Breakup Criterion Research Articles

A theoretical model for droplet breakup in turbulent dispersions

A theoretical model for the prediction of droplet breakup rate and daughter size distribution in turbulent dispersions has been developed. It considers the breakup contributed by a novel breakup criterion based on surface energy density increase, the droplet surface oscillation from previous collision and the eddies larger than original droplets. The breakup rate and daughter size distribution predicted by this model show a good agreement with the experimental data reported recently.

Droplet impingement and breakup on a dry surface

In this work, new results of droplet impingement and breakup have been obtained using three-dimensional lattice Boltzmann method. All four phases after impingement, the kinematic, spreading, relaxation and equilibrium phases, leading to breakup have been obtained for a range of Weber number, Reynolds number and density ratio. Conditions have been chosen such that Re ≪ We for comparison with available data in the literature. The maximum spread factor compares well with experiments as well as the theoretical value of 0.5 Re 0.25. At Oh < 0.15 and Capillary number, Ca < 1.0, the relaxation phase is marked by the presence of strong oscillations in the spreading diameter. An analytical solution for breakup based on the conservation of energy is provided. Criteria for three-dimensional droplet breakup have been developed as functions of Re and We.

Bubble splitting in oscillatory flows on ground and in reduced gravity

The stability of centimeter scale air bubbles is studied in quiescent suspending liquid under an imposed oscillatory acceleration field. Experiments were performed in reduced- and normal-gravity environments. A strong acceleration resulted in an instability leading to the breakups of the bubbles in both gravity environments. The breakup onset was investigated and found to be characterized by a critical acceleration a (cr). The influence of the liquid viscosity and the gravitational environment was studied. Empirical correlations for the onset are presented and discussed with the intention to reveal splitting mechanism. The inertial mechanism often deemed to cause the breakup of drops subjected to a rapid gas stream is shown to give explanations consistent with the experiments. A breakup criterion for both gravitational environments is proposed through discussions from an energetic point of view.

Numerical modeling of dimethyl ether (DME) bubble growth and breakup

A numerical program is written to simulate the process of vapor bubble growth with spherical symmetry from the thermodynamic critical radius in an initially uniformly superheated liquid. The program is validated by the experimental data of superheated water. The calculated results agree with those of experiments well. The program takes into account the variations of properties with temperature precisely to simulate the DME bubble growth under flash boiling conditions. Considering the influences of pressure, surface tension and viscous stress, the linear stability analysis method is adopted to deduce the dispersion equation to represent the disturbance development during the bubble growth, and a new criterion for bubble breakup is established. The results show the bubble becomes more unstable with the increase of bubble Weber number and void fraction, and that with the increase of bubble growth rate or the decrease of initial radius ration of droplet to bubble, the breakup time of bubble becomes shorter.

Particle Impact and Breakup in Aircraft Measurement

Abstract Measurements of cloud particle properties from aircraft by optical and impact techniques are subject to artifacts following particle breakup prior to detection. The impact kinetic energy to surface energy ratio (ℒ) provides a breakup criterion at ℒ ≥ 7 for water and ice with major fragmentation for ℒ &amp;gt; 100. This applies to optical imaging probes for particle concentration, size, and projected area spectra measurement. Uncertainty arises should impacting particles shatter and disperse, defeating the intent of the original measurements. Particle shatter is demonstrated in Formvar replicas (University of North Dakota Citation) and video records of particle approach and impact on the Cloudscope (NCAR C-130, NASA DC-8) at airspeeds of 130 and 200 m s−1. Sufficient impact kinetic energy results in drop splash and ice shatter, with conversion to surface energy and ultimately thermal energy through viscous dissipation and ice defect production occurring down to the molecular scale. The problem is minimized in design by reducing the regions responsible for particle breakup to a minimum and locating sensors in regions inaccessible to shatter fragments.

