Breakup Rate Research Articles

Numerical Simulation of Bubble Column Flows in Churn-Turbulent Regime: Comparison of Bubble Size Models

Numerical simulations of cylindrical bubble column operating in the churn-turbulent regime have been simulated using Euler–Euler approach incorporated with the RNG k–ε model for liquid turbulence. Single-size bubble model, double-size bubble model, and the multiple size group model (MUSIG), including the homogeneous and inhomogeneous discrete methods, are employed in the simulations. Mass conserved formulations of breakup and coalescence rates were used in the computation of bubble size distributions. The Schiller–Naumann drag force was used in the single-size model, and the Ishii–Zuber drag force was used for the MUSIG simulations. For the double-size bubble model, an empirical drag formulation was adapted. The simulation results of time-averaged axial velocity and gas holdup obtained with the three models were compared with reported experimental data in the literature. The results showed that only MUSIG models with lift force can reproduce the measured radial distribution of gas holdup in the fully developed flow regime and that the inhomogeneous MUSIG model performs a little better than other models in the prediction of axial liquid velocity. The RNG k–ε model was used in all simulations, and the results confirmed that this version of k–ε model did yield relatively high turbulence dissipation rates and high bubble breakup rates and, thus, resulted in a rational bubble size distribution. The ad hoc manipulation of the breakup rates was avoided. The simulation results indicated profound mutual effects of drag force, mean bubble sizes, and turbulence characteristics. An increase in drag force yielded a decrease in the relative velocity between phases, the later could result in decreases in k and ε. A large Sauter diameter results from a low bubble breakup rate which was directly connected to the dissipation rates of turbulence. The change of Sauter diameter, in turn, influenced the drag force.

Mechanism of flow-induced biomolecular and colloidal aggregate breakup

The drift-diffusion equation is first solved analytically for the dissociation rate and lifetime of a biomolecular or colloidal dimer bonded by realistic intermolecular potentials, under shear flow. Then we show using rigidity percolation concepts that the lifetime of a generic cluster formed under shear is controlled by the typical lifetime of a single bond in its interior. The latter, however, is also affected by collective stress transmission from other bonds in the aggregate, which we account for by introducing a semiempirical, analytical stress transmission efficiency $0\ensuremath{\leqslant}\ensuremath{\Gamma}\ensuremath{\leqslant}1$ calibrated on several simulation data sets. We show that aggregate breakup is a thermally activated process in which the activation energy is controlled by the interplay between intermolecular forces and the shear drift. The collective contribution to the overall shear drift term is dominant for large enough fractal aggregates, while surface erosion prevails for small and compact aggregates. The crossover between the two regimes occurs when $\ensuremath{\Gamma}N\ensuremath{\simeq}2$, where both the number of particles in the cluster $N$ and the stress transmission efficiency $\ensuremath{\Gamma}$ depend on the aggregate structure through the fractal dimension ${d}_{f}$. The analytical framework for the aggregate breakup rate is in quantitative agreement with experiments and can be used in future studies in the population balance modeling of colloidal and protein aggregation.

Experimental study and numerical simulation with a coupled CFD–PBM model of the effect of liquid viscosity in a bubble column

The effect of liquid viscosity on the hydrodynamic behavior in a bubble column was investigated by experimental study and numerical simulation with a coupled CFD–PBM (population balance model) model. The total gas holdup and volume fractions of small and large bubbles were determined by the dynamic gas disengagement method. In the low viscosity range, the total gas holdup and the volume fractions of small and large bubbles were almost independent of the liquid viscosity. In the high viscosity range, an increased viscosity gave a decrease in the total gas holdup and volume fraction of small bubbles and an increase in the volume fraction of large bubbles. The simulation captured these features and showed that when the liquid viscosity was <10mPas, the viscosity had negligible effect on the bubble breakup rate and daughter bubble size distribution, while a further increase of the liquid viscosity significantly decreased the bubble breakup rate and increased the probability of equal breakup. The influence of liquid viscosity on bubble coalescence was less important than its effect on bubble breakup for the hydrodynamic behavior. With the use of the multiple bubble breakup and coalescence models and the use of the bubble size distribution to describe the interphase forces, the coupled CFD–PBM model could describe the dependences of the total gas holdup and volume fractions of small and large bubbles on liquid viscosity in both the homogeneous and heterogeneous regimes.

