Breakup Probability Research Articles

The effect of emulsifier concentration on turbulent drop breakup – An experimental study based on single drop visualizations

HypothesisA modified Weber number can capture the effect of emulsifier concentration and the effect of external stress in turbulent drop breakup. Moreover, the effect of emulsifiers on turbulent drop breakup cannot be adequately understood from classic slow/laminar techniques and quasi steady state interfacial tension. ExperimentsSingle drop breakup visualizations are used to study the effect of polysorbate 20 on turbulent drop deformation and breakup. Comparisons are made to drop tensiometry and emulsification experiments. FindingsA high concentration of the emulsifier increases breakup probability and breakup rate and decreases breakup timescales. These effects scale with a Weber number, indicating a lowering of the effective interfacial tension to 71 % of its pure interface value. This is far less than the observed lowering of interfacial tension as measured by quiescent drop tensiometry. Mechanistically, this shows that adsorption during emulsification cannot be limited by diffusion. Studying the effect cross a range of emulsifier concentrations suggest an elastic resistance at intermediate concentrations, further helping to understand the origin of similar effects previously reported in emulsification experiments. Overall, the results show the need to study emulsifiers under turbulent conditions to understand their effects during emulsification, as opposed to the slow/laminar techniques previously used.

Drop breakup at reduced energy cost using a turbulent pulse –implications for improving efficiency in emulsification devices

Emulsification devices break drops by rapidly pushing them through a region of intense turbulence–a ‘turbulent pulse’. These devices are widely used in chemical engineering. However, the thermodynamic efficiency is low, and design modifications allowing more breakup at lower energy input is much in need.This study uses a combination of statistical models and direct numerical simulation coupled to high resolution interface tracking to investigate how a turbulent pulse should be designed to reach a desired breakup probability at minimum energy cost. It is concluded that breakup is not determined by the total energy input. Consequently, the energy cost of achieving a given breakup extent could be reduced by carefully tuning pulse amplitude and duration. The optimal pulse is compared to that delivered by homogenizers, revealing that the inability to dissipate turbulent kinetic energy in a sufficiently narrow region is partially responsible for the low efficiency.

Comprehension of breakup fusion reactions using forward recoil range distribution measurements

To understand the break-up fusion reaction dynamics, the forward recoil range distribution (FRRD) measurements of 12C + 165Ho system at the incident projectile energy of ≈ 88 MeV has been performed. The recoil catcher activation technique followed by the off-line gamma ray spectroscopy was implemented. It is observed that the FRRD measurements of the evaporation residues (ERs) populated via xn and pxn channels have a single Guassian peak at large cumulative thickness. This is attributed to complete momentum transfer from the projectile to the target nucleus. However, in case of the FRRD measurements of the ERs populated via αxn, αpxn and 2αxn emitting channels, in addition to peak corresponding to complete momentum transfer, the Gaussian peaks at lower cumulative thicknesses are also observed. This is accredited to the breakup fusion. Moreover, the effect of projectile breakup on complete fusion cross section is also studied. The suppression in fusion cross section is observed when compared with the universal fusion function, thus indicating the breakup probability of 12C projectile.

Peripheral reactions and elastic scattering induced by strongly bound, weakly bound and exotic nuclei

A phenomenological study of peripheral reactions induced by strongly bound, weakly bound and exotic projectiles on different targets is presented. A large number of experimental elastic scattering differential cross sections at energies close to the Coulomb barrier is studied on the basis of a simple nuclear optical model potential that depends on a small number of parameters. The derived wave functions, together with the imaginary component of the optical potential, allow the analysis of the radial peripheral absorption density distributions for the different kind of projectiles. These distributions, when appropriately normalized, show a clear correlation with the type of projectile regardless of the involved target and indicate that projectiles more prone to break up show a more peripheral absorption density distribution. This manifests in their magnitude, location and width. The relationship of these variables in the strongly bound group and the weakly bound group are described with a simple exponential function, while the exotic projectiles show two distinct groups, namely the neutron-halo and the proton-halo. For the neutron-halo projectiles such as He6, Li11 and Be11 there is a notable increment of the radial peripheral absorption density peak and the total reaction cross section as the breakup separation energy decreases. The same relationship is established for the proton-halo projectiles B8 and F17 but their reduced effective dipole charge leads to a lower probability of dipole Coulomb breakup that results in a substantial reduction in the extent of their peripheral absorption.

