Observed Mass Transfer Rates Research Articles

Evidence for reduced magnetic braking in polars from binary population models

ABSTRACT We present the first population synthesis of synchronous magnetic cataclysmic variables, called polars, taking into account the effect of the white dwarf (WD) magnetic field on angular momentum loss. We implemented the reduced magnetic braking (MB) model proposed by Li, Wu & Wickramasinghe into the Binary Stellar Evolution (bse) code recently calibrated for cataclysmic variable (CV) evolution. We then compared separately our predictions for polars and non-magnetic CVs with a large and homogeneous sample of observed CVs from the Sloan Digital Sky Survey. We found that the predicted orbital period distributions and space densities agree with the observations if period bouncers are excluded. For polars, we also find agreement between predicted and observed mass transfer rates, while the mass transfer rates of non-magnetic CVs with periods ≳3 h drastically disagree with those derived from observations. Our results provide strong evidence that the reduced MB model for the evolution of highly magnetized accreting WDs can explain the observed properties of polars. The remaining main issues in our understanding of CV evolution are the origin of the large number of highly magnetic WDs, the large scatter of the observed mass transfer rates for non-magnetic systems with periods ≳3 h, and the absence of period bouncers in observed samples.

Evolving LMXBs: CARB Magnetic Braking

Abstract The formation of low-mass X-ray binaries (LMXBs) is an ongoing challenge in stellar evolution. An important subset of LMXBs is the binary systems with a neutron star (NS) accretor. In NS LMXBs with nondegenerate donors, the mass transfer (MT) is mainly driven by magnetic braking (MB). The discrepancies between the observed MT rates and the theoretical models were known for a while. Theory predictions of the MT rates are too weak and differ by an order of magnitude or more. Recently, we showed that with the standard MB, it is not possible to find progenitor binary systems such that they could reproduce—at any time of their evolution—most of the observed persistent NS LMXBs. In this Letter we present a modified MB prescription, Convection And Rotation Boosted (CARB). CARB MB combines two recent improvements in understanding stellar magnetic fields and magnetized winds—the dependence of the magnetic field strength on the outer convective zone and the dependence of the Alfvèn radius on the donor’s rotation. Using this new MB prescription, we can reproduce the observed MT rates at the detected mass ratio and orbital period for all well-observed to-the-date Galactic persistent NS LMXBs. For the systems where the effective temperature of the donor stars is known, theory agrees with observations as well.

GALACTIC ULTRACOMPACT X-RAY BINARIES: DISK STABILITY AND EVOLUTION

We study the mass transfer rates and disk stability conditions of ultracompact X-ray binaries (UCXBs) using empirical time-averaged X-ray luminosities from Paper I (Cartwright et al. 2013) and compiled information from the literature. The majority of UCXBs are consistent with evolutionary tracks for white dwarf donors. Three UCXBs with orbital periods longer than 40 minutes have mass transfer rates above 10^{-10} Msun/year, inconsistent with white dwarf donor tracks. We show that if helium star donors can retain their initial high entropy, they can explain the observed mass transfer rates of these UCXBs. Several UCXBs show persistent luminosities apparently below the disk instability limit for irradiated He accretion disks. We point out that a predominantly C and/or O disk (as observed in the optical spectra of several) lowers the disk instability limit, explaining this disagreement. The orbital period and low time-averaged mass transfer rate of 2S 0918-549 provide evidence that the donor star is a low-entropy C/O white dwarf, consistent with optical spectra. We combine existing information to constrain the masses of the donors in 4U 1916-053 (0.064+-0.010 Msun) and 4U 1626-67 (<0.036 Msun for a 1.4 Msun neutron star). We show that 4U 1626-67 is indeed persistent, and not undergoing a transient outburst, leaving He star models as the best explanation for the donor.

Numerical simulation of CO2 absorption into aqueous methyldiethanolamine solutions

The CO2 absorption rate into aqueous N-methyldiethanolamine solutions was measured using a stirred cell with a flat gas-liquid interface. The measurements were performed in the temperature range of 293.15 to 333.15 K for various amine concentrations and CO2 partial pressures. A numerical model of mass-transfer with complex chemical reactions based on the film theory was developed to interpret the experimental results. The model predictions have been found to be in good agreement with the experimental values of CO2 absorption rates. A comparison is made between the enhancement factor predicted from the detailed model and the approximate solution of mass transfer equations with chemical reaction. The numerical results indicate that under the present experimental conditions, the effect of the reaction between CO2 and OH− on the observed mass transfer rates is negligible. The detailed mass transfer model was used for simulating the CO2 absorption process in terms of the enhancement factor under a variety of operating conditions.