Age of Child at Death Can Affect Parents’ Mortality

Back to table of contents Previous article Next article Clinical and Research NewsFull AccessAge of Child at Death Can Affect Parents’ MortalityAaron LevinAaron LevinSearch for more papers by this authorPublished Online:1 Feb 2013https://doi.org/10.1176/appi.pn.2013.1b17AbstractLosing a child to sudden, unexpected death may seriously affect the health and other key aspects of life of the parents.The tragic deaths of 20 children in Newtown, Conn., in December brought to the forefront recent research on the health outcomes of bereavement by parents who have lost their children.Parents in Newtown will be at risk for at least several years and should be followed to see that they have access to care, said James Bolton, M.D., an assistant professor of psychiatry at the University of Manitoba, in an interview with Psychiatric News.“We have to recognize that they are vulnerable and that treatment needs to be readily available.”Bereavement responses vary widely, of course. Some people are more resilient than others. However, the death of a child—regardless of age—can have harmful physical effects on surviving parents, wrote Mikael Rostila, Ph.D., and colleagues in the October 2012 Journal of Epidemiology and Community Health. Rostila is an associate professor of sociology at the Centre for Health Equity Studies (CHESS) at Sweden’s Stockholm University and the Karolinska Institute.The researchers distinguished between death by “natural” causes, such as disease, and “unnatural” ones, such as by suicide, homicide, or accident.“Our data . . . indicate that unnatural causes of child death have a stronger impact than natural deaths on parental mortality, but mainly among mothers who lost young children (aged 10-17 years),” said the researchers. The mortality effect on fathers in the Swedish study was not significant.“In other age groups we found no difference in the effect of natural versus unnatural child deaths on the mortality of parents,” said Rostila in an interview. “In other words, unnatural child deaths are particularly detrimental for mothers when the child is young at the time of death.” Mothers of children aged 10-17, the youngest age group in this study, faced an increased risk of 31 percent in all-cause mortality, but that increase was driven largely by an increased risk of 48 percent among mothers whose children died unnatural deaths.Although his study did not cover younger children, Rostila speculated that the death of a child under age 10 might be at least as detrimental given the strong emotional bond and attachment between the child and the parent.“The death of a young child is also extremely unexpected, which could lead to strong feelings of grief and difficulty in coping with the death,” he said.Rostila and colleagues also found a 26 percent to 33 percent increased association with mortality among the siblings of the deceased child. But so little research has been done on this group that Rostila called them “the forgotten griever[s].”The psychological effects on parents can crop up in a relatively short time, Bolton pointed out.In a study published online December 10, 2012, in Archives of General Psychiatry, Bolton and colleagues compared parents bereaved by the death of their children by either suicide or motor-vehicle crash. He and his colleagues found associations in both groups with increased rates of depression, anxiety, and marital breakup, although not with drug or alcohol use disorders.“There was quite a dramatic effect on parents, but there wasn’t much of a difference in outcomes relating to the specific cause of the child’s death,” said Bolton. “So the parents of children killed in a mass shooting will be a very vulnerable group, and the increased risk will be visible soon, even with the first two years.”Bolton’s two-year study was too short to observe physical effects on bereaved parents of a child’s death, but the short-term mental health effects are likely to translate into physical effects eventually, he said.In one respect, the aftermath was different for parents following a suicide. The stigma faced by the parents of children who died by suicide was often manifested by the surrounding community, which shunned them or at least felt awkward in approaching the family, said Bolton. That should not be the case in Newtown, however, where the community has rallied around the parents of the children who were shooting victims at the elementary school, he said. ■An abstract of “Mortality in Parents Following the Death of a Child: A Nationwide Follow-up Study From Sweden” is posted at http://jech.bmj.com/content/66/10/927.long. An abstract of “Parents Bereaved by Offspring Suicide” is posted at http://archpsyc.jamanetwork.com/article.aspx?articleid=1483982. ISSUES NewArchived

