Deviations Of Fraction Research Articles

The laws of establishing stationary composition in a droplet condensing in a binary vapor–gas environment

It is shown that the mole fractions of components within a droplet growing in an atmosphere of two condensing gases and a carrier gas approach their stationary values with a power-law behavior in time on a large scale and with exponential behavior on a small scale for both diffusion-controlled and free-molecular regimes of isothermal condensation. The parameters of the power and the exponential laws are specified for each regime of binary condensation and are linked to the thermodynamic and kinetic characteristics of condensing vapors and to the stationary mole fractions of the components in a growing binary droplet. The stationary composition of the solution within the droplet is shown to be established at a comparatively small relative increase of the droplet radius. A relaxation equation for the droplet composition at arbitrary initial deviations of mole fractions from their stationary values has been solved, and the limitations on the initial deviations allowing monotonic establishment of stationary composition in solution within a growing droplet have been considered.

In Vitro Analysis of Downstream Particulates with Mechanical Thrombectomy Devices: Comparison of 20-kHz Sonothrombolytic and Rotating Dispersion Wire Systems

To assess the potential of macroembolization, the authors compared the downstream particulate profile generated with use of two thrombectomy devices, a 20-kHz ultrasound-based sonothrombolytic (ST) device and a rotating dispersion wire (RDW). An arterial flow model was pressurized to 100 mm Hg and perfused with 1,000 mL/min normal saline. Tubing containing 7-mm x 30-cm bovine thrombus proximal to a 75% stenosis was inserted distal to a nonstenosed bypass. The effluent was passed successively through 1,000-, 500-, and 200-microm filters and a particle analyzer. The ST device and RDW were activated for 10 and 15 minutes, respectively, in randomized sequences of experimental sets with and without the use of 10-mg tissue-type plasminogen activator (tPA). Results are expressed as means and standard deviations of fraction of lysed clot in each category. The ST device produced significantly fewer particulates larger than 1,000 microm (1.3% +/- 1.4) than did the RDW (16.8% +/- 8.4, P < .001) and significantly more particulates smaller than 10 microm (90.7% +/- 7.6) than did the RDW (73.9% +/- 9.5; P < .001) at comparable thrombolytic efficacy (P = .982) and without significant effect from tPA (P = .988). There were no significant differences between particles measuring 500-1,000 microm (ST device: 0.3% +/- 0.3, RDW: 0.4% +/- 0.3; P = .653) and those measuring 10-199 microm (ST device: 7.5% +/- 7.5, RDW: 8.6% +/- 3.8; P = .624). The amount of particles on the 200-microm filter after RDW activation (0.4% +/- 0.3) exceeded those trapped after use of the ST device (0.1% +/- 0.1, P = .007) but contributed relatively little overall. In this in vitro model, the use of the ST device resulted in fewer large particulates than did the use of the RDW, with more clots being reduced to less than 10 microm.

Separation of Hexane/Ethanol Mixtures. LLE of Ternary Systems (Ionic Liquid or Hyperbranched Polymer + Ethanol + Hexane) at T = 298.15 K

Liquid−liquid phase equilibria (LLE) of hexyl(2-hydroxyethyl)dimethylammonium tetrafluoroborate (C6BF4) or hyperbranched polymer (a fatty-acid-modified dendritic polymer, Boltorn U3000) B-U3000 + ethanol + hexane, at T = 298.15 K have been measured. The results are discussed in terms of the selectivity of ethanol and hexane separation. Sloping of the tie lines toward the ethanol vertex is observed for both mixtures (C6BF4 or B-U3000 + ethanol + hexane). The results indicate high selectivity for separation of ethanol and hexane with the ammonium ionic liquid in solvent extraction. The nonrandom two-liquid NRTL model was successfully used to correlate the experimental tie lines. The maximum mean square deviation in mole fraction was 0.01.

Study on the Interaction Coefficients in PR Equation with vdW Mixing Rules for HFC and HC Binary Mixtures

The Peng-Robinson equation of state with the van der Waals mixing rules was used to correlate vapor–liquid equilibrium (VLE) data for HFC/HC, HFC/HFC, and HC/HC binary mixtures. The interaction parameter k ij was obtained for every binary mixture. It was assumed that k ij has contributions from the two components, and each component has its own constant contribution factor k i for the mixture, and the values of k ij indicate the degree in difference of properties between the two components. Therefore, the interaction parameters k ij is proposed as: k ij = k i − k j . The values of the mixing factor k i for Hydrofluorocarbons (HFCs) and Hydrocarbons (HCs), including propane, isobutane, n-butane, R23, R32, R125, R143a, R134a, R152a, R227ea R236fa, R236ea, and R245fa, were obtained by least-square fitting. In total, 39 refrigerant binary mixtures were analyzed on the basis of this method, and the results showed good agreement with experimental data. The overall average absolute deviations of pressure and vapor mole fraction are 1.3 % and 0.0089, respectively.

