Liquid-phase Diffusion Coefficients Research Articles

Estimation of liquid phase diffusion coefficients of gallium and antimony in germanium from segregation data in crystal growth experiments

The objective of this paper is to propose new determinations of the diffusion coefficients of gallium and antimony in liquid germanium. To do so, an analysis of effective segregation coefficients obtained in Czochralski growth experiments is carried out in the frame of a self-consistent solidification model. As such, the deduced diffusivity values should be taken as more reliable than previously published data based on the analysis of solute segregation profiles, but the accuracy of the technique is limited by the scatter of the composition measurements. Comparison with existing data supports the necessity of setting up a dedicated experimental program for the measurement of liquid phase diffusion coefficients in germanium.

Liquid-phase Mutual Diffusion Coefficients for Heavy Oil + Light Hydrocarbon Mixtures

: Liquid-phase mutual diffusion coefficients are a key parameter in reservoir simulation models related to both primary production and envisioned secondary recovery processes for heavy oil and bitumen. The measurement of liquid-phase mutual diffusion coefficients in bitumen and heavy oil + light hydrocarbon or gas mixtures present numerous experimental and data analysis challenges due to the viscosity and opacity of the mixtures, the variability of density, viscosity and mutual diffusion coefficient with composition, and the multi-phase nature of these mixtures. Data analysis challenges are particularly acute. For example, recently reported mutual diffusion coefficient values for liquid mixtures of bitumen + carbon dioxide vary over three orders of magnitude when different analysis methods are applied to the same experimental data. In this contribution, we illustrate the importance of measuring composition profiles within liquids as a function of time, as a basis for mutual diffusion coefficient computation, and for allowing explicitly for the variation of diffusion coefficient and liquid density with composition in the analysis of composition profile data. Such inclusions eliminate apparent temporal variations of mutual diffusion coefficients and yield values consistent with relevant theories and exogenous data sets. Liquid-phase mutual diffusion coefficients computed for the mixtures Athabasca Bitumen + pentane and Cold Lake Bitumen + heptane exemplify the experimental and data analysis approaches.

Liquid-Phase Mutual Diffusion Coefficients for Athabasca Bitumen + Pentane Mixtures

The liquid-phase mutual diffusion coefficients for Athabasca bitumen (1) + pentane (2), determined by a free diffusion method, and subsequent analyzing the composition profiles established by X-ray transmission tomography are reported at 295 K. Particular care was taken in the analysis of composition profiles. A method that accounts explicitly for the variation of mutual diffusion coefficient and density with liquid composition was employed in order to obtain time-independent diffusion coefficients consistent with relevant theories and exogenous data sets for mutual diffusivities in liquids.

Study of Heat and Mass Transfer to Determine Multicomponent Liquid Diffusion Coefficients in Partially Saturated Capillaries

A study of simultaneous heat and mass transfer in partially saturated capillaries has been performed in order to develop a method that determines the matrix of multicomponent diffusion coefficients in liquid phase. The literature provides a semi-empirical formula developed by Bandrowski and Kubaczka [4] to calculate the matrix of multicomponent diffusion coefficients. The method separates the kinetic and thermodynamic contributions to mass transfer, and it contains an empirical exponent to improve the calculations. The present work attempts an estimation of the empirical exponent by studying the redistribution of compositions in an unsaturated nonisothermal capillary, taking into consideration the nonideality described by the matrix of thermodynamic factors. Two different ternary mixtures were tested at different temperature gradients and saturation degrees. The results reveal that the method is effective since specific values of the empirical exponent that modifies the matrix of thermodynamic factors were obtained for each system. In addition, the exponent seems to be dependent on temperature.

Sonolytic degradation of halogenated organic compounds in groundwater: Mass transfer effects

Organic pollutants in liquid exposed to acoustic waves behave differently according to their physical and chemical properties. Laboratory batch experiments of sonication for the degradation of trichloroethylene (TCE) and ethylene dibromide (EDB) were carried out in groundwater at 20 kHz, and 12.5 and 35 W/cm 2. A theoretical model for the batch sonication system was derived to examine the mass transfer dependency of the ultrasonic degradation. Experimental results were supported with model predictions suggesting that both liquid phase diffusion coefficient and Henry’s law constant are important parameters for the sonolytic degradation of the halogenated organic compounds in groundwater. When compared with the effect of the diffusion coefficient, Henry’s constant exerts a greater influence on sonolytic degradation. When Henry’s constant exceeds a value of 1 (volume/volume ratio), however, it no longer has much influence on the degradation process. The results also suggest that degradation is enhanced with an increase in ultrasonic power probably due to a greater bubble residence time and the formation of larger bubble at high-energy intensities.