Parents Bereaved by Offspring Suicide

CONTEXT Suicide bereavement remains understudied and poorly understood. OBJECTIVES To examine outcomes of parents bereaved by the suicide death of their offspring and to compare these with both nonbereaved parent controls and parents who had offspring die in a motor vehicle crash (MVC). DESIGN Population-based case-control study. Suicide-bereaved parents were compared with nonbereaved matched control parents in the general population (n=1415) and with MVC-bereaved parents (n=1132) on the rates of physician-diagnosed mental and physical disorders, social factors, and treatment use in the 2 years after death of the offspring. Adjusted relative rates (ARRs) were generated by generalized estimating equation models and adjusted for confounding factors. SETTING Manitoba, Canada. PARTICIPANTS All identifiable parents who had an offspring die by suicide between 1996 and 2007 (n=1415). MAIN OUTCOME MEASURES Mental and physical disorders, social factors, and treatment use. RESULTS Suicide bereavement was associated with an increased rate of depression (ARR, 2.14; 95% CI, 1.88-2.43), anxiety disorders (ARR, 1.41; 95% CI, 1.24-1.60), and marital breakup (ARR, 1.18; 95% CI, 1.13-1.23) in the 2 years after the suicide of an offspring, as compared with the 2 years prior to the death. Suicide-bereaved and MVC-bereaved parents had very few differences on predeath to postdeath outcomes. Depression rate increases were greater for MVC-bereaved parents (19.9%) compared with suicide-bereaved parents (15.9%; P=.005), whereas suicide-bereaved parents had higher rate increases of hospitalization for mental illness (P=.049). Suicide-bereaved parents were more likely than their MVC-bereaved counterparts to have depression (ARR, 1.30; 95% CI, 1.06-1.61), physical disorders (ARR, 1.32; 95% CI, 1.19-1.45), and low income (ARR, 1.34; 95% CI, 1.18-1.51) before their offspring's death. CONCLUSIONS Suicide bereavement is associated with adverse mental health and social outcomes. These consequences appear similar to those associated with MVC bereavement. Parents who lose offspring to suicide appear to be a vulnerable group even prior to their offspring's death.

Analysis of X-ray radiography in atomizing sprays

Recent studies of spray-related flowfields using synchrotron-based X-ray radiography at the Advanced Photon Source (APS), Argonne National Lab, have produced useful results related to fuel mass. A companion article to this one analyzed X-ray phase contrast imaging and it identified several problems. Those results could potentially raise questions about radiography as well. Here, we simulate X-ray radiography using the same computational tools as before, but we reach a different set of conclusions. One important finding is the demonstration that radiography detects the total liquid mass along a line-of-sight, including both drops and intact liquid. As such, it can reveal liquid mass fraction, which is related to the spray breakup rate and gas entrainment; both critical for understanding of sprays. The potential for confusion between local signal reduction by diffraction and local signal reduction by absorption is also discussed. The issue is not unusual in such circumstances. This potential background problem can be avoided by careful arrangement of the experiment, and it is clear that it does not affect the results produced by the APS.

Numerical investigation of turbulent bubbly wakes created by the ventilated partial cavity

This paper presents a numerical study on the turbulent bubbly wakes created by the ventilated partial cavity. A semi-empirical approach is introduced to model the discrete interface of the ventilated cavity and its complex gas leakage rate induced by the local turbulent shear stress. Based on the Eulerian-Eulerian two-fluid modeling framework, a population balance approach based on MUltiple-SIze-Group (MUSIG) model is incorporated to simulate the size evolution of the sheared off microbubbles and its complex interactions with the two-phase flow structure in the wake region. Numerical predictions at various axial locations downstream of the test body were in satisfactory agreement with the experimental measurements. The captured bubbly wake structure illustrates that the bubbles may disperse as a twin-vortex tube driven by gravity effect. The predicted Sauter mean bubble diameter has confirmed the dominance of the coleascense process in the axial direction. As the bubbles develop downstream, the coleascense and breakup rate gradually reach balance, resulting in the stable bubble diameter. A close examination of the flow structures, gas void fraction distributions and the bubble size evolution provides valuable insights into the complex physical phenomenon induced by ventilated cavity.

