Mass transfer in laminar liquid jets: Measurement of diffusion coefficients

Laminar liquid jets used in mass transfer studies have been generally discharged from convergent nozzles or orifices. The use of long straight capillary tubes to discharge the liquid jet is studied in this work and numerical values of the jet diameter and surface velocity are obtained. These computed values are applied to predict the actual absorption rates in the laminar jet for different values of N_J= N_Re/N_Fr, N_we and the axial coordinate. The effect of N_we is slight and can be disregarded in analysing experimental data. Experimental values of absorption of CO₂ in water and water-glycerol solutions are obtained using a laminar liquid jet discharged from capillary tube and good agreement is found between the computed values and the measured absorption rates. The results are applied to the determination of diffusion coefficient for the CO₂ in water glycerol solutions.     

Regimes of Unstable Expansion and Diffusion Combustion of a Hydrocarbon Fuel Jet

Results of an experimental study of hydrodynamics and diffusion combustion of hydrocarbon jets are presented. Various regimes of instability development both in the jet flame proper and inside the source of the fuel jet are considered. The experiments are performed for the case of subsonic gas jet expansion into the air from a long tube 3.2 mm in diameter in the range of Reynolds numbers from 200 to 13 500. The fuel is the propane–butane mixture in experiments with a cold jet (without combustion) and pure propane or propane mixed with an inert dilutant (CO₂ or He) for the jet flame. The mean velocity and velocity fluctuations in the near field of the jet without combustion are measured. Among four possible regimes of cold jet expansion (dissipative, laminar, transitional, and turbulent), three last regimes are investigated. The Hilbert visualization of the reacting flow is performed. The temperature profiles in the near field of the jet are measured by a Pt/Pt–Rh thermocouple. An attached laminar flame is observed in the transitional regime of propane jet expansion from the tube. In the case of combustion of C₃H₈ mixtures with CO₂ or with He in the range of Reynolds numbers from 1900 to 3500, the transitional regime is detected in the lifted flame. Turbulent spots formed in the tube in the transitional regime exert a significant effect on the flame front position: they can either initiate a transition to a turbulent flame or lead to its laminarization.     

Modeling infinite dilution and Fickian diffusion coefficients of carbon dioxide in water

We propose a new model for calculating infinite dilution diffusion coefficients for carbon dioxide and water mixtures. The model takes into account temperature dependence of the dipole moment of water and polarizability of CO₂, and fits experimental CO₂? H₂O data at low and high pressures with an accuracy of 4.9%. Remarkably, the proposed model also accurately predicts infinite dilution diffusion coefficients for other binary water mixtures where solute polarizability is close to that of CO₂, such as CH₄, C₂H₆, C₃H₈, and H₂S. Moreover, we present—to the best of our knowledge—the first predictions of composition‐based Fickian diffusion coefficients for CO₂? H₂O mixtures over the temperature range 298.15–413.15 K, and pressures up to 50 MPa. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Determination of polystyrene-carbon dioxide-decahydronaphthalene solution properties by high pressure dynamic light scattering

The diffusion coefficients of polystyrene (PS) in decahydronaphthalene (DHN) and in solutions of carbon dioxide (CO₂) and DHN were measured for dilute PS solutions over a range of temperatures and CO₂-DHN ratios using high pressure dynamic light scattering. Infinite dilution diffusion coefficients (D₀) of PS and dynamic second virial coefficients (k_D) were determined for essentially monodisperse 308 kDa PS. At a system pressure of 20.7 MPa, PS diffusion coefficients increased by a factor of 2.5, and the activation energy of diffusion decreased by approximately 16% when DHN was “expanded” with 44 mol% CO₂. However, the hydrodynamic radius of PS at a given temperature was not particularly sensitive to the CO₂ concentration. Solvent quality, as measured by k_D, decreased at higher CO₂ concentrations. The addition of CO₂ to polymer solutions may offer a way to “tune” the properties of the solution to facilitate the heterogeneous catalytic hydrogenation of polymers.     

Prediction of mass diffusivity of CO2 into bitumen

The infinite dilution and mutual diffusion coefficients for the CO₂/bitumen system were predicted using existing correlations. Out of seven semi-empirical correlations tested, the Umesi-Danner correlation was found to be best suited for the prediction of gas-liquid infinite dilution diffusion coefficient. For the mutual diffusion coefficient, Teja's method based on the generalized corresponding states principle was successfully used. The predictions are compared with the limited CO₂/bitumen diffusivity data available in the literature.     

