Breakup Rate Research Articles

The interfacial tension between a thermotropic liquid crystalline copolyester and polyethersulfone: A comparison of methods

AbstractThree dynamic methods to determine the interfacial tension between the thermotropic liquid crystalline polymer (TLCP) Vectra A900 and polyethersulfone were evaluated: (1) thread breakup, (2) fiber retraction and (3) dynamic shear rheometry. The thread breakup and retraction methods, were suitable for measuring the interfacial tension, provided that the shear thinning flow behavior of the TLCP was taken into account. The viscosity of the TLCP during breakup or retraction was estimated from steady‐shear measurements at the observed overall rate of deformation during growth of capillary instabilities or during retraction. The calculation of the interfacial tension from breakup rates of TLCP threads was improved by accounting for transient flow behavior during distortion growth using a single‐element Maxwell model. Determination of the interfacial tension by oscillatory shear measurements on TLCP/PES dispersions using the emulsion model of Palierne, was not applicable for this system. Only for dispersions containing low TLCP volume fractions (e.g. 9 vol%) was there reasonable agreement between the emulsion model and measurements. At higher volume fractions agreement was poor, possibly because of different dynamic flow behavior of the TLCP in the pure form and in blends. The interfacial tension values obtained from thread breakup and fiber retraction ranged from 4 to 6 mN/m, which demonstrate that in‐situ determination of the interfacial tension is possible for blends containing TLCPs, despite their complex flow behavior.

Breakup of levitated frost particles

We have studied the sublimation and breakup of single 100–200 μm frost particles levitated electrically at temperatures in the range −2°C to −30°C. Breakup rates were largely independent of temperature and humidity in this range but strongly dependent on particle shape. Irregular particles of high aspect ratio were most likely to break up. Sublimation (evaporation) was accompanied by an increasing aspect ratio. A linearized sublimation model, presented in the appendix, accounts for the observation that thin neck regions were not subject to enhanced sublimation rates. Estimates of the forces involved in breakup suggest that the breaking strength of these frost particles is considerably less than that of bulk ice. We discuss possible implications of our results for ice particle multiplication in clouds.

A spectropolarimetric survey of northern hemisphere Wolf–Rayet stars

We present a homogeneous, high signal-to-noise spectropolarimetric survey of 16 northern hemisphere Wolf–Rayet (WR) stars. A reduction in polarization at emission-line wavelengths — the ‘line effect’— is identified in four stars: WRs 134, 137, 139, and 141. The magnitude of the effect in WR 139 (V444 Cyg) is variable, while WR 136, previously reported to show the line effect, does not show it in our data. Assuming the line effect generally to arise from axisymmetric distortions of stellar winds, we show that a model in which all WRs have the same intrinsic (equator-on) polarization, with the observed variations solely a result of inclination effects, is inconsistent with the observations. A model in which the intrinsic polarizations are uniformly distributed is more plausible, but best-fitting results are obtained if the distribution of polarizations is biased towards small values, with only ∼ 20 per cent of stars having intrinsic polarizations greater than ∼ 0.3 per cent. Radiative transfer calculations indicate that the observed continuum polarizations can be matched by models with equator:pole density ratios of 2–3. The model spectra have electron-scattering wings that are significantly stronger than observed (in both intensity and polarized flux), confirming that the winds of stars showing intrinsic polarization must be clumped on small scales as well as being distorted on large scales. We combine the results of our survey with observations from the literature to give a sample of 29 stars which have both accurate spectropolarimetric observations and physical parameters derived from standard-model analyses. We find that the line-effect stars are clustered at high M, L in the luminosity–mass-loss rate plane (although they are unexceptional in the terminal velocity–subtype and the surface-mass-flux–temperature planes). The mass-loss rates derived from radio-continuum observations for these stars are in good accord with the results of optical emission-line analyses, suggesting that (i) the wind structure of line-effect stars has a density contrast which is effectively constant with radius, and (ii) the high M values may be artefacts of large-scale wind structure. Assuming that observed spectroscopic and photometric variability of the line-effect stars is related to the WR rotation period, we compute equatorial rotation velocities. These velocities correspond to ∼ 10 per cent of the core breakup rates, and may be large enough to produce significant wind-compression effects according to the models of Ignace, Cassinelli & Bjorkman.

