Interfacial Transfer Coefficient Research Articles

In Situ Monitoring and Kinetic Analysis of the Extraction of Nitric Acid by Tributyl Phosphate in N-Dodecane Using Raman Spectroscopy

ABSTRACTUnderstanding the fundamental rates of transfer and complex formation is crucial in maintaining optimal efficiency and effectivity in solvent extraction. Methodologies to analyze solvent extraction systems are lacking in that they are commonly performed off-line in subsequent experiments. Thus, a method to proficiently investigate solvent extraction systems in a Lewis cell using in situ Raman spectroscopy paired with chemometric modeling has been developed to allow for on-line analysis and monitoring. Forward and reverse interfacial transfer coefficients for the extraction of nitric acid by tributyl phosphate, a process crucial to used nuclear fuel reprocessing, were measured by spectroscopic monitoring of both phases simultaneously in a two-phase solvent extraction system. Concentration data was derived from the chemometric modeling using Raman spectra. The concentration data was fit to a nonlinear least squares regression model to allow for the calculation of the transfer coefficients in the system. The reverse interfacial transfer coefficient, kr, was determined along with the parameter 95% confidence intervals and 95% prediction intervals. The forward interfacial transfer coefficient, kf, was then back calculated from kr and the aqueous phase and organic phase equilibrium concentrations. The average calculated values of kr and kf were 2.56 (± 0.50) × 10−5 m s−1 and 4.75 (± 1.13) × 10−6 m s−1, respectively. The information obtained regarding solvent extraction parameters and transfer can be applied in the study of systems of higher complexity, involving complex formation and their transfer across a liquid:liquid interface.

Coherent motions and time scales that control heat and mass transfer at wind-swept water surfaces

Forecast of the heat and chemical budgets of lakes, rivers and oceans requires improved predictive understanding of air-water interfacial transfer coefficients. Here we present laboratory observations of the coherent motions that occupy the air-water interface at wind speeds (U10) 1.1 to 8.9 m/s. Spatio-temporal near-surface velocity data and interfacial renewal data are made available by a novel flow tracer method. The relative activity, velocity scales and time scales of the various coherent interfacial motions are measured, namely for Langmuir circulations, streamwise streaks, non-breaking wind waves, parasitic capillary waves, non-turbulent breaking wind waves, and turbulence-generating breaking wind waves. Breaking waves exhibit a sudden jump in streamwise interfacial velocity wherein the velocity jumps up to exceed the wave celerity and destroys nearby parasitic capillary waves. Four distinct hydrodynamic regimes are found to exist between U10 = 0 and 8.9 m/s, each with a unique population balance of the various coherent motions. The velocity scales, time scales and population balance of the different coherent motions are input to a first-principles gas transfer model to explain the waterside transfer coefficient (kw) as well as experimental patterns of temperature and gas concentration. The model mixes concepts from surface renewal and divergence theories, and requires surface divergence strength (β), the Lagrangian residence time inside the upwelling zone (tLu), and the total lifetime of new interface before it is downwelled (tLT). The model's output agrees with time-averaged measurements kw, patterns of temperature in infrared photographs, and spatial patterns of gas concentration and kw from direct numerical simulations. Several non-dimensional parameters, e.g. βtLu and τstLT where τs is the interfacial shear rate, determine the effectiveness of a particular type of coherent motion for affecting kw. This article is protected by copyright. All rights reserved.

A nonparametric approach to estimating terrestrial evaporation: Validation in eddy covariance sites