General model and segregation coefficient measurement for ultrashallow doping by excimer laser annealing

A general model of ultrashallow doping by excimer laser annealing is derived from only one diffusion-segregation equation. In our model, the relative dopant profile after some laser shots reaches a stationary distribution, which only depends on the segregation and liquid-phase diffusion coefficients of the dopant but not on the laser-process parameters. From this result, a one-point method is proposed to experimentally determine the out-of-equilibrium segregation coefficient k. Only the relative dopant concentration at the material surface has to be measured prior to determine the k value. Experimental dopant profiles are compared to simulations generated with experimental k values.

Uptake of Organic Gas Phase Species by 1-Methylnaphthalene

Organic compounds are a significant component of tropospheric aerosols. In the present study, 1-methylnaphthalene was selected as a surrogate for aromatic hydrocarbons (PAHs) found in tropospheric aerosols. Mass accommodation coefficients (alpha) on 1-methylnaphthalene were determined as a function of temperature (267 K to 298 K) for gas-phase m-xylene, ethylbenzene, butylbenzene, alpha-pinene, gamma-terpinene, p-cymene, and 2-methyl-2-hexanol. The gas uptake studies were performed with droplets maintained under liquid-vapor equilibrium conditions using a droplet train flow reactor. The mass accommodation coefficients for all of the molecules studied in these experiments exhibit negative temperature dependence. The upper and lower values of alpha at 267 and 298 K respectively are as follows: for m-xylene 0.44 +/- 0.05 and 0.26 +/- 0.03; for ethylbenzene 0.37 +/- 0.03 and 0.22 +/- 0.04; for butylbenzene 0.47 +/- 0.06 and 0.31 +/- 0.04; for alpha-pinene 0.47 +/- 0.07 and 0.10 +/- 0.05; for gamma-terpinene 0.37 +/- 0.04 and 0.12 +/- 0.06; for p-cymene 0.74 +/- 0.05 and 0.36 +/- 0.07; for 2-methyl-2-hexanol 0.44 +/- 0.06 and 0.29 +/- 0.06. The uptake measurements also yielded values for the product HD(l)(1/2) for most of the molecules studied (H = Henry's law constant, D(l) = liquid-phase diffusion coefficient). Using calculated values of D(l), the Henry's law constants (H) for these molecules were obtained as a function of temperature. The H values at 298 K in units 10(3) M atm(-1) are as follows: for m-xylene (0.48 +/- 0.05); for ethylbenzene (0.50 +/- 0.08); for butylbenzene (3.99 +/- 0.93); for alpha-pinene (0.53 +/- 0.07); for p-cymene (0.23 +/- 0.07); for 2-methyl-2-hexanol (1.85 +/- 0.29).

Solute diffusion in liquid nickel measured by pulsed ion beam melting

Measurements of liquid-phase diffusion coefficients for dilute tungsten and molybdenum in molten nickel were made using a pulsed ion-beam melting technique. A high-intensity beam of nitrogen ions is focused on the surface of a nickel substrate that was implanted with known concentration profiles of W and Mo. Melting of the surface to a depth of ∼1 µm allows broadening of the implant profiles while molten. Solute concentration-depth profiles were determined before and after melting using Rutherford backscattering spectrometry. Using a series of numerical simulations to estimate the melt history and diffusional broadening for mean liquid temperatures in the range 1755 to 2022 K, an effective diffusion coefficient is determined in each case by comparison to the measured depth profiles. This is found to be (2.4±0.2)×10−5 cm2/s for W and (1.6±0.4)×10−5 cm2/s for Mo, with an additional systematic uncertainty of ±0.5×10−5 due to instrumental and surface effects.

Uptake of Gas-Phase Species by 1-Octanol. 1. Uptake of α-Pinene, γ-Terpinene, p-Cymene, and 2-Methyl-2-hexanol as a Function of Relative Humidity and Temperature

With use of a droplet train apparatus, the uptake by 1-octanol of gas-phase α-pinene, γ-terpinene, p-cymene, and 2-methyl-2-hexanol was measured as a function of relative humidity and temperature (263−293 K). 1-Octanol was selected as a surrogate for hydrophobic oxygenated organic compounds found in tropospheric aerosols. The mass accommodation coefficients (α) of γ-terpinene, p-cymene, and 2-methyl-2-hexanol obtained from these measurements exhibit negative temperature dependences. The upper and lower values of α at 265 and 290 K, respectively, are as follows: for γ-terpinene 0.12 and 0.076; for p-cymene 0.20 and 0.097; and for 2-methyl-2-hexanol 0.25 and 0.11. The uptake of α-pinene is solubility limited, yielding values for the product HDl1/2 for α-pinene in 1-octanol (H = Henry's law constant, Dl = liquid-phase diffusion coefficient). With use of estimated values of Dl the Henry's law constant is obtained as ln H (M/atm) = −(6.59 ± 1.16) + (3.80 ± 0.31) × 103/T. The presence of water vapor does not a...