The effect of CO2 dissolved in a diesel fuel on the jet flame characteristics

This paper is concerned with an experimental study of the jet diffusion flame characteristics of fuel containing CO₂. Using diesel fuel containing dissolved CO₂ gas, experiments were performed under atmospheric conditions with a diesel hole-type nozzle of 0.19 mm orifice diameter at constant injection pressure. In this study, four different CO₂ mass fraction in diesel fuel such as 3.13%, 7.18%, 12.33% and 17.82% were used to study the effect of CO₂ concentration on the jet flame characteristics. Jet flame characteristics were measured by direct photography, meanwhile the image colorimetry is used to assess the qualitative features of jet flame temperature. Experimental results show that the CO₂ gas dilution effect and the atomization effect have a great influence on the flame structure and average temperature. When the injection pressure of diesel fuel increased from 4 MPa to 6 MPa, the low temperature flame length increased from 18.4 cm to 21.7 cm and the full temperature flame length decreased from 147.6 cm to 134.7 cm. With the increase of CO₂ gas dissolved in the diesel fuel, the jet flame full length decreased for the jet atomization being improved greatly meanwhile the low temperature flame length increased for the CO₂ gas dilution effect; with the increase of CO₂ gas dissolved in the diesel fuel, the average temperature of flame increases firstly and then falls. Experimental results validate that higher injection pressure will improve jet atomization and then increased the flame average temperature.     

Experimentelle Bestimmung von molekularen und effektiven Diffusionskoeffizienten am Beispiel der gasunterstützten Abpressung von Speiseölen

The solvent‐free production of edible oils from oilseeds is steadily gathering more importance. Therefore, gas‐assisted pressing is an innovative process. Knowlegde of the diffusion kinetics of the gas is essential in order to optimize the process. In this paper experimentally obtained molecular diffusion coefficients of CO₂ in pure rapeseed oil as well as effective diffusion coefficients of CO₂ within the oil of oil‐bearing rapeseed presscake are presented. The acquired diffusion coefficients are compared to literature correlations and adjustments are presented. Comparison of molecular and effective diffusion coefficients resulted in an diffusion resistance factor of the surrounding solid of 2.1.     

Estimation of diffusion and solubility coefficients for water and CO2 in reaction injection molded parts

The evolution of gases from Reaction Injection Molded (RIM) parts during painting causes “pinhole” surface defects, which result in scrap. The transport of gases plays a major role in this outgassing. The diffusion rates of CO₂ and water through reaction injection molded parts is measured in this work. Despite the presence of glassy hard domains and dispersed microbubbles of size <25 μm (nucleated parts), the diffusion showed Fickian characteristics, and diffusion coefficients were independent of the concentration of water and CO₂ in nucleated and non-nucleated RIM parts. The presence of microbubbles enhances diffusion, which could be predicted from the diffusion rate through the non-nucleated material by using a simplistic one-dimensional model. The diffusion coefficients of water and CO₂ follow an Arrhenius relationship. The solubility coefficients follow a van't Hoff relationship over a wide range of 20 to 150°C. Apart from predicting diffusion and solubility coefficients, for various RIM materials and processing conditions, the estimated parameters will be used to interpret the outgassing phenomenon in a subsequent paper.     

Comprehensive reaction kinetics model of CO2 absorption into 1-dimethylamino-2-propanol solution

In the present work, the kinetics of the reactive absorption of CO₂ in 1-dimethylamino-2-propanol (1DMA2P) solution were experimentally measured using a laminar jet absorber over a temperature range of 298–313 K, 1DMA2P concentration range of 0.5–2.0 mol/L, and CO₂ loading range of 0–0.06 mol CO₂/mol amine. The measured kinetics data were then used to develop a comprehensive numerical kinetics model using a FEM-based COMSOL software. The reaction rate model of the CO₂ absorption into 1DMA2P solution were then validated by comparing model rates with the experimental rates. An excellent agreement of model data with experimental data was achieved with an absolute average deviation (AAD) of 6.5%. In addition, vapor–liquid equilibrium plots of all ions in the 1DMA2P-H₂O-CO₂ system were also developed. Further, this work has provided an effective criterion for evaluating CO₂ absorption, that can be used for both the conventional amines and alternative amines for the purpose of providing guidelines or information on how to effectively screen solvents.     