Combined experiments to measure low sublimation pressures and diffusion coefficients of organometallic compounds

Vapor pressures and sublimation pressures of organometallic (metalorganic) compounds are needed in several processes like chemical vapor deposition (CVD). Thermobalances at ambient pressures are often used to study the evaporation of such compounds. At least three strategies are found in the literature to evaluate the results using different theoretical approaches. In some of the frequently used approaches the diffusion out of a crucible is neglected. We present a simple theoretical approach which describes the interrelation between the observed mass transfer rate and the physical variables of typical TGA set-ups. It turns out that the mass transfer rate at a given total pressure and temperature is mainly a function of the diffusion coefficient and the vapor pressure of the sublimating substance. The vapor pressures may be determined from an independent measurement using the Knudsen cell and combined with the TGA to obtain the diffusion coefficients. Experiments have been performed with two well studied substances naphthalene and phenanthrene to check the present strategy. Further measurements were then performed for the metal organic CVD relevant compounds: ferrocene and Tris(2,2,6,6-tetramethyl-3,5-heptanedianato)cobalt III [Co(tmhd) 3].

Dissolution of residual non-aqueous phase liquids in porous media: pore-scale mechanisms and mass transfer rates

Experiments designed to elucidate the pore-scale mechanisms of the dissolution of a residual non-aqueous phase liquid (NAPL), trapped in the form of ganglia within a porous medium, are discussed. These experiments were conducted using transparent glass micromodels with controlled pore geometry, so that the evolution of the size and shape of individual NAPL ganglia and, hence, the pore-scale mass transfer rates and mass transfer coefficients could be determined by image analysis. The micromodel design permitted reasonably accurate control of the pore water velocity, so that the mass transfer coefficients could be correlated in terms of a local (pore-scale) Peclet number. A simple mathematical model, incorporating convection and diffusion in a slit geometry was developed and used successfully to predict the observed mass transfer rates. For the case of non-wetting NAPL ganglia, water flow through the corners in the pore walls was seen to control the rate of NAPL dissolution, as recently postulated by Dillard and Blunt [Water Resour. Res. 36 (2000) 439–454]. Break-up of doublet non-wetting phase ganglia into singlet ganglia by snap-off in pore throats was also observed, confirming the interplay between capillarity and mass transfer. Additionally, the effect of wettability on dissolution mass transfer was demonstrated. Under conditions of preferential NAPL wettability, mass transfer from NAPL films covering the solid surfaces was seen to control the dissolution process. Supply of NAPL from the trapped ganglia to these films by capillary flow along pore corners was observed to result in a sequence of pore drainage events that increase the interfacial area for mass transfer. These observations provide new experimental evidence for the role of capillarity, wettability and corner flow on NAPL ganglia dissolution.

Stagnant Mobile Phase Mass Transfer in Chromatographic Media: Intraparticle Diffusion and Exchange Kinetics

Pulsed field gradient nuclear magnetic resonance has been successfully applied to a direct and detailed experimental study of topological and dynamic aspects involved in the exchange of small, nonsorbed fluid molecules between the intraparticle pore network and the interparticle void space in chromatographic columns packed with spherical-shaped, porous particles. The approach provides quantitative data about the effective, intraparticle diffusion coefficients (and tortuosity factors) and about the associated, diffusion-limited mass transfer kinetics, including stagnant boundary layer contributions. In view of the recorded exchange kinetics, an analytical description for solute diffusion into/out of spherical particles is offered and addresses the influence of the particle size distribution and particle shape on the observed mass transfer rates and calculated diffusivities. The combined analyses of the steady-state intraparticle pore diffusion data and the associated exchange kinetics with Peclet numbers up to 500 reveals the existence of external stagnant fluid where all the interparticle fluid-side resistance to diffusion is localized. It is represented by a thin stagnant boundary layer around the particles and can be accounted for by the introduction of a hydrodynamically effective particle diameter which is found to depend on the Peclet number. The approach appears to be promising for a selective, detailed study of the boundary layer dynamics. Concerning the investigation of different chromatographic media and intraparticle morphologies, we demonstrate that the actual correlation (or randomness) of interconnection between intraparticle pores of different size has a profound effect on the observed tortuosity factors and the diffusion-limited stagnant mobile phase mass transfer kinetics. Compared to intraparticle pore networks with a random assignment of different pore sizes, hierarchically structured bidisperse porous particles offer a superior network topology, which can form the basis for an increased chromatographic performance.