An evaluation and improvement of microphysical parameterization from a two-moment cloud microphysics scheme and the Southwest Monsoon Experiment (SoWMEX)/Terrain-influenced Monsoon Rainfall Experiment (TiMREX) observations

[1] This study evaluates the simulated cloud properties, especially the simulated raindrop size distribution, by the Chinese Academy of Meteorological Sciences bulk microphysics scheme (CAMS BMS) and two other two-moment microphysics schemes (Morrison and WDM6) in the Weather Research and Forecasting model (WRF v3.1). Measurements from a mesoscale convective system that occurred on 14 June 2008 during the Southwest Monsoon Experiment (SoWMEX) and Terrain-influenced Monsoon Rainfall Experiment (TiMREX) are used. The model reflectivity (ZH), differential reflectivity (ZDR), and microwave brightness temperature (TB) are compared with the corresponding observations by the S band dual-polarization Doppler radar (S-Pol) and the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). Results show that the simulated ZDR, which is sensitive to the drop size distribution (DSD) of raindrops, from the original CAMS BMS and Morrison schemes are larger than those from the S-Pol observations. On the other hand, the simulated ZDR values from the WDM6 scheme are smaller than the radar observations. To improve the model results, modifications are made by controlling the intercept parameter of raindrop DSD and by increasing the raindrop breakup rates in the original CAMS BMS scheme. The modifications reduce the raindrop size and consequently increase the rain evaporation rate. The improved simulations of ZH and ZDR indicate that the modified CAMS BMS scheme adequately simulates the amount and size of liquid hydrometeors. Moreover, the simulated brightness temperatures at liquid water absorption frequency and the simulated surface precipitation rates are also significantly improved by using the modified CAMS BMS scheme.

Study of the effects of the injector length/diameter ratio on the surface properties of turbulent liquid jets in still air using X-ray imaging

The disintegration of turbulent liquid jets in gases, a process termed turbulent primary breakup, has many industrial applications, especially in liquid injection systems whose injector internal flow results in enhanced turbulence generation. An investigation was carried out by using X-ray diagnostics at the Advanced Photon Source (APS) facility of Argonne National Laboratory on two injectors with a smooth entry followed by round passage with different length-to-diameter ratios of 10 and 40, operating at the same injection speed. The test matrix was designed to eliminate cavitation and to isolate the effect of length/diameter ratio of the injector passage and to determine the importance of jet turbulence compared to aerodynamic forces. The X-ray diagnostics used allowed the surface and internal topography of liquid jets to be visualized and the spatial distribution of the surface ligaments to be revealed in the near-injector region. The present results show that the separation distance between a ligament and its neighbors depends on the ligament sizes, and the injector length/diameter ratio affects the rates of breakup.

Analytical solution of the droplet breakup equation by the Adomian decomposition method

The droplet population balance equations (PBEs), which despite its importance rarely has an analytical solution. However, few cases with assumed functional forms of breakup rate, daughter droplet distribution exist, where most of these solutions are for the batch stirred vessel. A new framework for solving (PBEs) for batch and continuous systems is proposed in this work, which uses the Adomian decomposition method. This technique overcomes the crucial difficulties of numerical discretization and stability that often characterize previous solutions in this area. The technique used in this work has been tested for the droplet breakup equation. The solutions are presented for several cases, for which analytical solutions are available, for batch and continuous systems for droplet breakup in stirred vessels. In all cases, the predicted droplet size distributions converge exactly in a continuous form to that of the analytical solution.