Terrestrial evaporation is essential to the global hydrological cycle and climate systems. It is a complicated energy and mass transfer process that involves radiation, conduction, diffusion, convection, and surface–atmosphere interactions. The energetic and diffusive controls on evaporation were combined in the contemporary theory (e.g. the Penman–Monteith equation), in which surface–atmosphere interfacial transfer coefficients were adopted and parameterized semi-empirically or empirically to achieve a solution to evaporation. The solution achieved through this parameterization leaves unsolvable uncertainty. Thus, the theory of evaporation remains diagnostic rather than predictive. Here we show that terrestrial evaporation can be predicted without parameterization. Terrestrial evaporation, as a mechanical and thermodynamic process, follows Hamilton's principle in the macro-state. With surface temperature as a generalized coordinate of the Hamiltonian, and incorporating equilibrium evaporation, we present a nonparametric solution in a simple analytical form. We used observational data collected at 26 eddy covariance sites to test the effectiveness and the generality of the solution. Results showed good agreements between the estimated and the observed values, by an absolute difference of 10.3±20.2Wm−2 for latent heat flux (evaporation) and −11.8±21.0Wm−2 for sensible heat flux, for all the tested sites. Further examination demonstrated that the proposed approach achieved the performance compatible to the Penman–Monteith approach. We anticipate our analysis to be a starting point for more sophisticated investigation into the complex nature of terrestrial evaporation. Its simplicity should have potential value in applications, in addition to contributing to fundamental theory.

A general diffusion model for mass transfer in colloidal liquid aphron systems

A general diffusion model for solute transport in colloidal liquid aphron (CLA) systems is proposed in terms of diffusive mass transfer. The model incorporates five specific mass transfer resistances occurred at interfaces and in liquid phases. The experimental cases conducted in CLA systems are simulated successfully to verify the validity of numerical procedure and underlying assumptions. Both numerical results and experimental data show that apparent diffusion coefficient of CLA systems is far smaller than that in pure solvent systems. This can be well explained considering the role of surfactants, which cause the interfacial resistance and micelles (or reverse micelles) hindrance. The interfacial resistances of adsorbed surfactants and formed micelles (or reverse micelles) hindrance are estimated by the simplex method from the experimental data. It is shown that both interfacial transfer coefficient and micellar diffusion coefficient decrease with the increase of surfactants concentration.

Soil moisture and vegetation controls on evapotranspiration in a heterogeneous Mediterranean ecosystem on Sardinia, Italy

Micrometeorological measurements of evapotranspiration (ET) can be difficult to interpret and use for validating model calculations in the presence of land cover heterogeneity. Land surface fluxes, soil moisture (θ), and surface temperatures (Ts) data were collected by an eddy correlation‐based tower located at the Orroli (Sardinia) experimental field (covered by woody vegetation, grass, and bare soil) from April 2003 to July 2004. Two Quickbird high‐resolution images (summer 2003 and spring 2004) were acquired for depicting the contrasting land cover components. A procedure is presented for estimating ET in heterogeneous ecosystems as the residual term of the energy balance using Ts observations, a two‐dimensional footprint model, and the Quickbird images. Two variations on the procedure are successfully implemented: a proposed two‐source random model (2SR), which treats the heat sources of each land cover component separately but computes the bulk heat transfer coefficient as spatially homogeneous, and a common two‐source tile model. For 2SR, new relationships between the interfacial transfer coefficient and the roughness Reynolds number are estimated for the two bare soil–woody vegetation and grass–woody vegetation composite surfaces. The ET versus θ relationships for each land cover component were also estimated, showing that that the woody vegetation has a strong tolerance to long droughts, transpiring at rates close to potential for even the driest conditions. Instead, the grass is much less tolerant to θ deficits, and the switch from grass to bare soil following the rainy season had a significant impact on ET.

Verification of Onsager's reciprocal relations for evaporation and condensation using non-equilibrium molecular dynamics

Non-equilibrium molecular dynamic (NEMD) simulations have been used to study heat and mass transfer across a vapor–liquid interface for a one-component system using a Lennard-Jones spline potential. It was confirmed that the relation between the surface tension and the surface temperature in the non-equilibrium system was the same as in equilibrium (local equilibrium) [A. Røsjorde, D.W. Fossmo, S. Kjelstrup, D. Bedeaux, B. Hafskjold, J. Colloid Interface Sci. 232 (2000) 178]. Interfacial transfer coefficients were evaluated for the surface, which expressed the heat and mass fluxes in temperature and chemical potential differences across the interfacial region (film). In this analysis it was assumed that the Onsager reciprocal relations were valid [A. Røsjorde, S. Kjelstrup, D. Bedeaux, B. Hafskjold, J. Colloid Interface Sci. 240 (2001) 355]. In this paper we extend the number of simulations such that we can calculate all four interface film transfer coefficients along the whole liquid–vapor coexistence curve. We do this analysis both for the case where we use the measurable heat flux on the vapor side and for the case where we use the measurable heat flux on the liquid side. The most important result we found is that the coupling coefficients within the accuracy of the calculation are equal. This is the first verification of the validity of the Onsager relations for transport through a surface using molecular dynamics. The interfacial film transfer coefficients are found to be a function of the surface temperature alone. New expressions are given for the kinetic theory values of these coefficients which only depend on the surface temperature. The NEMD values were found to be in good agreement with these expressions.