Infrared photometry of WY Sge: just an ordinary old nova?

We present IR photometry of the eclipsing old nova WY Sge (Nova Sagittae 1783), for which we derive a new ephemeris. The ratio of light from the disc and white dwarf to that of the secondary star is typical for an old nova, but at least nine times larger than that of similar period eclipsing dwarf novae. To account for the phase of maximum light it is necessary to invoke some heating of the inner face of the Roche lobe filling star. From this we infer that the heating energy absorbed is 25 ± 10 per cent of the intrinsic luminosity of the secondary. The colours in and out of the eclipse are used to set limits on the distance and reddening. The dereddened colours are compared with other old novae; there appears to be no significant difference. We conclude that WY Sge is not a dwarf nova and thus has remained at a high mass transfer rate. We suggest that if the mass transfer is driven by irradiation then it is unlikely to decrease in the near future. In any case, models suggest that the irradiation measured is unlikely to be sufficient to drive the observed mass transfer rate.

Modeling of transfer phenomena on heterogeneous Ziegler catalysts: Differences between theory and experiment in olefin polymerization (an introduction)

AbstractThis article begins by briefly reviewing the more important contributions to the area of modeling heat and mass transfer, and particle growth during the polymerization of olefins on Ziegler–Natta catalysts. It is shown that these models are capable of identifying the critical areas involved in heat and mass transfer, and of modeling polymerizations where the observed activity is less than approximately 5,000 g of polymer per gram of catalyst per hour (g/g/h). However, it is not possible to use these models “as‐is” to model more modern catalysts whose activity levels can surpass the 50,000 g/g/h mark because they predict prohibitively large concentration gradients inside the growing particles during slurry polymerizations, and temperature gradients outside the particles during polymerization in the gas phase. An analysis of the mass and heat transfer Peclet numbers (Pe) reveals that certain simplifying assumptions may not always be valid. Pe values in the transition range suggest that convection inside the particles during polymerization in the liquid phase may help to explain why observed mass transfer rates are higher than the predicted rates. In an opposite vein, a Pe analysis shows that conductive heat transfer may play an important role at length scales characteristic of those in the early stages of polymerization. A new mechanism for heat transfer at reduced length scales is proposed. © 1995 John Wiley &amp; Sons, Inc.

Friction on a solid sphere exposed to gas–liquid and gas–liquid–solid flow in bubble column and fluidized bed reactors

AbstractLocal velocity gradients on a solid spherical surface have been studied in a bubble column and in two‐ and three‐phase fluidized beds, in order to clarify the influence of gas flow. The electrochemical method, measuring apparent local mass transfer coefficients, was verified and used to obtain the local velocity gradients, shear stresses and total frictional forces. The observed mass transfer rate was independent of liquid velocity, owing to a non‐changing flow structure around the particles and not to averaging opposing effects. The identity in flow structure also held for three‐phase fluidized beds up to a superficial gas velocity of 5 cm s−1. The dramatic increase in velocity gradient on gas introduction was not a result of decreased homogenous density, but was caused by a change in the turbulent structure around a particle, leaving a larger portion of the total drag as frictional drag, thus improving the mass transfer characteristics of the bed. Use of velocity gradient measurements, including span of fluctuations and exposure time, to predict biomass growth and mechanical degradation in a reactor is also discussed.

Mass transfer to droplets formed by the controlled breakup of a cylindrical jet—physical absorption

A novel experimental system, well suited for mass transfer studies in liquids dispersed as droplets in a gas, was constructed. This system produces monodisperse droplets by the controlled breakup of a cylindrical jet by a vibrating orifice. Carbon dioxide-water was chosen as the gas-liquid system for study. Attention was confined throughout this study to the liquid-side mass transfer coefficient. The droplets formed by the breakup of a cylindrical jet are not internally stagnant. Convection within the droplet, due to the formation process, tremendously enhances the mass transfer rate. The experimentally observed mass transfer rates into a stream of closely spaced, well-mixed droplets are well correlated by the Levich theory of mass transfer into a turbulent fluid.