Price dispersion and the stability of trade*

AbstractResearch on trade relationships has documented a high rate of relationship breakup and churning. We use data on Norwegian exports to document two stylized facts about the stability of trade relationships. First, the probability of relationship breakup increases in the deviation of the relationship‐specific price from a reference price. Second, relationship hazards follow Zipf's law. We propose a search model with limited information and search frictions to explain these facts. Reference prices provide information on outside trade options that inform optimal breakups, leading to the first stylized fact. Strong heterogeneity in breakup frictions across relationships can explain the Zipf's law hazards.

Insights into gas flow behavior in venturi aerator by CFD-PBM model and verification of its efficiency in sludge reduction through O3 aeration

The use of ozone has become a new direction in residual sludge reduction. In order to improve the mass transfer efficiency and utilization efficiency of ozone, the structure of the venturi aerator was optimized by simulating the gas flow behavior with the CFD-PBM model. The gas volume fraction slowly decreased as the inlet angle increased. Besides, the ratio of throat diameter and throat length gradually increased, increasing bubble crushing rate and breakup probability. The turbulent eddy dissipation decreased with increasing outlet angle and moved from the central region to the sidewall, reaching a maximum at the throat. Thus, the optimal parameters for the venturi aerator were determined to be an inlet angle of 15°, a ratio of throat diameter to throat length of 1 and an outlet angle of 3°. Regarding the sludge reduction effect, the sludge dissolution efficiency after treatment with an optimized venturi aerator and traditional disc aerator was 35.3 % and 28.6 %, respectively. When the ozone dosage was 100 mg/g·MLSS, the venturi aerator had a better effect on ozone utilization than the disc aerator. At an ozone inlet flow rate of 2 L/min, the mass transfer coefficient of ozone in a venturi aerator was higher than that of the disc aerator. This study demonstrates the operational feasibility of ozone combined with a venturi aerator to reduce residual sludge production.

When Does a Light Sphere Break Ice Plate Most by Using Its Net Buoyance?

A free-rising buoyant sphere can break an ice plate floating above it. The problem is when the light sphere breaks the ice plate most, or the optimal relative density of the sphere which can break the ice plate the most severely. This experimental study was done to answer this problem. A set of experimental devices were designed, and a high-speed camera system was adopted to record the whole dynamic process, including the free-rising of the sphere, the collision between the sphere and the ice plate, the crack initiation and propagation, as well as the breakup of the ice plate. The failure mode of the ice plate under impact load was analyzed. It was found that conical cracks were formed under the reflected tensile wave at the top surface of the ice plate. On this basis, the influences of ice thickness, the initial submergence depth, and the relative density of the sphere on icebreaking were further investigated. An optimal relative density of the sphere was found when the sphere was released at a certain initial submergence depth, at which point the ice was damaged the most severely. For example, when the dimensionless initial submergence depth of the sphere was 2.31, the optimal relative density of the sphere was close to 0.4, with the probability of the ice plate breakup as high as 91.7%. It was also found from the experiments that the degree of damage to the ice plate correlated well with the kinetic energy of the sphere just before collision. Results showed that the optimal relative density can be estimated by theoretical analysis of the kinetic energy of the sphere, which will provide a reference for potential icebreaking applications in the future.