A diffuse interface model for the interfacial transfer coefficient

Based on an extension to non-equilibrium problems, of Cahn’s interface layer thermodynamics, we demonstrate that the matrix of transfer coefficients across a coherent interface between two phases, α and β, can be viewed as a correction to the Onsager’s matrix of mobility coefficients along the continuous concentration profile. The latter coefficients are defined along the equilibrium concentration profile in the interfacial layer and in the α- and β-phases. Combining the above definition with that of solute interfacial excess, we can define transfer coefficients relative to two components chosen arbitrarily, the values of which are intrinsic properties of the interfacial layer, independent of its precise location and thickness.

Transfer coefficients for evaporation

An analysis of the recent experimental results by Fang and Ward is given. They found a temperature jump almost upto 10 K across the evaporating surface of water, octane and methylcyclohexane. We use nonequilibrium thermodynamics to obtain the appropriate boundary conditions at the surface. Interfacial transfer coefficients, appearing in these boundary conditions, can then be determined from the experiments. We present them in a form useful for engineering calculations. A comparison is made with the predictions for the transfer coefficients from kinetic theory. For the three materials the kinetic theory values were found to be 30 to 100 times larger than those found from the experiment. It is explained why this gives a liquid surface, which is colder than the adjacent vapor, contrary to the prediction by the kinetic theory. The relative magnitude that we find for the interfacial transfer coefficients, suggests that the condensation coefficient of the kinetic theory decreases with increasing internal degrees of freedom in a molecule. However, a lower value of this coefficient is not sufficient to explain the small value of the transfer coefficients. As a possible explanation for this, we forward the hypothesis that the single-particle collision model used in the kinetic theory for this phenomenon, should be modified to account for multiparticle events.

Modelling diffusion-controlled kinetics in equilibrium and driven alloys

We introduce a very simple model for thermally activated atomic migration on a lattice, and several techniques to handle it. For thermodynamical systems, the model can be used for simulating decomposition paths taking into account relevant metallurgical features. Close to equilibrium, the simplest mean-field approximation of the model can be linearized with respect to the departure from equilibrium; one then gets a microscopic interpretation of classical phenomenological coefficients, such as mobility, interfacial transfer coefficient, rate constants for the coupled relaxation of concentration and order fields. Further away from the equilibrium, the nonlinearities can be taken into account in a consistent way. For driven alloys, i.e. alloys submitted to external forcing, forced atomic migration is added to the model and new features emerge: the model is supported by several experimental results some of which confirmed its predictions a posteriori.

Simulated canopy microclimate using estimated below-canopy soil surface transfer coefficients

Numerical models are often used to simulate the complex energy and mass transfer processes in soil-plant-atmosphere systems. The objective of this study was to develop relationships from measurements of interfacial transfer coefficients at the soil surface beneath a plant canopy to improve a numerical model describing within-canopy energy and mass transfer processes. Equations based on dimensionless variables are presented that predict interfacial heat and water vapor transfer coefficients at the soil surface beneath a maize ( Zea mays L.) canopy throughout a growing season. The derived relationships include the effects of surface roughness, the scale of turbulent eddies, and turbulence intensity. The equation for interfacial heat transfer coefficients was incorporated into the comprehensive soil-plant-atmosphere model Cupid where it was used to estimate heat and mass transfer coefficients at the soil surface. Comparison of model predicted and measured canopy microclimate characteristics showed that the new formulation produced transfer coefficients that were more consistent and more closely correlated to within-canopy wind speed than those obtained by three estimation techniques used in the model previously. The new transfer coefficient relationship generally improved model predictions and has the advantage of being based on more direct experimental evidence than previous relationships.