Solubility of Alcohols and Aromatic Compounds in Imidazolium-Based Ionic Liquids

Liquid−liquid equilibria for 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) or 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]) + 1-propanol, + 1-butanol, and + 1-pentanol in the temperature range of (293.92 to 364.88) K and the solubility of benzene, toluene, and thiophene in [BMIM][PF6] and [BMIM][BF4] in the temperature range of (298.15 to 343.15) K have been measured using the cloud point method. The liquid−liquid equilibrium data were correlated by the nonrandom two-liquid (NRTL) equation, and the root-mean-square deviations of the mole fractions for [BMIM][PF6] or [BMIM][BF4] + 1-propanol, 1-butanol, and 1-pentanol are shown as follow: 0.0041, 0.0065, 0.0043, 0.0065, 0.0053, and 0.0019, respectively. In addition, it is found that the solubility of benzene, toluene, and thiophene in the ionic liquids was independent of temperature.

Liquid−Liquid Equilibrium of Ternary Systems of Cyclohexane + (Benzene, + Toluene, + Ethylbenzene, or + o-Xylene) + 4-Methyl-N-butyl Pyridinium Tetrafluoroborate Ionic Liquid at 303.15 K

Liquid−liquid equilibrium data are critical for designing the extraction equipment or calculating the thermodynamic limit of a given separation. In this work, the LLE data were measured for the cyclohexane + (benzene, + toluene, + ethylbenzene, or + o-xylene) + 4-methyl-N-butyl pyridinium tetrafluoroborate ([bmpy]BF4) systems at 303.15 K under atmospheric pressure. The consistency of the measured LLE data was tested using the Othmer−Tobias correlation and the root-mean-square deviation (rmsd) in the mass fraction of [bmpy]BF4 in the lower phase and the average value of the absolute difference (AAD) between experimental mass fraction of cyclohexane in the upper phase and that calculated using the Othmer−Tobias correlation.

Hydrogen-bonding athermal lattice chains compared with associating hard-sphere chains

With its flexibility and simplicity in derivation, the Veytsman statistics is proved to provide a powerful tool for representing association contributions to Helmholtz free energy of lattice fluids. However, based on a heuristic argument the probability function in the statistics is in need of a critical review as to its accuracy and parameter characteristics. For these purposes different probability functions were compared with molecular simulation data of associating hard-sphere chains in this work. Association energy of lattice fluids was found to be equal to the square-well depth of off-lattice fluids. The form and parameter value for probability functions were reviewed and a new probability function was proposed for the best agreements with molecular simulation data. The proposed probability function with optimized parameter yielded the average absolute deviations of monomer fractions and compressibility factors less than 0.04 and 7%, respectively.

Fluid phase topology of ethanol+benzene+cyclohexane at 101.3 kPa

In this article, isobaric vapor–liquid equilibria for the ternary mixture of ethanol + benzene + cyclohexane was experimentally investigated at atmospheric pressure. Vapor–liquid equilibria data for ethanol + benzene + cyclohexane at 101.3 kPa were obtained with a Othmer-type ebulliometer. Data were tested and considered thermodynamically consistent. The experimental results showed that this ternary mixture is completely miscible and exhibits three binary homogeneous azeotropes and a ternary minimum azeotrope at the studied conditions. Satisfactory results were obtained for correlation of equilibrium compositions with UNIQUAC activity coefficients model and also for prediction with UNIFAC method. In both cases, low root mean square deviations of vapor mole fraction and temperature were calculated. The capability of ethanol as modified distillation agent at atmospheric condition is discussed in terms of the thermodynamic topological analysis. However, owing to the complex topology of the ternary mixture it leads to a distillation scheme with three columns and difficult operation and thus, ethanol is not recommended as a separating agent for benzene + cyclohexane azeotrope.