Measurement and prediction of diffusion coefficients of supercritical CO2 in molten polymers

The solubility and diffusivity of supercritical carbon dioxide (sc‐CO₂) in low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polypropylene (PP), ethylene‐ethylacrylate copolymer (EEA) and polystyrene (PS) were measured at temperatures from 150°C to 200°C and pressures up to 12 MPa by using the Magnetic Suspension Balance (MSB), a gravimetric technique for gas sorption measurements. The solubility of CO₂ in each polymer was expressed by Henry's constant. The interaction parameter between CO₂ and polymer could be obtained from the solubility data, and it was used to estimate the Pressure‐Volume‐Temperature relationship and the specific free volume of polymer/CO₂ mixtures. The diffusion coefficients were also measured by the MSB for each polymer. The resulting diffusion coefficients were correlated with the estimated free volume of polymer/CO₂ mixture. Combining Fujita's and Maeda and Paul's diffusion models, a model was newly developed in order to predict diffusion coefficients for the polymers studied. Polym. Eng. Sci. 44:1915–1924, 2004. © 2004 Society of Plastics Engineers.     

Absorption of SO2 in CaCO3-slurry in a laminar jet absorber

The laminar jet reactor has so far only been used for studying systems without gas phase resistance. In this case however, a modified laminar jet reactor has been built, in which the gas phase resistance easily can either be theoretically calculated or experimentally determined. In the new reactor the SO₂—N₂ system has been studied and especially the SO₂-absorption in CaCO₃-slurry.     

Gas transport in rubbery polymers

Permeability coefficients have been measured for CO₂ and CH₄ in polyethylene membranes at 20, 30, and 40°C and at applied gas pressures up to ca. 2 MPa and for CH₄ in three kinds of rubber films at 25, 30, and 35°C and at applied gas pressures up to ca. 2.4 MPa. The pressure dependence of the logarithms of permeability coefficients became linear except for the CO₂—polyethylene system, where the pressure dependence became quadratic, with a minimum at a certain value of pressure. The linear and quadratic dependences can be interpreted by a free volume model of diffusion of a gas molecule in polymers. The temperature dependence of the permeability coefficients at zero pressure difference across the polymer film for each system obeyed an Arrhenius type equation.     

Multicomponent gas diffusion in hardened cement paste at temperatures up to 350 °C

Diffusional gas transport of a H₂/CO₂ mixture versus N₂ in the pore system of hardened cement pastes was studied at four temperatures up to 350 °C in a Wicke-Kallenbach cell. The pastes possessed separation factors α_H2,CO2 from 1.42 to 3.43, i.e. the diffusion of hydrogen took place considerably faster than the diffusion of carbon dioxide. The separation factors depended on the threshold radii of the pastes, smaller threshold radii leading to higher separation factors. The Knudsen numbers of the controlling constrictions of the pore system and the temperature dependence of the effective diffusion coefficients of the gases show that gas transport in these constrictions takes place in the transient regime between Knudsen diffusion and bulk diffusion, smaller constriction widths leading to predominating Knudsen diffusion. It is therefore possible to use cement paste membranes to separate gas components of low molecular weight from higher weight components.     

Diffusion and sorption for carbon dioxide in Kapton at extremely low pressure

Pressure-dependent solubility and diffusion coefficients for carbon dioxide in glassy polymers have been well described using the “dual sorption and transport model.” However, the plastisization effect by high-pressure carbon dioxide seems to promote the pressure dependence of the sorption and transport coefficients. To avoid the relaxation process by the plastization which is superimposed on the diffusion process, the diffusion and sorption of carbon dioxide were measured at extremely low pressure (below 1 cmHg). Linear isotherms observed for CO₂ sorption into Kapton were interpreted in terms of the dual model equation at extremely low pressure. From the permeation curve of the Kapton/CO₂ system, the diffusion and permeation coefficients were obtained according to the usual manner, and both coefficients were independent of pressure. Sorption and transport parameters were obtained from sorption isotherms and average values of the permeation coefficients. The parameters thus obtained were substituted in an approximated dual sorption and transport equations at extremely low pressure and the pressure independence of the diffusion and permeation coefficients were sufficiently reproduced. It is a good technique to experiment at such extremely low pressure when the validity of the dual model is evaluated. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 1013–1017, 1998     

Interaction of CO2 with a series of detached organic films

Data obtained from gaseous sorption isotherms of CO₂ on eight organic films at three temperatures and three pressures were evaluated for evidences of chemisorption and physical adsorption. The rates of sorption, affected by both temperature and pressure, were analyzed by calculating the perameters of the Elovich equation and those of Barrer's solution of Fick's law for diffusion. Through a consideration of the Elovich parameters, the sorption coefficients, the limiting diffusion coefficients, and the activation energies for diffusion it appears that the rate of interaction of CO₂ with these organic films is primarily a diffusion-controlled process.     