ChemInform Abstract: MASS TRANSFER AT WIPED PLATES

AbstractEs wird eine Methode zur Verbesserung der Massenübertragung, ohne Bewegung der ′ Flüssigkeitsmenge, untersucht.

Mass transfer at wiped plates

A method for enhancing mass transfer without moving the bulk of the liquid was investigated. Plates were wiped by nets moving continuously across the surface. The mass transfer rates were determined electrochemically by measuring the limiting current. The wiping velocity v ranged from 0·3 to 5 cm/s, the electrode length L from 0·2 to 20 cm and the inter-thread distances d were 0·5 and 2·5 mm. A dimensionless plot of the results yielded the correlations Sh L = 29·45 ( Re L L/d ) 0·369 for nets moving upwards Sh L = 25·07 ( Re L L/d ) 0·377 for nets moving downwards with 10 < ( Re L L/d ) < 3 × 10 7. The thickness d′ of the threads was 80 and 250 μm. The results could also be correlated with d′ instead of d, the exponents then being 0·372 and 0·381, the preexponential factors 13·17 and 10·94, respectively. The observed mass transfer rates were compared with those for other kinds of flow. It was found that there is some similarity with a fully developed type of flow.

Effects of product condensation on reaction-enhanced vaporization rates and on the transition from homogeneous to heterogeneous reaction in high-temperature metal oxidation

In order to predict the vaporization rate of fume-forming condensed phases into reactant-rich gases it is necessary to account for the strong augmentation of vapor transport rates caused by bulk flow into the reaction-condensation zone. For this purpose a simple film theory is developed based on the idealization of a thin reaction-condensation “front” supplied by convection-diffusion processes normal to the surface, but with condensate removal by convection processes parallel to the vaporizing surface. The steady-state position or “stand-off distance” of the front and, hence, its effect on the observed mass transfer rate, are determined by the demands of local reactant stoichiometry at the front and species conservation throughout the two-part film, subject to the imposed vapor and oxidizer boundary concentrations. As applied to the problem of metal vaporization into reactive atmospheres, it is shown that while we recover the results of Turkdogan, Grieveson, and Darken in highly dilute isothermal systems (i.e., metals far from their boiling points vaporizing into dilute oxygen-inert gas mixtures) appreciable additional effects due to the condensation process are predicted in the limit of oxidizer-rich ambient gases. Combining this extended theory with the notion that there is an upper limit to the attainable magnitude of the vaporization rate enhancement at which the reaction regime must change from homogeneous to heterogeneous, leads to predicted critical (transition) oxidizer pressures valid even approaching the practically important limit of pure gaseous ozidizer. On the assumption that this transition will occur when the metal vaporization rate approaches that expected in a vacuum (as has been experimentally observed by Turkdogan, Grieveson, and Darken), illustrative calculations are presented for the metals Na, Mg, Ca, Al, Be, Fe, and Zr vaporizing into oxygen-inert gas mixtures, and conclusions are drawn concerning the impossibility of the vapor phase reaction mode at surface temperatures too far below the metal boiling (or sublimation) point. It is also shown that the formalism can be extended to incorporate an alternative critical condition, perhaps more realistic under some experimental conditions, viz., oxygen penetration to the surface due to the finite thickness of the reaction zone. In either event, the model can be readily used to predict the homogeneous-heterogeneous transition locus and its dependence on the occurrence or nonoccurrence of product condensation, and physical, chemical, and aerodynamic parameters.

Acoustic Streaming near a Cylinder in Crossflow

Several investigators have found increases in heat and mass transfer rates of several hundred percent from a circular cylinder in crossflow with an intense sound field acting perpendicular to the cylinder and the crossflow. A rough, two-dimensional approximation of the flow field was obtained by superposition of potential flow over a cylinder and Schlichting's solution for acoustic streaming about a cylinder in an unbounded quiescent fluid. Photographs were taken of the actual flow field at various sound pressure levels and crossflow velocities. Tobacco smoke was used to render the flow visible. The approximate model and the photographs were compared. Limitations of the model and a hypothesis for the observed mass transfer rate increases are discussed.