Binary Diffusion Experiments Research Articles

A Loschmidt cell combined with holographic interferometry for binary diffusion experiments in gas mixtures including first measurements on the argon–neon system

A new variant of the Loschmidt technique has been developed for measuring binary diffusion coefficients in gas mixtures in a temperature range from 10 to 80 °C and for pressures between 0.1 and 1 MPa. The two half cells of the thermostatted diffusion cell have a rectangular cross section and are fixed one upon the other. They can be connected and separated by means of a sliding plate provided with a pneumatically operated seal. The concentration in both half cells is determined simultaneously during the diffusion process using an optical system for holographic interferometry for each. The change in the refractive index results in an interference pattern which is recorded as a function of time. The concentrations of the diffusing components are derived by means of the Lorentz–Lorenz equation. The binary diffusion coefficients are calculated via the integrated ideal diffusion equation for the complete mole fraction range performing only a unique diffusion experiment. The performance of the apparatus is demonstrated on first measurements on the argon–neon system at 293.15 K. Separate refractive index measurements are carried out leading to values for the first refractivity virial coefficient of the pure gases with an estimated uncertainty of ±0.1%. This low uncertainty is required for the aimed uncertainty of ±0.5…1% for the diffusion measurements to determine the concentration and density dependences of the binary diffusion coefficient.

Experimental Study of Gas Transport Parameters in Unsaturated Silica Flour

An experimental study was conducted to assess the relative contributions of molecular and Knudsen diffusions for gas‐phase transport in unsaturated silica flour with an intrinsic permeability of 1 ∼ 2 × 10−14 m2 Single‐gas phase flow and binary diffusion experiments were performed on the same soils to determine the Knudsen diffusion and the effective gas‐phase diffusion coefficients, respectively. These results were further used to assess the diffusibility factor for Fick's law of diffusion and the obstruction factor for the Dusty Gas Model theory. These factors were used to account for impedance to gas diffusion caused by the tortuous nature of soil pores. The Knudsen diffusion coefficient was found to be one to two orders of magnitude greater than the effective diffusion coefficient for silica flour at water saturations ranging from 53 to 75% (v/v), which suggested that the Knudsen effect has negligible impact on the effective diffusion coefficient for the unsaturated silica‐flour system at water saturations lower than 75%. For unsaturated silica flour with air‐filled porosity <0.2, the diffusibility factor (or the obstruction factor) value can be more than 10 times smaller than the values estimated by other diffusibility correlations published in the literature.

Software supporting optimal experimental design: A case study of binary diffusion using EFCOSS

Methods for optimal experimental design aim at minimizing uncertainty in parameter estimation problems. Despite their long tradition in applied mathematics and importance in practical applications, they are currently not widely used in computational science and engineering. To make the techniques of optimal experimental design more accessible to a broader community, we introduce a novel software environment called EFCOSS and demonstrate its ease of use and versatility in two case studies of binary diffusion experiments. Through the use of a component-based software architecture, integration of automatic differentiation technology and facilitated interfacing to optimization algorithms, EFCOSS minimizes the computational overhead for the user who can thus focus on model development and analysis itself. The presented case studies focus on diffusion experiments in liquids since these experiments are typically very demanding. The use of optimal experimental design techniques allows to reduce experimental time and effort significantly.

Influence of capillary condensation effects on mass transport through porous membranes

The importance of capillary condensation effects in connection with properly quantifying the rate of mass transport through porous media has been already described (J. Coll. Interf. Sci. 110 (1986) 544; J. Membr. Sci. 66 (1992) 259; J. Membr. Sci. 182 (2001) 91). However, there is still not enough work done in order to understand, quantify and possibly exploit this phenomenon. In this work permeation and binary diffusion experiments have been performed at ambient temperature in combination with measurements of the adsorption isotherms using porous Vycor glass possessing a mean pore radius of approximately 4 nm. Main focus was set on a comparison of the transport of (a) permanent gases (helium, nitrogen, methane and hydrogen) and (b) condensable gases (butane, propane and freon 112) as a function of the pressure conditions in the membrane. The adsorption isotherms of the condensable gases were measured using a volumetric method. The results indicate the occurrence of capillary condensation at a reduced pressure P/P0 of approximately 0.8 for all three gases. There is a good agreement between the volume of condensate at saturation and the pore volume determined in independent porosimetric studies. Results of a large set of experiments with butane revealed that the permeation is only a function of the mean gas pressure in the membrane. This contradicts the available models suggested in (J. Coll. Interf. Sci. 110 (1986) 544; J. Membr. Sci. 66 (1992) 259) predicting that the transport mechanism in pores changes with different pressure conditions. Finally, in binary isobaric diffusion experiments with pure helium on one side of the membrane and pure butane on the other, a remarkable increase in selectivity of the transport process with increasing pressure in the membrane was observed.