Breakup of two-dimensional into three-dimensional Kadomtsev-Petviashvili solitons

This paper reports on three-dimensional simulations that follow exact, $z$-symmetric soliton solutions to an important model equation of plasma physics and superfluid helium (Bose condensate). This is the Kadomtsev-Petviashvili equation. Solitons are seen to break up when perturbed along $z$. Dependence of growth on the wave number of the perpendicular perturbation is found numerically. This leads to a wave number producing the maximum rate of breakup. Due to numerical instabilities, a somewhat smaller wave number must be used. Fully three-dimensional entities are produced. After a while they become virtually identical to known, azimuthally symmetric solutions. Based on this, implications for the reconnection hypothesis formulated by Feynman, used in superfluid helium II theory, are indicated.

Bubble flow characteristics in bubble columns at elevated pressure and temperature

AbstractHydrodynamic characteristics of bubble columns are studied by considering both the local/bubble‐scale and global/column‐scale properties of the system, with specific emphasis on their dependency on operating pressure and temperature. The local‐scale properties include single‐bubble characteristics and interactive dynamics involving bubble coalescence and breakup, while the global‐scale properties include gas holdup. Experiments are conducted in a bubble column with a multiorifice ring sparger for pressures as high as 20 MPa and temperatures ranging from 27 to 78°C. Density, viscosity, and surface tension, the liquid phase properties, are measured in situ by using hydrostatic weighing, falling‐ball and emerging‐bubble techniques, respectively. The bubble behavior is examined through direct‐flow visualization. Pressure and temperature affect the bubble rise velocity mainly by varying physical properties of the fluids. Effects of pressure and temperature on the rates of bubble formation, coalescence and breakup, and the initial bubble size and maximum stable bubble size are illustrated. Elevating pressure and/or temperature increases gas holdup; the increasing rate depends on the operating conditions through their effects on the fluid physical properties.

Fragmentation–diffusion model. Existence of solutions and their asymptotic behaviour

An infinite system of reaction–diffusion equations that represents a particular case of the discrete coagulation–fragmentation model with diffusion is studied. The reaction part of the model describes the rate of clusters break-up into smaller particles. Diffusion constants are assumed to be different in each equation and concentration-dependent fragmentation coefficients are considered. Existence of solutions is studied under fairly general assumptions on fragmentation coefficients and initial data. Uniqueness in the class of mass-preserving solutions is proved. Convergence of solutions to spatially homogeneous equilibrium state is obtained.

Drop breakup in the flow through fixed beds via stochastic simulation in model Gaussian fields

Shaqfeh and Koch have shown that the flow through a dilute disordered fixed bed of fibers produces large polymer conformation change beyond a certain critical flow rate [J. Fluid Mech. 244, 17 (1992)]. We now examine the effect of this flow on the shape and breakup of viscous drops. Because the flow through a dilute fixed bed is equivalent to a certain anisotropic Gaussian flow field, we follow our previous paper and reproduce a model of the flow through a spectral expansion where the wave number vectors are chosen from statistical distributions which ensure that the desired velocity field will be realized [Phys. Fluids 9, 1222 (1997)]. We examine the dynamics of model drop shapes, averaged over the Gaussian statistics of the flow field, by synthesizing a large number of flow realizations. The drop surface is modeled using the first, second, and third order small deformation theories which can accurately predict critical conditions in classical strong flows. While the first order model yields a bounded average drop shape for all flow conditions, the second and third order models demonstrate that the flow through fixed beds is indeed “strong” since beyond a certain value of the pore-size capillary number, Ca∼0.15, large average drop deformation occurs and the average drop shape becomes unbounded (“drop breakup”). This critical condition is determined for various viscosity ratios and fixed bed particle volume fractions. Similar to a simple shear flow, we find that there is a critical viscosity ratio, χ∼2.5, beyond which breakup is not observed in the fixed bed for any Ca. In addition, the critical condition is shown to depend heavily on the transient nature of the flow in the bed since approximately half of the flow fields in which drop breakup occurs would not break an initially spherical drop at any Ca if they were steady. For supercritical capillary numbers, we define conditions under which the unbounded drop shapes fragment into smaller droplets and we examine the drop breakup rates as a percentage of the drop population.