Diffusion coefficient of ketones in liquid media within mesopores

The liquid-phase diffusion coefficient of several ketones within mesopores was estimated by measuring the change in UV absorbance of mesoporous plates immersed in a solvent. Monolithic plates of silica gel with different mesopore sizes at ca. 4 and 10 nm were used for the measurement after their pore surface had been modified with trimethylsilyl groups. In the modified silica plates, the diffusion coefficient of ketones, Dp, decreases with increasing the molecular size of the solvent, whereas little dependence is observed on the molecular size of solutes. This indicates that diffusivity of the solute in the mesopores is determined by the diffusivity of the solvent. A zigzag tendency (i.e. the Dp in alkane solvents with an odd number of carbons is larger than those with an even number of carbons) was observed in the small pores with a diameter of ca. 4 nm. The zigzag in Dp can explain a similar zigzag trend in the reaction rate observed only in the small mesopores of the Raney nickel catalyst with a diameter of 3.8 nm in the hydrogenation of several ketones.

In situ 1 H NMR Imaging Study of Propagation of Concentration Waves in an Autocatalytic Reaction in a Fixed Granular Bed

The in situ 1 H NMR technique was used to study the propagation of chemical waves during the liquid-phase Belousov-Zhabotinsky (BZ) reaction in a model fixed bed of grains consisting of chemically inert glass beads or quartz sand. The propagation ol autocatalytic chemical waves in this bed is determined by the size of pores between the grains. The rate of wave front propagation is independent of the size of the grains involved in this bed but is much lower than that in the bulk of the homogenous aqueous phase. This may be attributed to the difference in the effective diffusion coefficients in the homogeneous liquid phase and in the bed.

Effect of Electrolyte Diffusion on the Growth of NaCl Particles by Water Vapour Condensation

The hygroscopic growth of NaCl particles was investigated both experimentally and theoretically. Straightforward experiments done with a humidity controlled microbalance show that a macroscopic time (hours to days) is required before the final (equilibrium) size is reached. The developed model shows that the droplets are not homogeneous salt solutions and that a finite liquid phase diffusion resistance exists. This is clearly evident from the experimental data also: the initial stage of growth shows a linear mass growth in time. This would not be possible without the liquid-phase resistance. It was also possible to determine the liquid-phase diffusion coefficient. Although the value depends on composition and temperature, the best fit with experimental data was obtained by using a value of 1.5 × 10-9 m2/s, which agrees well with available experimental data for strong NaCl−water electrolytes.

Influence of sucrose solution concentration on kinetics and yield during osmotic dehydration of mango

The effect of the sucrose solution concentration on the process kinetics and yield during osmotic dehydration of mango (Kent var.) cylinders has been studied. Processes were carried out at 30 °C, using 35, 45, 55 and 65 °Brix sucrose, at atmospheric pressure (osmotic dehydration) and by applying a vacuum pulse (50 mbar for 10 min) at the beginning of the process (pulsed vacuum osmotic dehydration, PVOD). Kinetics of sugar gain, and water loss, as well as changes in sample mass and volume was analysed. Effective diffusion coefficients in the fruit liquid phase were also estimated. Microstructure of the mango samples after 15 min of PVOD treatments were examined by scanning electron microscopy. Effective diffusion coefficient in the fruit liquid phase increased when sucrose concentration decreased and was always higher in pulsed vacuum osmotic processes. These give rise to tissue impregnation with sucrose solution to an exceptional extent for the treatment with 45 °Brix, which induces a very high sugar gain-water loss ratio.

Effect of Si Content on Diffusion Coefficient of Nickel Nitrate in Wet Silica Gel.