Condition for Break-up of Non-Wetting Fluids in Sinusoidally Constricted Capillary Channels

Analysis of capillary-pressure distribution in single channels with sinusoidal profile shows that surface tension-driven flow in such channels is controlled by the pressure extrema at their “crests” and “troughs”. Formulating the geometric condition for the pressure in the troughs to exceed that in the crests leads to a simple criterion for the spontaneous break-up of the non-wetting fluid in the necks of the constrictions. The criterion reduces to the condition for the Plateau-Rayleigh instability as a limiting case. Similar pressure analysis is applicable to the case of a non-wetting fluid invading an open pore body. Computational-fluid-dynamics experiments have verified the validity of the break-up predicted from the capillary-pressure argument. Although the geometric criterion for the break-up is valid for small capillary numbers, it provides a common framework in which the results of various published studies of a non-wetting phase choke-off in capillary constrictions for a wide range of capillary numbers can be explained and understood.

Field studies of ice breakup and jamming in lower Peace River, Canada

Abstract Since the late 1960s, a paucity of ice-jam flooding in the lower Peace River has resulted in prolonged dry periods and considerable reduction in the area covered by lakes and ponds that provide habitat for aquatic life in the Peace–Athabasca Delta region. To help identify the causes of this trend and assess future conditions under a changing climate, a field observation program was conducted during 1999–2003. Limited data were also obtained during a significant event in 2007. This program has furnished the first detailed documentation of ice processes in the lower Peace. Though focusing on the breakup period, relevant antecedent conditions were also documented. Freezeup often involves formation of thickened ice covers, which lead to high freezeup stages and potentially to enhanced growth of the solid-ice layer during the winter. Ice decay prior to breakup can be moderate to severe, and is manifested in saturation and candling. The type of observed breakup ranged from essential melt-out in 2000, to occasional jamming upstream of the delta reach in 2003, and to a moderate delta flood in 2007. The field observations and measurements, including the only ice jam profile that has been measured in the lower Peace, are shown to be consistent with current physical understanding of breakup and jamming processes. The main factors conducive to ice-jam flooding are identified and their relative importance is assessed using physically-based breakup criteria. Breakup patterns are shown to be strongly influenced by the very low slope of the river, which amplifies the importance of waves generated by ice jam releases.

Simulations of liquid nanocylinder breakup with dissipative particle dynamics

In this work, we use a dissipative-particle-dynamics-based model for two-phase flows to simulate the breakup of liquid nanocylinders. Rayleigh's criterion for capillary breakup of inviscid liquid cylinders is shown to apply for the cases considered, in agreement with prior molecular dynamics (MD) simulations. Also, as shown previously through MD simulations, satellite drops are not observed, because of the dominant role played by thermal fluctuations which lead to a symmetric breakup of the neck joining the two main drops. The parameters varied in this study are the domain size, cylinder radius, thermal length scale, viscosity, and surface tension. The breakup time does not show the same scaling dependence as in capillary breakup of liquid cylinders at the macroscale. The time variation of the radius at the point of breakup agrees with prior theoretical predictions from expressions derived with the assumption that thermal fluctuations lead to breakup.

River ice cover flexure by an incoming wave

Abstract A river's ice cover can be broken up by unsteady flows that may result from a sudden increase in discharge resulting from a dam break event, an ice jam release event or a flash-flood. As the resulting wave (surge or ‘jave’) travels downstream, if it is not strong enough to break the cover, its amplitude and celerity will be dampened whereas if it is, they may be amplified. It is therefore important to know what rise in levels is required to break an intact ice sheet. In this paper, 1D and 2D numerical models are used to investigate the wave–ice cover interaction in order to formulate simple river ice sheet breakup criteria. The 1D model (based on the theory of beams on an elastic foundation) uses an iterative, in-house, finite difference method to converge on a solution that correctly models the limiting effect that the ice sheet's freeboard has on the imposed load. The analyses show the importance of non-linear ice sheet response to increasing wave amplitudes and/or water surface slopes as a function of ice sheet thickness. The paper also presents an analysis of water shear effects on axial and bending stresses. Lastly, a finite element method (FEM) is used to resolve the 2-D problem. For ice sheets frozen into or simply attached to the river banks, computed stresses are shown to be significantly different from the 1-D solution.