Oil‐assisted agglomeration for toner deinking: Population balance model and experiments

AbstractThis study examines the selective agglomeration of hydrophobic toner particles from a repulped paper fiber slurry by adding an immiscible oil that preferentially wets the toner particles. Effects of cationic starch additives, agitation rate, time, temperature and oil composition are examined experimentally in terms of the dynamic and steady‐state evolution of the particle‐size distribution produced. A simple, but effective, population balance model is solved numerically to simulate the agglomeration process and provides quantitative relationships between process variables and the effectiveness and rate of agglomeration. These relations are simple and clear. The process is shown to be controlled by the composite effect of the aforementioned variables on the aggregation and breakup rates, and the observed hehavior is understood in these terms. Practical recommendations for agglomeration, a process potentially useful for deinking toner‐printed paper, are deduced from the results.

Fluorescence capillary photometry for characterization of liquid–liquid dispersions

AbstractThe behavior of droplet swarms in liquid–liquid dispersions, especially found in extraction columns, are analyzed by a new fluorescence measurement technique, which represents an extension to the capillary suction method. The measuring principle developd benefits from detectable‐emission light intensity of a fluorescent dye even in a trace concentration. The addition of this nontransferring dye to the dispersed phase enables in situ determination of bivariate drop‐size/drop‐concentration distributions, which provides important information on droplet history for the evaluation of coalescence and breakup rates. Furthermore, the measuring method represents a new approach for the measurment of droplet‐size‐dependent residence times in extraction columns.

Exact Solution and Multifractal Analysis of a Multivariable Fragmentation Model

Most theoretical kinetic approaches proposed so far to describe fragmentation processes rely on the assumption that the fragments can be characterized by a unique relevant variable, for example their size or mass h. We investigate the consequences of introducing additional variables by considering a fragmentation model in which the fragments are described by two internal variables, h, w, and a breakup rate proportional to hw~. The exact solution. already partly presented in reference ill, is derived and discussed in details with an emphasis on the fragment distribution function. It is shown that~ because of the random multip)icative nature of the process, no reduction to an effective one-variable problem is usually possible. The fragment mass distribution has no simple scaling properties; it rather exhibits multiscaling, a feature that is interpreted in the framework of a multifractal formalism.

Size, structure and dynamics of “large” bubbles in a two-dimensional slurry bubble column

This paper reports preliminary results of a study on the hydrodynamics of a two-dimensional slurry bubble column. Experiments have been carried out with air/paraffin oil slurries with solids concentrations of 0, 28.3 and 38.6 vol% of porous silica particles (mean diameter of 38 μm). Bubble sizes, bubble coalescence and bubble break-up rates were determined by video image analysis. Increasing slurry concentration increases the size and size distribution of the “large” bubbles, defined here as having diameters larger than 10 mm. Increasing slurry concentration reduces the total gas holdup to a significant extent; this reduction is to be largely attributed to the destruction of the “small” bubble population, which have bubble diameters smaller than 10 mm. Video imaging experiments lead to new insights into the mass transfer mechanisms from “large” bubbles. These “large” bubbles are continually coalescing and breaking up. The coalescence and breakup rates were determined by a frame-by-frame analysis of the video recordings and found to be at least 4 s −1. A population model for mass transfer has been set up and used to establish that frequent bubble-bubble interactions could lead to an order of magnitude increase in the mass transfer rates for the large bubble class.

MAXIMIZING SELECTIVITY OF LIQUID-LIQUID REACTION SYSTEMS. CONTROL OF THE DISPERSION PROCESS

Abstract Currently available information on droplet coalescence and break-up rates in turbulent flows in mixing vessels can be used to control drop sizes in dispersed phase equipment. The effect of drop size distributions on the selectivity and productivity in multi-reaction systems is examined in this paper. The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up. The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed.

Theoretical model for drop and bubble breakup in turbulent dispersions

AbstractA theoretical model for the prediction of drop and bubble (fluid‐particle) breakup rates in turbulent dispersions was developed. The model is based on the theories of isotropic turbulence and probability and contains no unknown or adjustable parameters. Unlike previous work, this model predicts the breakage rate for original particles of a given size at a given combination of the daughter particle sizes and thus does not need a predefined daughter particle size distribution. The daughter particle size distribution is a result and can be calculated directly from the model. Predicted breakage fractions using the model for the air–water system in a high‐intensity pipeline flow agree very well with the available 1991 experimental results of Hesketh et al. Comparisons of the developed model for specific particle breakage rate with earlier models show it to give breakage‐rate values bracketed by other models. The spread in predictions is high, and improved experimental studies are recommended for verification.