The liquid-phase diffusion coefficient of nickel nitrate in wet silica gels with different Si content as well as in mesoporous silica gel was measured by the flow-cell method, where absorbance of a gel plate placed in a flow cell was monitored as a function of time. For diffusion in the mesoporous silica gel with pore diameter of 12nm, the tortuosity was as low as 1.2, suggesting that the liquid-phase diffusion of nickel nitrate is not restricted in the large mesopores. In contrast, the diffusion coefficient in wet silica gels monotonously decreased with increasing Si content in the gels, and the tortuosity in the wet gel, 1.7-3.5, was larger than that in the mesoporous silica gel. The wet gel is considered to consist of crosslinked polymeric network of silica. The tortuosity in the wet gel would vary depending on the mesh size in the network and on the number of free side chain.

Uptake of Methanol Vapor in Sulfuric Acid Solutions

The uptake of gas-phase methanol by liquid sulfuric acid has been investigated over the composition range of 40−85 wt % H2SO4 and the temperature range of 210−235 K. Laboratory studies were performed with a flow-tube reactor coupled to an electron-impact ionization mass spectrometer to detect trace gases. While reversible uptake was the primary mechanism at low acid concentrations, an irreversible reaction between methanol and sulfuric acid at low temperatures, forming methyl hydrogen sulfate and dimethyl sulfate, was observed at all concentrations. At compositions >65 wt % H2SO4, more than 90% of uptake was found to be reactive. On the basis of the uptake data and the calculated liquid-phase diffusion coefficients, the product of the effective Henry's law constant (H*) and the square root of the overall liquid-phase reaction rate (kl) was calculated as a function of acid concentration and temperature. The results suggest that the reaction with sulfuric acid forming methyl hydrogen sulfate and dimethyl sulfate is the dominant loss mechanism of methanol and that the oxidation of methanol is only a minor source of hydroxyl radicals in the upper troposphere.

Kinetics of the reactive uptake of ozone on oleic acid aerosols

Heterogeneous reactions involving particles and gas-phase species can alter important chemical and microphysical properties of aerosols, complicating modeling efforts to assess their effects on climate and human health. Organic aerosols are common in the troposphere; precursors include vegetation, the ocean surface, and various combustion processes. Ozone is an important oxidant in the troposphere (Finlayson-Pitts and Pitts, 1997), often in concentrations sufficient to cause adverse effects on human health and vegetation. Oleic acid is one of a group of organic species proposed as an important tracer species for use in source characterization of ambient aerosols (Rogge et al., 1991). However, the relative fraction of these species may change as the particle ages, and new product species are likely to be introduced. Little is known about the kinetics of organic species in atmospheric aerosols. Such knowledge is necessary for quantitative assessment of field studies as well as for use in climate models. With this motivation, we have chosen oleic acid (one of the simplest condensed phase organics with atmospheric relevance) as the first species to be used in a series of experiments aimed at investigating the dynamic evolution of the composition and size of organic particles in the presence of ozone. Our experimental setup includes an atmospheric pressure flow reactor, in which oleic acid particles of a pre-selected size are allowed to interact with ozone for a controlled time, coupled to a newly developed aerosol mass spectrometer (AMS), (Jayne et al., 2000), which monitors changes in the size distribution and composition of the aerosols. This AMS/flow reactor system permits a new approach to kinetic studies in that the depletion of the particle-phase reactant (rather than the gas-phase reactant) is monitored. In the present study we report the size dependent rate of reactive uptake of ozone by three different sizes of oleic acid particles. Depletion of oleic acid, appearance of product species, and the growth of particle size are all observed simultaneously. With interaction times from 2 to 11 seconds, a given run takes place at nearly constant ozone concentration. The figure below indicates the fraction of oleic acid remaining in a particle as a function of ozone exposure time. We are developing an uptake model which allows determination of the following fundamental physico-chemical parameters: Henry's Law solubility constant for ozone in oleic acid, H, the liquid phase diffusion coefficient for ozone in oleic acid, D, and the second order rate coefficient for ozone reacting with oleic acid, k 2. The plotted curves show a preliminary fit to the size dependent reaction data, yielding the values shown at 293°K. These parameters allow calculation of the reactive collision probability, γ, which ranges from about 10 −3 to 10 −5 (decreasing with a decrease in oleic acid concentration). Our data also show a dependence in the uptake on the purity of the oleic particles, an increase in viscosity upon reaction, and an increase in particle diameter as the interaction time increases. These effects (including those of secondary reaction of products) are currently being modeled in order to assess aerosol phase oleic acid atmospheric lifetimes.