Improved Quantum Molecular Dynamics Model and Its Application to Ternary Breakup Reactions

Collisions of very heavy nuclei 197Au+197Au at the energy range of 5–30 A MeV have been studied within the improved quantum molecular dynamics (ImQMD) model. A class of ternary events satisfying a nearly complete balance of mass numbers is selected and we find that the probability of ternary breakup depends on the incident energy and the impact parameter. It is also found that the largest probability of ternary breakup is located at the energy around 24 A MeV for the system 197Au+197Au. The experimental mass distributions and angular distributions for the system 197Au+197Au ternary breakup fragments can be reproduced well by the calculation with the ImQMD model at the energy of 15 A MeV. The modes and mechanisms of ternary and quaternary breakup are studied by time-dependent snapshots of ternary events. The direct prolate, direct oblate, and cascade ternary breakup modes, are manifested and their production probabilities are obtained. The characteristic features in ternary breakup events, three mass-comparable fragments, and the very fast, nearly collinear breakup, account for the two-preformed-neck shape of the composite system. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary breakup with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.

Microscopic mechanism for nanoparticle-laden droplet–droplet electrocoalescence: A molecular dynamics study

Electrocoalescence is an energy-efficient and environmentally friendly process for separating water-in-oil emulsions. In this study, nanoparticle-laden droplet–droplet electrocoalescence behaviors under external electric fields were numerically investigated using molecular dynamics (MD) methods. Good agreement was obtained between numerical results and experimental validation work. The influences of electric field strength, droplet diameter, nanoparticle (NP) concentration, NP size, and electric frequency were systematically examined, analyzed, and discussed from the perspective of intermolecular interactions. The NPs migrated to the liquid bridge to form nanoparticle shell under electric fields, and the NP brown motion increased the breakup probabilities, leading to partial electrocoalescence, which is undesirable in oil–water separation process. As to unequal droplets (droplet pairs of 6&4 nm, 6&6 nm, and 6&8 nm), the daughter droplets were always ejected from the apex of the small droplet. The NP concentrations influence not only the film coalescence process but also the droplet approach process, and high concentrations (0.15, 0.22 and 0.29 mol L−1) resulted in partial coalescence. The NP size also played significant roles during electrocoalescence. At large NP sizes (0.86 & 1.16 nm), the electrostatic repulsion between NPs played the dominant roles in the overall system, accounting for the PC mode with increasing NP size. In addition, applying high frequency (10 & 40 GHz) AC electric fields was found to be a time-saving and high-efficiency method. The results of this work will be potentially useful for optimizing the design of compact and efficient oil–water separators.

Experimental study on breakup of a single bubble in a stirred tank: Effect of gas density and liquid properties

AbstractBubble breakup plays an important role in gas–liquid flows, but detailed studies are still scarce. In this work, the breakup behavior of a single bubble in a stirred tank was experimentally studied with a high‐speed camera, focusing on the effect of gas density, liquid properties, agitation speed, and mother bubble size. The bubble breakup time, breakup probability, breakup rate, and daughter bubble size distribution were determined. The internal‐flow phenomenon that the gas flowed from the smaller part to the larger part of a deformed mother bubble was observed by a high‐speed camera. The results showed that with increasing gas density, agitation speed, mother bubble size and decreasing surface tension, the bubble breakup rate and probability of equal‐size distribution significantly increased. With increasing liquid viscosity, the bubble breakup rate decreased especially in the high viscosity range. An M‐shaped daughter bubble size distribution was observed, which was consistent with our previous bubble breakup model.

Numerical calculation of intermolecular bonds under the action of ultrasonic cavitation

The linear model of macromolecules was proposed. Expression for probability of macromolecules breakup under ultrasonic cavitation action was obtained. The fractional composition and viscosity of uncured polymer were calculated. As a result of the calculations, it was evaluated that the cavitation-acoustic effect for a time of no more than 1 min at an vibration intensity of at least 6 W/cm2 and an initial viscosity of 0.2 Pa· s reduces the viscosity of polymers by at least 8 times. At the same time, it was theoretically revealed that the cavitation-acoustic effect is also capable of reducing the viscosity of polymers with an initial viscosity of more than 1 Pa·s up to 4 times.

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.