Predicting Catastrophic Phase Inversion on the Basis of Droplet Coalescence Kinetics

A predictive model for catastrophic phase inversion, based on the kinetics of droplet breakup and coalescence, is presented here. Two inversion mechanisms can be distinguished, depending on the direction of the phase inversion process. With the surfactant predominantly present in the dispersed phase, the coalescence rate is high and phase inversion takes place at relatively low volume fractions. Going in the other direction, surfactant is predominantly present in the continuous phase. The coalescence rate is dramatically lowered because of the Gibbs-Marangoni effect, and difficult inversion will not take place up to relatively high volume fractions. Experiments were carried out in a stirred vessel, where phase inversion was detected by a jump in emulsion conductivity. Easy inversion points were found on the order of 20-50% volume fraction of the dispersed phase. Difficult inversion was not detected up to 97% dispersed phase. The easy inversion point increases with dispersed phase addition rate and is independent of the stirrer speed below a stirrer speed of 1500 rpm. A simple model based on the breakup and coalescence rate of emulsion droplets in the easy inversion regime allows us to calculate the stationary droplet size as a function of the volume fraction of the dispersed phase, as well as the evolution of the droplet size in time under addition of dispersed phase. The stationary droplet size diverges above a critical volume fraction of 26.4%, indicating phase inversion. This model can qualitatively describe hysteresis and the phase inversion point dependence on stirrer speed and dispersed phase addition rate, as found in our experiments.

The Sociodemographic and Reproductive Characteristics of Cuban Women

Cuba has maintained low fertility in the Latin American region throughout the period 1955-87. The socioeconomic changes brought about by the revolutionary takeover in 1959 speeded the demographic transition. Cuban population numbered 10869218 of which 22.7% were aged under 15 years and 12.2% were aged 60 years and older. Although economically underdeveloped Cuba completed its demographic transition by 1992. By the early 1990s 57.3% of university students were women. 30% received degrees in scientific and technical fields. Female economic activity increased. 39.1% of economically active persons in 1991 were women. 58% of all professionals were women. Fertility rates for daughters were below replacement during 1955-60 increased to over replacement during 1961-64 and declined thereafter to a low of 0.94 daughters/woman. During 1970-87 fertility decline was dominated by declines in rural areas. In 1953 and 1970 the greater share of fertility was among women aged over 25 years. During the early 1980s a large proportion of fertility was accounted for by women aged under 20 years. During the late 1970s and early 1980s fertility was dominated by women aged 15-19 years. In the late 1980s fertility was concentrated among women aged 25-29 years. Recent trends favor early childbearing which is attributed to early sexual activity without contraception ignorance or insufficient knowledge about sexuality lack of responsibility for childbearing and lack of parental and educational guidance. The 1987 Fertility Survey indicated a high level of knowledge about contraception. During 1970-90 the number of abortions increased by 109%. During 1989-90 rates of fertility and abortion declined but menstrual regulation increased 2.4 times. The proportion of single and married women declined and the proportion in consensual unions increased by 1987. The divorce rate and break-up rate varied during 1975-90.

Shattering transition in a multivariable fragmentation model.

We introduce a linear fragmentation model in which the fragments are described by two correlated variables x and y, and for the power law breakup rate a(x,y)=${\mathit{x}}^{\mathrm{\ensuremath{\alpha}}}$${\mathit{y}}^{\mathrm{\ensuremath{\beta}}}$, we derive its exact solution. The large fluctuations of the additional variable prevent any mean-field reduction to a one-variable model. New features, such as shattering with power law decay of the mass, are obtained.