A fundamental study on the removal of air pollutants (sulfur dioxide,nitrogen dioxide and carbon dioxide) by adsorption on activated carbon

Gravimetrically measured adsorption and desorption dynamics of sulfur dioxide, nitrogen dioxide and carbon dioxide on a commercial activated carbon are interpreted by a single-particle model based on three transport processes: macropore, micropore and sorbed-phase diffusion. Additional phenomena, concentration-dependent sorbed-phase diffusivity and sorbent non-isothermality, are incorporated to expand the applicability of the model. The dynamic sorption behaviour of all three gases is adequately described, without resorting to a different particle tortuosity factor for each sorbate. The value of the tortuosity factor (8) and the extracted diffusion coefficients are consistent with literature values. The affinity of the activated carbon for the adsorbates is, in increasing order, CO₂ < SO₂ < NO₂, while the extracted diffusion coefficients show the reverse trend, NO₂ < SO₂ < CO₂.     

Solubility and diffusivity of CO2 in carboxylated polyesters

The solubility of CO₂ in saturated polyester resins at different temperatures (306 and 343 K) and pressures (0.1-30 MPa) has been measured using a magnetic suspension balance. The solubility data were used for estimating the binary diffusion coefficients. The results show a good solubility of CO₂ in polymers, up to 0.64 g CO₂/g polymer. The diffusion coefficients of supercritical CO₂ in polymers have generally high values and are in the range from 0.156 × 10⁻⁸ to 10.38 × 10⁻⁸ cm²/s. DSC and XRD analyses of the semi-crystalline polymer samples indicate that amorphous degree of polymers after exposure to CO₂ is increased. The observed structural effects are dependent on pressure, temperature and time of exposure to CO₂.     

Supercritical fluid dyeing of PMMA films with azo-dyes

In situ ultraviolet–visible spectroscopy has been used to study diffusion of two azo-dyes in a CO₂-swollen matrix of poly(methyl methacrylate) (PMMA). The diffusivity of both dyes can be tuned simply be changing the system pressure. Higher pressure of CO₂ enhances diffusion of a dye in PMMA. The diffusion of dyes in CO₂-swollen PMMA can also be influenced by specific interactions. The partitioning of the dyes between the polymer phase and the fluid phase was measured, and the partition coefficients are large (10⁴–10⁵). Thus, supercritical fluid dyeing is possible, although the solubility of the dyes in the fluid phase is low. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 911–919, 1998     

Facilitated transport of carbon dioxide through an immobilized liquid membrane of K2CO3/KHCO3 aqueous solution

The facilitated transport of CO₂ through a hydrophilic polymeric membrane immobilized with K₂CO₃/ KHCO₃ buffer solution has been investigated. The reactions of dissolved CO₂ in electrolyzed alkaline solution must consider hydration of CO₂ with water, chemical reaction of CO₂ with OH^- and dissociation of HCO ₃ ^2- into CO ₃ ^2- . It is necessary to simplify these reactions as a simple model, which is used to analyze the transport system. From experiments in the liquid membrane with alkaline buffer solution, it is shown that the flux of CO₂ into K₂CO₃KHCO₃ aqueous solution can be enhanced by the presence of CO ₃ ^2- . A diffusion model with an overall reaction based on the film theory is proposed that predicts the experimentally observed facilitation factor with reasonable accuracy. The present model is compared with the rigorous diffusion model involving the complicated conventional chemical reactions.     

Molecular dynamics simulation of the synergistic effect of a compound surfactant on the stability of CO2 oil-based foam

It is of great significance to study the stability of foams in the petroleum industry. Therefore, the stability mechanism of Span 20, the fluorinated surfactant FCO-80 and their mixture FS in a CO₂ oil-based foam system were studied by molecular simulation. The sandwich model of CO₂ oil-based foam was constructed to reveal the stability of the foam system from the microscopic perspective. The result shows that under the synergistic effect of Span 20 and FCO-80, the oil–CO₂ distance of the FS foam system and the coordination number of oil molecules are larger than those of Span 20 and FCO-80 foam system. In FS foam system, the diffusion coefficients of CO₂ molecules are small, and the surface tension is reduced, which can improve the stability of foam. The results can supplement previous experimental results on the stability of oil-based foam.