The effect of allanite inclusions on U–Pb step-leaching ages and Sm–Nd isotope systematics of garnet from the Ogcheon metamorphic belt, South Korea

The Ogcheon metamorphic belt consists primarily of metasedimentary and metavolcanic rocks that have experienced polyphase tectonometamorphism since the Neoproterozoic. Peak metamorphism reaching up to lower-amphibolite facies produced ubiquitous garnet porphyroblasts in pelitic and mafic schists. To determine the timing of their formation, step-leaching experiments were undertaken for five garnet fractions separated from pelitic and quartz-hornblende-garnet schists. The U–Pb ages from three samples are identical within 2σ errors, ranging from 291 ± 41 Ma to 276 ± 29 Ma. The quasi-linearity of leachates in 238U– 206Pb and 208Pb– 206Pb diagrams suggests that U and Pb are released from a single mineral phase and that minor chemical fractionation between U and Pb may have occurred during the leaching experiment. Deviations of residues and bulk garnet fractions from the linear trend are attributed to partial dissolution of refractory inclusions of detrital zircon. Th/U ratios of leachates are in the range of 3.4–12, much higher than those of pure garnet, and suggest the contribution of allanite. Negative relationships in the Sm–Nd isochron diagram and similar 147Sm/ 144Nd ratios between whole rock and garnet corroborate the influence of light rare earth element (LREE)-rich allanite on the Sm–Nd isotopic system. Simple mass-balance calculations indicate that only a trace amount (0.35 modal%) of allanite inclusions should govern the U–Th–Pb systematics of garnet. Petrographic evidence together with the consistency in U–Pb ages suggests that allanite is a product of prograde metamorphism. Thus, peak metamorphism responsible for the growth of allanite-bearing garnet porphyroblasts in the Ogcheon metamorphic belt is best estimated to be Early Permian.

Azeotropic behaviour of (benzene + cyclohexane + chlorobenzene) ternary mixture using chlorobenzene as entrainer at 101.3 kPa

In this paper, the azeotropic behaviour of the (benzene + cyclohexane + chlorobenzene) ternary mixture was experimentally investigated with the aim of enhancing the knowledge for the feasible use of chlorobenzene as an entrainer for the azeotropic distillation of the binary azeotrope. Such a study has not been reported in the literature to the best of the authors’ knowledge. (Vapour + liquid) equilibria data for (benzene + cyclohexane + chlorobenzene) at 101.3 kPa were obtained with a Othmer-type ebulliometer. Data were tested and considered thermodynamically consistent. The experimental results showed that this ternary mixture is completely miscible and exhibits an unique binary homogeneous azeotrope, an unstable node at the conditions studied, and the propitious topological characteristics (residual curve map and relative volatility) to be separated. Satisfactory results were obtained for the correlation of equilibrium compositions with the UNIQUAC activity coefficients model and also for prediction with the UNIFAC method. In both cases, low root mean square deviations of the vapour mole fraction and temperature were calculated. The capability of chlorobenzene as a modified distillation agent at atmospheric condition is discussed in terms of the thermodynamic topological analysis. A conceptual distillation scheme with reversed volatility is proposed to separate the azeotropic mixture. In order to reduce the operational cost requirements of the sequence of columns proposed, the range for optimal reflux and the ratio for feed flow conditions were studied.

Laser diffraction, transmission electron microscopy and image analysis to evaluate a bimodal Gaussian model for particle size distribution in soils

The Shiozawa and Campbell Gaussian bimodal model describes the particle size distribution (PSD) in soils as a weighted sum of two fractions: the primary minerals (sand and silt) and the secondary minerals (clay) fraction, each described by a Gaussian function. This model was developed and tested using traditional sedimentation techniques analysis for PSD such as sieving and hydrometer. Because of the lack of particle size distribution data in the clay range, Shiozawa and Campbell set the mean and the standard deviation in the clay fraction as a constant. Today, the availability of laser diffraction (LD) techniques makes it possible to overcome this limit and test the model by using a soil dataset that includes the clay fraction distribution. This paper describes the results of the test of the Shiozawa and Campbell Gaussian bimodal model on eight samples, six of them from different locations in Washington State (USA) and two from a hillside area of Northern Italy. PSD analysis was performed with sedimentation techniques, small-angle laser diffraction apparatus and transmission electron microscopy, the latter allowing measurement of very fine particles (sizes down to 0.05 μm). To test the effect of the PSD technique on the particle-size measurement and therefore on the model reliability, a comparison between sedimentation techniques and LD was performed. Moreover a validation of the LD method in the clay range was performed by comparison of LD to Transmission Electron Microscopy and Image Analysis methodologies. The results from the bimodal model showed that the model provides a good characterization of PSD for five of the eight samples analyzed only, revealing that more complex distributions are required for a loam, a silt loam and for a clay soil, where multimodal modes were found. The comparison between sedimentation technique and LD showed that the volume percentage of the clay-size fraction obtained by laser diffraction was lower than the mass percentage of the clay-size fraction measured by pipette. The silt fraction displayed the opposite trend. Transmission Electron Microscopy and Image Analysis of the clay fraction showed that Laser Diffraction provides an overestimation of the mean diameter in the clay fraction, when particles are assumed to be represented as spheres.