Investigation of bubble breakup and coalescence in a packed-bed reactor – Part 1: A comparative study of bubble breakup and coalescence models

In a packed-bed reactor a comparative study of bubble breakup and coalescence models has been investigated to study bubble size distributions as a function of the axial location. The bubble size distributions are obtained by solving population balance equations that describe gas–liquid interactions. Each combination of bubble breakup and coalescence models is examined under two inlet flow conditions: (1) predominant bubble breakup flow and (2) predominant bubble coalescence flow. The resulting bubble size distributions, breakup and coalescence rates estimated by individual models, are qualitatively compared to each other. The change of bubble size distributions along the axial direction is also described with medians. The medians resulting from CFD analyses are compared against the experimental data. Since the predictions estimated by CFD analyses with the existing bubble breakup and coalescence models do not agree with the experimental data, a new bubble breakup and coalescence model that takes account of the geometry effects is required to describe gas–liquid interactions in a packed-bed reactor.

Bubble Sizes, Breakup, and Coalescence in Deepwater Gas/Oil Plumes

Bubble size distribution (BSD) plays a major role in transport and fate of gas or oil released in deepwater. However, no reliable method is available to estimate gas or oil BSD after a deepwater spill. Breakup and coalescence have been identified as key processes controlling BSDs in turbulent jets. The present work introduces bubble breakup and coalescence processes for deepwater gas or oil spill models. A population balance equation representing bubble volumes is used to model the evolution of bubble sizes caused by breakup and coalescence. Existing theories for bubble breakup and coalescence rates in bubble columns are adopted to deepwater plumes. The advantage of the present model is that the BSD is generated as a result of breakup and coalescence; and therefore, a predefined BSD is no longer necessary for simulations. The comparison of model-computed results with laboratory and field data shows a good agreement. Scenario simulations show that the seed diameter given to start computations affects only for a short distance from the release point. Simulations also show that bubble breakup and coalescence is important only during the early stages of the plume where turbulence is dominant. The importance of accounting for gas bubble breakup and coalescence in estimation of gas dissolution is also demonstrated.

Measurement of ocular surface protection under natural blink conditions

PurposeTo evaluate a new method of measuring ocular exposure in the context of a natural blink pattern through analysis of the variables tear film breakup time (TFBUT), interblink interval (IBI), and tear film breakup area (BUA).MethodsThe traditional methodology (Forced-Stare [FS]) measures TFBUT and IBI separately. TFBUT is measured under forced-stare conditions by an examiner using a stopwatch, while IBI is measured as the subject watches television. The new methodology (video capture manual analysis [VCMA]) involves retrospective analysis of video data of fluorescein-stained eyes taken through a slit lamp while the subject watches television, and provides TFBUT and BUA for each IBI during the 1-minute video under natural blink conditions. The FS and VCMA methods were directly compared in the same set of dry-eye subjects. The VCMA method was evaluated for the ability to discriminate between dry-eye subjects and normal subjects. The VCMA method was further evaluated in the dry eye subjects for the ability to detect a treatment effect before, and 10 minutes after, bilateral instillation of an artificial tear solution.ResultsTen normal subjects and 17 dry-eye subjects were studied. In the dry-eye subjects, the two methods differed with respect to mean TFBUTs (5.82 seconds, FS; 3.98 seconds, VCMA; P = 0.002). The FS variables alone (TFBUT, IBI) were not able to successfully distinguish between the dry-eye and normal subjects, whereas the additional VCMA variables, both derived and observed (BUA, BUA/IBI, breakup rate), were able to successfully distinguish between the dry-eye and normal subjects in a statistically significant fashion. TFBUT (P = 0.034) and BUA/IBI (P = 0.001) were able to distinguish the treatment effect of artificial tears in dry-eye subjects.ConclusionThe VCMA methodology provides a clinically relevant analysis of tear film stability measured in the context of a natural blink pattern.

Surfactant‐free microdispersion process of gas in organic solvents in microfluidic devices

AbstractThe scaling of bubble/slug formation in organic solvents at microscale without surfactant was initially investigated by using T‐junction and symmetrically cross‐shaped microfluidic devices. Four unique organic solvents and three dispersion methods were used, forming different flow patterns and dispersion size. The flow pattern of uniform slug flow was investigated. Both the gas–liquid flow and dispersion size, which ranged from 400 to 1400 μm in length and 270 to 430 μm in diameter, depended on several factors including dispersion method, two‐phase flow rates, physical properties of the liquid phase, and structure of microchannels. A general equation L/w = k(QG/QL)αCaβ was used to characterize the dispersion size with modification of QG/QL for different dispersion methods, considering the influences of breakup rate and transformation of the interface shape on the dispersion process. Three models were developed to predict the dispersion size for different dispersion methods, and calculated data were in good agreement with the experimental results. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

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.