Fluidization dynamics of wet Geldart D particles by pressure fluctuation analysis

The increase of liquid saturation badly affects the fluidization dynamics, even resulting in the failure of fluidization. Nevertheless, few researches focus on characterizing the flow pattern transition of wet particles. In this work, we discuss the effects of the liquid saturation, gas velocity and the particle size on the global fluidization dynamics of Geldart D particles by analyzing the pressure fluctuations in the fluidized bed. The results show that the bubble dynamics is intensified with the increasing liquid saturation and decreasing particle size. When the superficial gas velocity increases, the fluidization regimes change from expanding regime, to multi-bubbling regime and slugging. During the normal fluidization and slugging, the liquid bridge forces prevent the growth of large bubbles and promote the probability of bubble break-up. Thus, the average bubble size decreases and the number of bubbles increases, which lead to the intense bubble behavior. With the decreasing particle size, the effect of liquid bridge forces is enhanced, contributing to the intensified bubble dynamics, including fast rising, frequent coalescence and eruption of a large number of bubbles. Compared to dry particles, wet particles are easily to cause defluidization when the gas velocity is small. The PSD patterns have the sharp narrow peaks at frequency lower than 0.8 Hz. When the liquid saturation is increased to 30%, a gas channel forms in the bed, which resists the normal works of the fluidized bed. Basically, reducing the liquid saturation is a reasonable way to avoid defluidization.

Effect of neutron excess in the entrance channel on the O18+Nb93 system: An experimental study relevant to incomplete-fusion dynamics

The incomplete fusion dynamics in the $^{18}\mathrm{O}+^{93}\mathrm{Nb}$ system at energies above the Coulomb barrier has been investigated. The experimentally measured cross sections have been compared with the theoretical predictions of the statistical model code pace4. To examine the effect of entrance channel parameters on the onset and strength of incomplete fusion, relative contributions of complete and incomplete fusion have been deduced from the analysis of measured excitation functions. The contribution of incomplete fusion deduced from the analysis of excitation functions has been studied in terms of various entrance channel parameters, namely, entrance channel mass asymmetry (${\ensuremath{\mu}}_{A}$) of interacting projectile and target combination, Coulomb factor (${Z}_{P}{Z}_{T}$), ground state $\ensuremath{\alpha}\text{\ensuremath{-}}Q$ value of the reaction, and neutron skin thickness of target nuclei. It has been found that the probability of incomplete fusion depends strongly on entrance channel parameters. Further, the incomplete fusion contribution for the $^{18}\mathrm{O}$ projectile with two excess neutrons is noticed to be relatively larger as compared to $^{16}\mathrm{O}$. This may be due to the larger probability of breakup for the $^{18}\mathrm{O}$ projectile resulting in rather weak binding forces as compared to $^{16}\mathrm{O}$. The existence of incomplete fusion below critical angular momentum (${\ensuremath{\ell}}_{\mathrm{crit}}$), i.e., $\ensuremath{\ell}\ensuremath{\leqslant}\phantom{\rule{4pt}{0ex}}{\ensuremath{\ell}}_{\mathrm{crit}}$, has also been observed for the studied system.

Transformation of single drop breakup from binary to ternary and multiple in turbulent jet flows

By releasing liquid drops in turbulent jet flows, we investigated the transformation of single drop breakup from binary to ternary and multiple. Silicone oil and deionized water were the dispersed phase and continuous phase, respectively. The probability of binary, ternary, and multiple breakup of oil drops in jet flows is a function of the jet Reynolds number. To address the underlying mechanisms of this transformation of drop breakup, we performed two-dimensional particle image velocimetry (PIV) experiments of single-phase jet flows. With the combination of drop breakup phenomenon and two-dimensional PIV results in a single-phase flow field, these transformation conditions can be estimated: the capillary number ranges from 0.17 to 0.27, and the Weber number ranges from 55 to 111.