Large deviations of the empirical volume fraction for stationary Poisson grain models

We study the existence of the (thermodynamic) limit of the scaled cumulant-generating function L_n(z)=|W_n|^{-1}\logE\exp{z|\Xi\cap W_n|} of the empirical volume fraction |\Xi\cap W_n|/|W_n|, where |\cdot| denotes the d-dimensional Lebesgue measure. Here \Xi=\bigcup_{i\ge1}(\Xi_i+X_i) denotes a d-dimensional Poisson grain model (also known as a Boolean model) defined by a stationary Poisson process \Pi_{\lambda}=\sum_{i\ge1}\delta_{X_i} with intensity \lambda >0 and a sequence of independent copies \Xi_1,\Xi_2,... of a random compact set \Xi_0. For an increasing family of compact convex sets {W_n, n\ge1} which expand unboundedly in all directions, we prove the existence and analyticity of the limit lim_{n\to\infty}L_n(z) on some disk in the complex plane whenever E\exp{a|\Xi_0|} 0. Moreover, closely connected with this result, we obtain exponential inequalities and the exact asymptotics for the large deviation probabilities of the empirical volume fraction in the sense of Cram\'er and Chernoff.

Vapor−Liquid Equilibria of the Binary System 1-Pentanol + Anisole and the Quaternary System Benzene + Cyclohexane + 1-Pentanol + Anisole at 101.32 kPa

Vapor−liquid equilibrium (VLE) at 101.32 kPa has been measured for the quaternary system benzene + cyclohexane + 1-pentanol + anisole in an isobaric equilibrium still with secondary recirculation of vapor and liquid phases covering a wide range of concentration. Accurate prediction of activity coefficients and the equilibrium compositions with the UNIFAC group contribution model were obtained with low standard deviations of vapor mole fraction and equilibrium temperatures. The consistency of the measured VLE data were tested with the McDermott and Ellis method.

Total Vapor Pressure Measurements for 2-Ethoxyethanol with Carbon Tetrachloride, Chloroform, and Dichloromethane at 303.15 K

Total pressure measurements are reported for the binary mixtures of 2-ethoxyethanol with carbon tetrachloride, chloroform, and dichloromethane at 303.15 K. The data were obtained using a Van Ness type apparatus and were fitted with a modified Margules equation using Barker's method. The total pressure data are represented by the model to within an average absolute deviation of approximately 0.06 kPa. Solutions of 2-ethoxyethanol with carbon tetrachloride show positive deviations from ideality, while those of 2-ethoxyethanol with chloroform and with dichloromethane show negative deviations at low chloroalkane mole fraction and positive deviations at high chloroalkane concentration.

TURBULENT MASS TRANSPORT IN SATURATED RIGID POROUS MEDIA

We present derivations of mass transport equations for turbulent flow in permeable structures. Equations are developed following two distinct procedures. The first method considers time averaging of the local instantaneous mass transport equation before the volume average operator is applied. The second methodology employs both averaging operators but in a reverse order. This work is intended to demonstrate that both approaches lead to equivalent equations when one takes into account both time fluctuations and spatial deviations of velocity and mass fraction. A modeled form for the final transport equation is presented where turbulent transfer is based on a macroscopic version of the κ-e model

Isobaric Vapor−Liquid Equilibria of the Binary Systems Cyclohexane with o-Xylene, m-Xylene, p-Xylene, and Ethylbenzene at 101.3 kPa

Isobaric vapor−liquid equilibria were measured for cyclohexane + o-xylene, + m-xylene, + p-xylene, and + ethylbenzene at 101.3 kPa using a dynamic still with circulation of both phases. Experimental data were tested for thermodynamic consistency and satisfactorily correlated by different equations. The four systems exhibit positive deviations from ideal behavior. A comparative analysis was performed by application of the ASOG, original UNIFAC, modified UNIFAC (Dortmund), and modified UNIFAC (Lyngby) systems, and low root-mean-square deviations of vapor mole fraction and temperature were computed.