Additional transport by oscillatory buoyancy driven convection in diffusion experiments

A model for the transverse g-jitters induced transport in binary diffusion experiments is presented. The flow is supposed parallel and oscillating at a single frequency supposed high compared to the solute lateral diffusion time scale. This model applies to long aspect ratio experiments. A time-averaged effective diffusivity approach allows us to recover several recently published results and to provide a better understanding of the underlying physics. In the case of a given fully established velocity profile, the variation of the effective diffusion coefficient is such that (D eff -D)/D follows an ω 2 or an ω -7/2 law respectively for low and high frequency compared to the momentum lateral diffusion time scale. The transport by this type of flow is shown to be hardly significant in typical impurity diffusion experiment in microgravity

Mass transfer within the gas-phase of porous media

The laws of various transport modes—viscous flow, diffusion and Knudsen flow—can be caused by the gradients of concentration, total and partial pressure. Their combined transports are derived and proved by selected experiments in the continuum as well as in the Knudsen region. The combination of these transport modes leads to phenomena like pressure diffusion, slip flow and diffusive slip. The three transport coefficients—the permeability, the binary diffusion coefficient and the Knudsen coefficient—can be determined by steady-state permeability and diffusion measurements. Nonsteady-state measurements deliver additional information about the pore structure of the porous medium. The presented measurements were carried out at cylindrical samples of rock salt with low porosity. Hydrogen and nitrogen were used as nonadsorbing gases. The binary diffusion experiments confirm Graham’s law with good accuracy.

Experimental assessment of gas transport mechanisms in natural porous media: Parameter evaluation

An understanding of vapor transport in natural porous media is critical to the assessment of a wide range of environmental problems. In this work a comprehensive experimental program was undertaken to evaluate the relative importance of different gaseous transport mechanisms in natural porous media. The dusty gas model was used as a framework for this evaluation. The experimental program was divided into two parts: the first emphasizes the measurement of porous media transport parameters, and the second explores flux mechanisms in organic vapor transport. Results of the first part are presented in this paper. Single and binary gas experiments were conducted to obtain governing transport parameters (coefficients of permeability, Knudsen diffusion, and diffusibility) in dry porous media. To conduct these experiments, a special experimental apparatus was built that incorporates a diffusion cell that represents an open system where the pressure gradient and absolute pressures can be regulated by controlling the flow rates of the component gases at both ends of the soil sample. Soils tested included three uniform materials, a sea sand, an Ottawa sand, and kaolinite clay, and five graded mixtures of these uniform soils. Results of the single‐gas experiments illustrate the importance of Knudsen diffusion in permeability measurements. Two new transport parameter correlations are developed from the presented data and compared with available literature correlations. The correlation for the Knudsen diffusion radius has a functional dependence upon the square root of intrinsic permeability, selected as a characteristic length of the porous medium. Binary diffusion experiments, using an equimolar pair of gases, are employed to develop a correlation for a composition independent diffusibility.

Prediction of cross-term coefficients in binary diffusion: Diffusion in zeolite

A theoretical framework is derived for predicting the cross-term phenomenological coefficients, L ij , from the main-term coefficients, L ii and L jj , resulting in ▪, where − 1 ⩽ λ ⩽ + 1. For diffusion in zeolite, a theory is given for predicting λ, which requires equilibrium adsorption information of the gas mixture. For Langmuirian gases following ideal adsorbed solution behavior, i.e. with no lateral interactions, λ = + 1 for co-diffusion and λ = −1 for counter-diffusion. Since the Fickian diffusivities ( D tii and D ij ) can be related to the L coefficients (based on certain assumptions), it is possible to use the theory to predict all multicomponent Fickian diffusivities from the single-component Fickian diffusivities. Results are also reported for thirteen series of binary diffusion experiments of CO 2/C 2H 6 in 4A zeolite using the differential adsorption bed technique. Reasonable agreements are obtained between the experimental data and theoretical predictions. For both counter- and co-diffusion, the multicomponent effects are most pronounced for the fast-diffusing component. The multicomponent effects are to enhance both fluxes in co-diffusion and to reduce both fluxes in most cases of counter-diffusion.