Simultaneous measurements of deforming Hinze-scale bubbles with surrounding turbulence

Abstract

Global descriptions and decay rates for continuum excitation of weakly bound nuclei

In this work we will present an overview of our global studies on continuum excitations induced by protons, for the weakly bound nuclei $$^6\hbox {Li}$$ , $$^7\hbox {Li}$$ and $$^9\hbox {Be}$$ , presenting strong clustering modes. Measurements are made in inverse kinematics and extensive simulations have been developed, to corroborate the analysis and interpretation of the results. The focus of the measurements is on the breakup reaction, but simultaneously this research is complemented by the study of all involved reaction channels, including elastic scattering. In this respect our theoretical interpretation in a Continuum Discretized Coupled Channel approach can be fully validated. Between our sound conclusions we can underline the following: the non reciprocity between the strengths of the breakup probability and the coupling to continuum; the experimental validation of a continuum discretization for three body Continuum Discretized Coupled Channel theories; and last but not least the unique possibility for deducing continuum decay rates of borromean nuclei in proton induced studies, by considering the kinematics of the target recoil. Other specific conclusions for each system will be discussed.

A probability model for predicting the bubble size distribution in fully developed bubble flow in vertical pipes

Bubble flow has good characteristics of mass and heat transfer, and is widely used in industrial practice. In bubble flow, the gas phase is mixed with the liquid phase in the form of bubbles. The gas-liquid two-phase structure of bubble flow is investigated by analyzing the motion and force states of bubbles. The most crucial bubble behaviors include the bubble collision and breakup, which continuously occur in the movement process of bubble flow. The bubble collision is usually brought by the fluid turbulence, buoyancy and laminar shear stress. The coalescence efficiency of bubble collisions is analyzed to describe the bubble coalescence behavior. A novel theory of bubble breakup is established according to the probability field analyses of turbulent eddies. Then, the generation and elimination rates of an entire bubble group can be obtained by calculating the collision and breakup probabilities of a single bubble. Combing with the investigations on the random motion rules of a single bubble and an entire bubble group, a theoretical model is first developed to predict the overall bubble size distribution in fully developed bubble flow. The predictions from the probability model generally agree with the experimental data of the bubble size distribution, validating the applicability and easier usage of the theoretical model.

Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank

AbstractThe direct experimental data for breakup parameters of drop breakup time, multiple breakage, and breakup rate are urgently required to understand drop breakup phenomena. In this regard, drop breakup experiments were carried out in a stirred tank using a high‐speed online camera. The influences of the rotating speed, interfacial tension, and drop viscosity on the above breakup parameters were then quantitatively investigated. An mechanism correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem Eng Sci, 2015;131:219‐234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d/dmax can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.

Environment capacity as an early mission design driver

In recent years, several metrics have been proposed to quantify the impact of a mission on the space debris environment. In our previous work, we introduced the environmental capacity as the number and typology of missions that are compatible with the stable evolution of the debris environment. This concept enables the evaluation of the effectiveness of mitigation guidelines by looking at the use of environmental capacity due to existing missions. The current work will investigate how the same concept can also be applied as a tool during the design of a mission, facilitating the comparison of different mission architectures depending on their overall contribution to the debris environment. First, the paper will present the latest updates to the debris index used as a metric of the environment capacity, including the inclusion of a penalisation for objects with low trackability and an improved model for the break-up probability. Then, several application cases will be discussed to demonstrate its use as design driver. First, the relevance of adopting operational best practices (i.e. collision avoidance and disposal manoeuvres) will be studied for different spacecraft classes as a way of quantifying better than required behaviour. Then, the environmental impact of a mission will be analysed considering the case when the mission is realised through a single large satellite or through a constellation of smaller satellites. Finally, different end-of-life scenarios will be assessed to demonstrate the use of the method to discriminate between various technologies on a case-by-case basis. The adoption of passive de-orbiting systems will be compared to conventional disposal through de-orbit burns or operations at lower altitudes to gain insight into how two different options, both compliant to existing guidelines, differ in terms of the resulting environmental impact. Finally, a scenario with active-debris-removal will be considered, showing how the quantification of the impact on the debris environment can support the selection of parameters such as the rendez-vous altitude, based on the expected success rate of the capture and final disposal phase.