On the grain boundary grooving in thin filaments

The process of grain boundary grooving in thin filaments with bamboo microstructure is considered. A criterion for filament break-up is obtained. It is shown that original Mullins’ theory of grain boundary grooving considerably overestimates thermal stability of thin filaments.

Deformation and breakup of a non-Newtonian slender drop in an extensional flow

The deformation and breakup of a non-Newtonian slender drop in a Newtonian liquid in a simple extensional and creeping flow has been theoretically studied. The power-law was chosen for the fluid inside the drop, and the deformation of the drop is described by a single ordinary differential equation, which was numerically solved. Asymptotic analytical expressions for the local radius were derived near the center and close to the end of the drop. The results for the shape of the drop and the breakup criterion are presented as a function of the capillary number, the viscosity ratio and type of non-Newtonian fluid inside the drop. An approximate analytical solution is also suggested which is in good agreement with the numerical results.

マイクロスケール2焦点レーザ流速計による高速高濃度噴霧の計測(OS7-2マイクロ・ナノフルイディクス(マイクロ・ナノ流体物理))

In order to investigate the dggect of needle lift on the early tage of spray desintegration, simultaneous measurments of velocity and size of droplets were conducted by a mewly developed laser 2-focus velocimeter (L2F). The micro-scale prove is consisted of two foci tiwh a distance of 30u.m. The tested nozzle has single hole with a diameter D of 0.2 mm. The measurements of injection pressure, needle lift, and crank angle were synchronized with the L2Fmeasurements, It is clearly showm that droplets are desintegrated remarkably on the transient needle opening condition, Droplets with higher velocity and larger size than the breakup criteria are observed near the spray center on the full nedle lift condition. It is understood that large droplets penetrate along the spray axis and small droplets scatter radially near the nozzle exit.

The sensitivity of the ESA DELTA model

The debris environment long term analysis (DELTA) model, developed by QinetiQ for the European Space Agency (ESA), allows the future projection of the debris environment throughout Earth orbit. To ensure a sound basis for such future projections, and consequently for assessing the effectiveness of various mitigation measures, it is essential that the sensitivity of the model is examined. This paper discusses the sensitivity of the DELTA model to changes in key model parameters and assumptions. Specifically, the variation in future traffic rates, including the deployment of satellite constellations, and the variation in the break-up model and criteria used to simulate future explosion and collision events.

Drop breakup and fragment size distribution in shear flow

We report a study on the deformation and breakup of drops in an impulsively started shear flow under Stokes flow conditions using boundary-integral simulations and video-microscopy experiments. Two independent techniques are used for determining the physical parameters of the system from the combined use of numerical simulations and experiments. Accurate breakup criteria (critical capillary numbers) are presented for a range of viscosity ratios. The time required for breakup events has a broad minimum corresponding to moderate shear rates. The size distribution of droplets produced by breakup events is shown to scale with the critical size drop for breakup in shear. A simplified model, based on this finding, is developed for the size distribution in a sheared emulsion. According to the model, the drop size distribution in a given emulsion depends only on the average initial drop size and the shear rate.

Applicability of Criterion for Onset of River Ice Breakup

The breakup of an ice cover may lead to ice jamming. However, tested methods for predicting the ice cover breakup are lacking. One method uses hinge resistance at riverbanks as a tentative criterion for ice cover breakup in relatively straight rivers. In the present study, data from 6 years of observations of the Mississippi River at Anoka, Minn. are used to evaluate the applicability of that criterion. The observations include the date, the flow, and the thickness of the ice cover at the onset of cover breakup. An effort is made to estimate the shear stress on the ice cover with reasonable accuracy; and this shear stress is used to determine the counteracting hinge resistance at the onset of cover breakup. The calculated value of hinge resistance does not vary much from year to year, and thus the proposed criterion appears to be applicable for the study site.