Fragmentation of Colloidal Aggregates Induced by Polymer Adsorption

Using a particle counter technique, we investigated the fragmentation process of aggregates of polystyrene suffonate latices induced by the adsorption of polyvinylpyridine at the particle-liquid interface by determining the aggregate size distribution c( x, t), concentration of aggregates of size x, and the weight S( t) and number N ( t) average sizes at time t. The fragmentation of two typical aggregates were studied. The first aggregates obtained under conditions of perikinetic diffusion-limited aggregation (1 M NaCl and pH 3.0 medium) were transferred to aqueous polyelectrolyte solutions at different concentrations in the presence of 0.15 M NaCl and at pH 3.0. The second aggregates obtained under conditions of reaction-limited aggregation (0.15 M NaCl and pH 3.0 medium) were transferred to aqueous polyelectrolyte solutions in the presence of 0.0225 M NaCl and at pH 3.0. We determined that fragmentation is a very slow process. The size distribution of the fragments was self-similar and the variation in the number average size N( t) and the weight average size S( t) as a function of time followed dynamic scaling laws whose exponents depended on the mode of formation and the initial size of the aggregates, as well as on the concentration and the molecular weight of the polymer. Using Cheng and Redner's theory ( Phys. Rev. Lett. 60, 2450 (1988); J. Phys. A: Math Gen. 23, 1233 (1990)), we calculated the rate of aggregate breakup, which was found to be independent of the initial size of the aggregates and of the polyelectrolyte concentration. The mode of aggregate formation and the molecular weight of the polymer in the fragmenting medium were found to fix the rate of breakup and the fragment size distribution. The discrepancies between the rate of aggregate break-up and the rates of fragmentation determined from the variation of the average sizes were attributed to the existence of a concomitant aggregation during fragmentation.

Carbon deposition over transition metal alloys—II. Kinetics of deposition over 〈FeNi〉 and 〈FeCo〉 alloy foils

The effects of 〈FeNi〉 and 〈FeCo〉 alloy composition on the deposition of filamentous carbon was investigated. This was accomplished by comparing the relative rates of carbon formation over pure Fe, Ni, and Co foils along with their respective carbide(s), to those over 〈FeNi〉 and 〈FeCo〉 alloys and the associated metal phases. It was observed that the heat treatment to which a foil is subjected prior to carbon-depositing conditions can affect the rate of carbon deposition. Heat treatment causes grain nucleation and growth, decreases internal stresses, as well as allowing dislocation migration. These changes within the foil inhibit subsequent carbide formation, decreasing the rate of surface break-up, leading to longer induction periods. Alloy foils ranging from pure Fe to either pure Ni or Co were exposed to a reaction gas having an a ̂ C of 10. This a ̂ C is sufficiently high to favor solid carbon deposition and, depending on the alloy concentration, ≤ 50 wt% Ni in 〈FeNi〉, or ≤ 35 wt% for Co in 〈FeCo〉 alloys, Fe 3C is thermodynamically favored to form at these conditions. For the 〈FeNi〉 system it was determined that when iron carbides are among the thermodynamically favored solid phases, the rate of carbon deposition was high (75 to 100 μg/cm 2/min). If iron carbides were not favored then the rate was low, <30 and <5 μg/cm 2/min for 〈FeNi〉 and Ni 3C, 〈FeNi〉, respectively. Also, 〈FeCo〉 alloys near 45 wt% Co were exposed to various gas mixtures with a ̂ Cs ranging from ≈ 10 to ≈35. It was determined that when iron carbides are among the thermodynamically favored solid phases, the rate of carbon deposition was high (80 to 100 /μg/cm 2/min). If iron carbides were not favored, then the rate was significantly lower, <30 and < 10 μg/cm 2 min for 〈FeCo〉 and Co 2C, 〈FeCo〉, respectively. If the 〈FeCo〉 alloy foils were preoxidized then the rate of carbon deposition increased. For the 〈FeCo〉 system the increased rates of carbon deposition are attributed to an increase in the surface area of the “catalyst” as Fe 3C forms and breaks up the foil's surface.

Superficial Rate of Bubble Breakup in a Bubble Column.

The frequencies of bubble passage were experimentally measured in a bubble column and the results were analysed and correlated

The impact of a child death on marital adjustment

One continuing concern in the sociological and psychological literature has been with the mental health consequences of stressful life events. Occasionally such stressful events have been linked to other outcomes such as deterioration in the extent or quality of the relationship between a cohabiting (usually married) couple. This paper takes data from a longitudinal study of parents of an infant who has died (due to a Stillbirth, Neonatal Death or Sudden Infant Death), to determine whether the relationship between the parents is adversely affected. The follow-up data is available 2 months and 6–8 months after the infant death. The results indicate there is an increased marital break-up rate for parents whose infant has died. Further, shortly after the death there is evidence of a deterioration of the quality of the marital relationship between the partners whose relationship has remained intact. Both these consequences of an infant death are unlikely to be due to chance, but their magnitude is relatively modest. At the 6 month follow-up, there is evidence of a deterioration in the quality of the relationship for those partners whose infant survived, such that at 6 months there are no longer any marital adjustment differences between parents experiencing an infant death and parents whose infant survived.