Heterogeneous Chemistry of Acetone in Sulfuric Acid Solutions: Implications for the Upper Troposphere

The uptake of acetone vapor by liquid sulfuric acid has been investigated over the range of 40−87 wt % H2SO4 and between the temperatures 198 and 300 K. Studies were performed with a flow-tube reactor, using a quadrupole mass spectrometer for detection. At most concentrations studied (40−75 wt %), acetone was physically absorbed by sulfuric acid without undergoing irreversible reaction. However, at acid concentrations at or above 80 wt %, reactive uptake of acetone was observed, leading to products such as mesityl oxide and/or mesitylene. From time-dependent uptake data and liquid-phase diffusion coefficients calculated from molecular viscosity, the effective Henry's law solubility constant (H*) was determined. The solubility of acetone in liquid sulfuric acid was found to increase with increasing acid concentration and decreasing temperature. In the 75 wt % and 230 K range, the value for H* was found to be ∼2 × 106 M/atm. This value suggests that acetone primarily remains in the gas phase rather than absorbing into sulfate aerosols under atmospheric conditions.

HOBr in Sulfuric Acid Solutions: Solubility and Reaction with HCl as a Function of Temperature and Concentration

A detailed study of the interaction of HOBr and HCl in cold sulfuric acid solutions has been performed using a coated-wall flow tube coupled to an electron-impact mass spectrometer. The liquid-phase bimolecular rate constants, measured over a temperature range from 213 to 238 K and in solutions from 59.7 to 70.1 wt % composition, show a strong positive dependence on both acid composition and temperature. The solubility of HOBr has also been measured in these solutions by analyzing its time-dependent uptake. Henry's Law constants (H) determined from the measured values of HD1/2 and the liquid-phase diffusion coefficient (D) are independent of acid composition over the above range of solution compositions. The values of H demonstrate a clear Clausius−Clapeyron temperature dependence, with a heat of solution of −9 ± 1 kcal/mol. When the atmospheric importance of these data is assessed, two conclusions are reached. In the stratosphere, under aerosol conditions observed soon after the Mt. Pinatubo volcanic eru...

Modeling Oxidizing Scrubbers for Odor Control

In an oxidizing scrubber for odor control, the odorant is absorbed in a scrubber and must be oxidized to allow steady-state operation. The rate of absorption depends on the Henry's law coefficient, the gas- and liquid-phase mass transfer coefficients, and the rate of the oxidation reaction. The effect of a liquid-phase reaction on the liquid-phase mass transfer is often expressed in terms of an enhancement factor. Pseudo-first-order reaction rates were estimated for chlorination reactions for selected odorants. For simple amines and ammonia, the pseudo-first-order reaction rate is very fast, resulting in high enhancement factors for typical values of the mass transfer coefficients and odorant liquid-phase diffusion coefficients. For phenol and toluene, the reaction rate is relatively slow, and the enhancement factor is very close to unity.

Heterogeneous uptake of HCl by sulfuric acid solutions

The uptake of HCl molecules by aqueous sulfuric acid droplets was measured in the temperature range 230–264 K at 39, 49, 54, 59, and 69 wt % acid and as a function of time (2–15 ms). These experiments utilized a droplet train apparatus in which a stream of monodisperse droplets (120–250 μm in diameter) is passed through a low‐pressure flow containing HCl(g). The droplet area is changed in a step‐wise fashion, while the HCl(g) density is continuously monitored by infrared absorption. The uptake coefficient is obtained from the measured change in the HCl density. The product of H*Dl1/2 (H*, solubility; Dl, liquid phase diffusion coefficient) and the mass accommodation coefficient a of the species as a function of temperature and sulfuric acid concentration were obtained from the uptake coefficient. The good agreement of measured and modeled H*Dl1/2 values validates current formulations of HCl reactivity in stratospheric aerosols. While the solubility of HCl decreases steeply with sulfuric acid concentration because increasing acidity reduces the dissociation of HCl into H+ and Cl− in solution, the mass accommodation coefficient is independent of acid concentration in the region studied. As with previously studied species, α is inversely proportional to temperature increasing from ∼0.06 at 294 K to near unity at ∼230 K. The mass accommodation coefficient is well expressed in terms of an observed Gibbs free energy as α/(1 − α) = exp (−ΔGobs/RT), suggesting that the clustering model for the accommodation process is applicable in this case as well. The mass accommodation measurements are well fitted by the parameters ΔHobs = −13.8±0.9 kcal mol−1 and ΔSobs = −52.2±0.3 cal mol−1 K−1. Under stratospheric conditions α for HCl is unity. Implications of the HCl uptake studies for atmospheric chemistry are examined.