A ONE-DIMENSIONAL BREAKUP MODEL FOR LOW-SPEED JETS

A one-dimensional model is developed for the primary breakup of low-speed jets using the technique of tracking the wave growth on the liquid-gas interface. The continuity and momentum equations are reduced to one-dimensional (1-D) forms to calculate the growth of waves on the jet surface. A novel symmetrical initial condition is proposed to handle finite-length jets and complex disturbances. A fast Fourier transform (FFT) is used to capture the surface wave structure. The drop size distribution is calculated/row the Fourier series by assuming that the diameter of each drop is proportional to the wavelength of its corresponding wave and the mass associated with each drop size is proportional to its Fourier coefficient. A breakup criterion is proposed based on the growth of the surface area. This model is validated by comparing with linear theories and with measurements for low-speed jets. breakup characteristics, such as the drop size distribution and Sauter mean diameter (SMD), are studied for a range of injection velocities.

IMPROVED TAB MODEL FOR PREDICTION OF SPRAY DROPLET DEFORMATION AND BREAKUP

An improved Taylor analogy breakup (TAB) model been proposed for more accurate prediction of the deformation and breakup of a spray. Especially, the effects of the droplet deformation on the droplet aerodynamic external force are considered in this model, which was neglected in the TAB model. It is found that the predicted droplet deformation using the present improved TAB model shows better agreement with experimental data than those of other models for the droplets in both bag-type and shear-type breakup regimes. A new breakup criterion has been proposed to predict more reasonable breakup quantities, such as breakup deformation length and breakup time; it is defined that the breakup occurs when the internal liquid-phase pressure of the deformed droplet at the equator is greater than that at the pole. The proposed breakup criterion shows more physical relationship between the degree of droplet deformation at breakup and the corresponding breakup Weber number as compared with the results using the TAB and the droplet deformation (DDB) models. Therefore, it provides better predictions of the experimental data than the TAB and DDB models for the droplet deformation and breakup time in both the bag-type and shear-type breakup regimes.

On the breakup of gas bubbles in a liquid under the action of a finite-amplitude pressure wave

A mechanism for breaking up gas bubbles in a liquid in a high-intensity pressure wave field is considered. Breakup criteria are obtained. An anomalous dependence of the breakup pressure on the initial bubble radius is found and explained.

Modelling of Break-up of Liquid Drops Impacting on Immiscible Liquids.

Break-up phenomena of liquid drops impacting on immiscible liquids have been investigated. Oscillation of falling drops was found to play an important role in break-up in a certain range of falling height. Criteria for break-up were discussed, and it was found that either Reynolds or Weber number was not adequate in describing the criteria of break-up of a liquid drop impacting on an immiscible liquid target. From the experimental results of the present study, empirical models have been formulated, which enables to predict the critical falling height for the first break-up of a drop. Conditions for break-up of liquid iron drops impacting on a liquid slag were predicted using the models. The prediction showed that the majority of metal drops propelled to the top space of an intensive reactor should suffer break-up during the fall through the slag layer.

Dynamics of a drop of magnetic liquid in a rotating magnetic field

We report the first observation of the breakup of a rotating drop suspended in a viscous liquid. To produce the motion, a magnetic liquid is used as the material of the drop and the entire system is placed in a uniform, rotating, low-frequency magnetic field. The frequency dependence of the breakup of the drop into two smaller drops is investigated. A theoretical description is given for small Reynolds numbers. The drop is assumed to be ellipsoidal. The flow in the exterior and interior regions and the drag coefficient of the liquid ellipsoid with respect to rotational motion are calculated. A criterion for breakup of the drop is estimated and a comparison is made with experimental data.