On the behavior of mud floc size distribution: model calibration and model behavior

In this paper, we study a population balance equation (PBE) where flocs are distributed into classes according to their mass. Each class i contains i primary particles with mass m p and size L p. All differently sized flocs can aggregate, binary breakup into two equally sized flocs is used, and the floc’s fractal dimension is d 0 = 2, independently of their size. The collision efficiency is kept constant, and the collision frequency derived by Saffman and Turner (J Fluid Mech 1:16–30, 1956) is used. For the breakup rate, the formulation by Winterwerp (J Hydraul Eng Res 36(3):309–326, 1998), which accounts for the porosity of flocs, is used. We show that the mean floc size computed with the PBE varies with the shear rate as the Kolmogorov microscale, as observed both in laboratory and in situ. Moreover, the equilibrium mean floc size varies linearly with a global parameter P which is proportional to the ratio between the rates of aggregation and breakup. The ratio between the parameters of aggregation and breakup can therefore be estimated analytically from the observed equilibrium floc size. The parameter for aggregation can be calibrated from the temporal evolution of the mean floc size. We calibrate the PBE model using mixing jar flocculation experiments, see Mietta et al. (J Colloid Interface Sci 336(1):134–141, 2009a, Ocean Dyn 59:751–763, 2009b) for details. We show that this model can reproduce the experimental data fairly accurately. The collision efficiency α and the ratio between parameters for aggregation and breakup α and E are shown to decrease linearly with increasing absolute value of the ζ-potential, both for mud and kaolinite suspensions. Suspensions at high pH and different dissolved salt type and concentration have been used. We show that the temporal evolution of the floc size distribution computed with this PBE is very similar to that computed with the PBE developed by Verney et al. (Cont Shelf Res, 2010) where classes are distributed following a geometrical series and mass conservation is statistically ensured. The same terms for aggregation and breakup are used in the two PBEs. Moreover, we argue, using both PBEs, that bimodal distributions become monomodal in a closed system with homogeneous sediment, even when a variable shear rate is applied.

Improved recursive algorithm for calculation of probability density in breakup models

Modeling the breakup of fluid particles in turbulent flows plays a central role in chemical engineering. A very large amount of contributions are proposed to model the breakup mechanism that can mainly be classified as algorithmic models and phenomenological models. Among these models, phenomenological models have received extensive interest from researchers over the years. However, uncertainties regarding the reliability of such models lead to quite different forms of breakage functions when similar physical arguments are used. The model proposed by Luo and Svendsen was quite different from other models since it needs no adjustable or experimentally-determined parameter. This model was based on the theories of isotropic turbulence and probability, and has been widely used in recent years. Based on the same framework, several attempts to improve this model have been appeared in the literature. Among these works, Kostoglou and Karabelas proposed a unified framework for the derivation of breakage functions based on the statistical description of isotropic turbulence. A literature review on the existing theoretical breakup models can be found in a recent article by Liao and Lucas. One of the main drawbacks in breakup modeling is the calculation of breakup rate and daughter-size distribution, which are time-consuming because a triple integral is involved in the governing equations, and, therefore, the need for an efficient algorithm to calculate the integrals appeared in the model is essential. This has led to the development of numerical algorithms over the last few years. Among these algorithms, the one proposed by Wang and coworkers has received many interest as can be seen in the literature. The algorithm uses a recursive procedure to calculate the breakup probability density, which reduces the triple integral into a double integral by introducing a cutoff energy as the upper limit of integration. The accuracy of the solution depends severely on the discretization of breakage fraction. An improved recursive algorithm to calculate the probability density in breakup models is presented. The modified algorithm gives considerably faster solutions than the one proposed by Wang et al. A structured discretization is also used for breakup fraction which significantly improved integration accuracy and computational efficiency.

