found for Weber number distributions in the inter blade flow. Though, different sensitivities and locations for secondary breakup occurrence are observed in dependence of applied droplet deformation model and breakup criterion. In spite of incisive model simplifications to reduce its computational effort, the non-linear droplet deformation model (NLTAB3) in combination with a physically substantiated breakup criterion showed good agreements with qualitative experimental data.

A model for drop and bubble breakup frequency based on turbulence spectra

In this article, a new Eulerian model for breakup frequency of drops induced by inertial stress in homogeneous isotropic turbulence is developed for moderately viscous fluids, accounting for the finite response time of drops to deform. The dynamics of drop shape in a turbulent flow is described by a linear damped oscillator forced by the instantaneous turbulent fluctuations at the drop scale. The criterion for breakup is based on a maximum value of drop deformation, in contrast with the usual critical Weber criterion. The breakup frequency is then modeled as a function of the power spectrum of Weber number (or velocity square), based on the theory of oscillators forced by a random signal, which can be related to classical statistical quantities, such as dissipation rate and velocity variance. Moreover, the effect of viscosities of both phases is included in the breakup frequency model without resorting to any additional parameter. © 2018 American Institute of Chemical Engineers AIChE J, 65: 347–359, 2019

Tunable Droplet Breakup Dynamics on Micropillared Superhydrophobic Surfaces.

Functional materials with controllable droplet breakup properties have extensive application prospects in aircraft anti-icing, spraying cooling, surface coating, and so on. Here we show that introducing micropillar arrays with various morphologies to fabricate superhydrophobic surfaces could either facilitate or suppress droplet splitting. The spacing and height of micropillars play an essential role in tuning the splitting patterns. Delayed splashing occurs on dense pillars which support the liquid lamella and provide channels for air to escape. A novel droplet breakup mechanism is found on sparse tall pillars, which rises from the instability of lateral liquid jets and significantly reduces the droplet breakup threshold. The critical Weber number of the rupture of low-viscous liquid is solely determined by the geometric parameters of micropillars and droplets. This work unveils the impact of ordered microstructures on the droplet breakup dynamics and provides a quantitative analysis of the geometric parameters in revising the breakup criteria.

Droplet Breakup Criterion in Airfoils Leading Edge Vicinity

A new breakup criterion is proposed in this paper for droplets subject to the flowfield generated by an incoming airfoil (that is, the criterion should be applied only to this type of aerodynamics flow). This criterion is based on the study of the characteristic times involved in the problem. These are the characteristic external flowfield variation time and the characteristic droplet deformation time. The criterion takes the shape of an empirical correlation that relates the Weber number at the onset of the breakup to the external flowfield and droplet characteristics. Experimental data on the droplet deformation and breakup tests conducted in a rotating arm facility are used to generate the data used to develop the correlation. Droplets, with diameters in the range of 0.3–3.6 mm, are allowed to fall in the path of an incoming airfoil attached to the end of a rotating arm. Airfoil velocities vary between 50 and . The airfoil leading-edge radius varies from 0.030 to 0.103 m. Experiments are recorded with a high-speed camera using the shadowgraph illumination technique. The empirical breakup correlation applies to droplets that break in the bag and stamen mode. Some additional limited data on droplets that break in the bag and the shear mode are analyzed to see how they fit into the correlation.