Accuracy and reproducibility of left ventricular function from quantitative, gated, single photon emission computed tomography using dynamic myocardial phantoms: effect of pre-reconstruction filters.

We have investigated the accuracy and reproducibility of left ventricular (LV) functions using quantitative, gated, single photon emission computed tomography (SPECT) software dependent on critical frequencies of pre-reconstruction filters. This study incorporated dynamic myocardial phantoms (myocardial and cone shapes). Gated SPECT of 8-interval sets were pre-filtered with Butterworth filters (critical frequency varying between 0.16 and 1.16 cycles/cm, order 5) and with no filter. Phantoms were repositioned, and SPECT acquisitions were repeated. As the critical frequency increased, the estimated LV volume increased to reach a plateau at the level of the critical frequency, 0.54 cycles/cm. Conversely, the values of ejection fractions, wall motion and wall thickening with different filters which used critical frequency of > or =0.39 cycles/cm remained unchanged. However, LV functions and volumes were underestimated when any pre-reconstruction filter was used. Standard deviations of LV functions after repeated measurements were unaffected by different filters with critical frequencies of > or =0.39 cycles/cm. Standard deviations of LV volume, ejection fraction, wall motion and wall thickening were <2.2 ml, <0.9%, <0.6 mm and <8.7%, respectively. Therefore, with the exception of low critical frequencies, LV functions and volumes were highly reproducible when these routine reconstruction filters were used.

Phase Equilibria of the Ternary System Benzene + Cyclohexane + 1-Pentanol at 101.3 kPa

Vapor−liquid equilibrium at 101.3 kPa has been measured for the ternary system benzene + cyclohexane + 1-pentanol in an isobaric equilibrium still with secondary recirculation of both vapor and liquid phases. Satisfactory results were obtained for the prediction of activity coefficients and the equilibrium compositions with the ASOG and UNIFAC group contribution models; low standard deviations of vapor mole fraction and temperature were computed. Azeotropic behavior was observed only in the benzene + cyclohexane mixture. The correlation parameters for the Tamir−Wisniak and UNIQUAC equations are presented.

00/03641 Thermodynamic analysis of binary and ternary silicate systems by a structural model

The cubic equation of state/excess Gibbs free energy (CEoS/GE) model is a new idea to predict non-ideal systems. In this study, the Peng-Robinson (PR) EoS combined with the Wong-Sandler (WS) mixing rule and the modified UNIFAC group contribution activity model was used to calculate the vapor liquid equilibrium (VLE) data. The average absolute relative deviations (AARD) of pressure and the average absolute deviations (AAD) of the vapor phase mass fraction between the calculated results and experimental data are 0.87% and 0.005 for fluoroethane (R161) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) over the temperature range of (283.15–323.15 K) and at pressures varying from 0.4 MPa to 1.8 MPa, respectively. The liquid and vapor phase mass fraction deviations are within ±0.028 and ±0.025 for difluoromethane (R32) + pentafluoroethane (R125) + 1,1,1,2-tetrafluoroethane (R134a) system at temperatures of (205–350 K), respectively. The VLE behavior for the strongly-zeotropic mixture of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) + trifluoromethane (R23) + tetrafluoromethane (R14) which is suitable for the three-stage auto cascade refrigeration system was calculated at pressures of (0.2–2.2 MPa) and the corresponding three-dimensional phase diagrams were constructed. It was found that the sliding temperature increases with the decrease of pressure and the maximum predicted sliding temperature reached 73 K.

Vapor−Liquid Equilibria for the Ternary System Acetone + Methanol + Water at 101.325 kPa

The vapor−liquid equilibrium at 101.325 kPa has been measured for the ternary system acetone + methanol + water in an equilibrium still with circulation of phases. Satisfactory results were obtained for the prediction of activity coefficients and the equilibrium compositions with group contribution models (ASOG, UNIFAC, UNIFAC−Dortmund, and UNIFAC−Lyngby). Small standard deviations of vapor molar fraction and temperature were calculated. Azeotropic behavior was observed only in the acetone + methanol mixture. The correlation parameters for the Tamir−Wisniak and UNIQUAC equations were presented.