Race and Ethnicity in Fragile Families

Robert Hummer and Erin Hamilton note that the prevalence of fragile families varies substantially by race and ethnicity. African Americans and Hispanics have the highest prevalence; Asian Americans, the lowest; and whites fall somewhere in the middle. The share of unmarried births is lower among most foreign-born mothers than among their U.S.-born ethnic counterparts. Immigrant-native differences are particularly large for Asians, whites, and blacks. The authors also find racial and ethnic differences in the composition and stability of fragile families over time. Although most parents of all racial and ethnic groups are romantically involved at the time of their child's birth, African American women are less likely to be in a cohabiting relationship than are white and Hispanic mothers. Over time, these racial and ethnic differences become more pronounced, with African American mothers having the lowest rates of marriage and cohabitation and the highest breakup rates, and Mexican immigrant mothers having the highest rates of marriage and cohabitation and the lowest breakup rates. Fragile families have far fewer socioeconomic resources than married families, though resources vary within fragile families by race and ethnicity. White mothers, in general, have more socioeconomic resources than black, Mexican American, and Mexican immigrant mothers; they are more likely to have incomes above the poverty limit, more likely to own a car, less likely to have children from a prior relationship, and more likely to report living in a safe neighborhood. Access to health care and child care follows a similar pattern. The exception is education; black and white unmarried mothers are equally likely to have finished high school, and Mexican immigrant and Mexican American mothers are less likely to have done so. The authors argue that socioeconomic differences are by far the biggest driver of racial and ethnic differences in marriage and family stability, and they support reforms to strengthen parents' economic security. They also discuss how sex ratios and culture affect family formation and stability. In particular, they note that despite severe poverty, Mexican immigrant families have high rates of marriage and cohabitation--an advantage that erodes by the second generation with assimilation. To address the paradox that marriage declines as socioeconomic status improves, they support policies that reinforce rather than undermine the family ties of Mexican immigrants.

Effect of coalescence and breakup on bubble size distributions in a two-dimensional packed bed

Bubble size distributions in a two-dimensional packed bed are investigated as a function of axial direction by using image processing techniques with a large number of bubble samples. Two inlet conditions, controlled sized bubbles and uncontrolled sized bubbles, are conducted to study the characteristic behaviors of bubbles. With the uncontrolled sized bubbles, the average bubble size corresponding to the two-dimensional bed is found, and is not affected by decrease or increase of flow rates. With the controlled sized bubbles, dominant bubble breakup and coalescence flows are separately simulated to investigate bubble breakup and coalescence rates. Unique behavior of bubble size distributions for dominant bubble breakup and coalescence has been seen, and changes in bubble size distributions along axial direction are studied with median bubble size. Near the inlet the median changes rapidly due to the dominant bubble mechanism of either coalescence or breakup, and far away from the inlet the median reaches asymptotic value due to the balance of bubble breakup and coalescence. For both dominant breakup and coalescence flows, the asymptotic values are close to the average bubble size. Therefore, the average bubble size, resulting from the balance of bubble coalescence and breakup at far downstream, is irrespective of inlet flow conditions.

Molecular dynamics study of thermal-driven methane hydrate dissociation

Nonequilibrium molecular dynamics simulations have been performed to investigate the thermal-driven breakup of both spherical methane hydrate nanocrystallites (with radii of approximately 18 and 21 A) and planar methane hydrate interfaces in liquid water at 280-340 K. The melting temperatures of each cluster were estimated, and dissociation was observed to be strongly dependent on temperature, with higher dissociation rates at larger overtemperatures vis-a-vis melting. For the 18 and 21 A radius nanocrystals, breakup was also seen to be dependent on cluster size, and different methane compositions (85%, 95%, and 100% of maximum theoretical occupation) in the planar case also lead to slight differences in the initial dissociation rate. In all cases, the diffusion of the methane into the surrounding liquid water was found to be an important step limiting the overall rate of breakup. A simple coupled mass and heat transfer model has been devised for both the spherical and planar hydrate systems that explains these findings, and distinguishes between the role of the overall thermal driving force and methane diffusional mass transfer in controlling the break-up rate.