Modelling Diffusion Controlled Kinetics in Equilibrium and Driven Alloys

We introduce a very simple model for thermally activated atomic migration on a lattice, and several techniques to handle it. For thermodynamical systems, the model can be used for simulating decomposition paths taking into account relevant metallurgical features. Close to equilibrium, the simplest mean-field approximation of the model can be linearized with respect to the departure from equilibrium; one then gets a microscopic interpretation of classical phenomenological coefficients, such as mobility, interfacial transfer coefficient, rate constants for the coupled relaxation of concentration and order fields. Further away from the equilibrium, the nonlinearities can be taken into account in a consistent way. For driven alloys, i.e. alloys submitted to external forcing, forced atomic migration is added to the model and new features emerge: the model is supported by several experimental results some of which confirmed its predictions a posteriori.

Heat and mass transfer between a porous medium and a parallel external flow. Application to drying of capillary porous materials

A numerical method allowing heat and mass transfer between an unsaturated porous medium and an external air flow to be predetermined is presented. Various numerical simulations are carried out in order to study the behaviour of the heat and mass convective transfer coefficients at the interface during drying. The simulations show that leading edge effects give rise to a space non-uniformity of the variables at the interface. It follows that the interfacial transfer coefficients differ from the standard values corresponding to boundary layer flows on the flat plate with uniform temperature or concentration at the wall. Furthermore, it is shown that one-dimensional simulation of the phenomena inevitably leads to incorrect results when the leading edge effects concern a sufficiently large part of the porous body. Lastly, the effect of the occurrence of large-scale heterogeneities of water content at the interface during drying is also studied.

Nonequilibrium thermodynamics of pressure solution

This paper is concerned with the thermodynamic theory of solution and precipitation processes in wet crustal rocks and with the mechanism of steady pressure-solution slip in ‘contact zones,’ such as grain-to-grain contacts, fracture surfaces, and permeable gouge layers, that are infiltrated by a mobile aqueous solution phase. A local dissipation jump condition at the phase boundary is fundamental to identifying the thermodynamic force driving the solution and precipitation process and is used here in setting up linear phenomenological relations to model near-equilibrium phase transformation kinetics. The local thermodynamic equilibrium of a stressed pure solid in contact with its melt or solution phase is governed by Gibbs's relation, which is rederived here, in a manner emphasizing its independence of constitutive assumptions for the solid while neglecting surface tension and diffusion in the solid. Fluid-infiltrated contact zones, such as those formed by rough surfaces, cannot generally be in thermodynamic equilibrium, especially during an ongoing process of pressure-solution slip, and the existing equilibrium formulations are incorrect in overlooking dissipative processes tending to eliminate fluctuations in superficial free energies due to stress concentrations near asperities, defects, or impurities. Steady pressure-solution slip is likely to exhibit a nonlinear dependence of slip rate on shear stress and effective normal stress, due to a dependence of the contact-zone state on the latter. Given that this dependence is negligible within some range, linear relations for pressure-solution slip can be derived for the limiting cases of diffusion-controlled and interface-reaction-controlled rates. A criterion for rate control by one of these mechanisms is set by the magnitude of the dimensionless quantitykδ/2C pD, wherek is the interfacial transfer coefficient, δ is the mean diffusion path length,C p is the solubility at pressurep, andD is the mass diffusivity.

Interfacial transfer kinetics of 22Na + across a synthetic phospholipid—protein membrane

Diffusion equations were solved using the method of Laplace transformation to describe the flux of solutes across a model biological membrane. The theory is applicable to obtain either a permeability coefficient or an interfacial transfer rate constant. Previously published data were analyzed using the mathematical functions derived and the magnitude of the interfacial transfer coefficients discussed. These results may prove relevant to the general understanding of passive membrane transport as encountered in many model systems such as black lipid films and liposomes.

Diffusion of proteins across a liquid-liquid interface

A study of the rate of diffusion of some proteins across a liquid-liquid interfaces has been carried out using a two-phase system obtained by mixing aqueous solutions of the polymers polyethyleneglycol adn dextran. Six proteins with molecular weights in the range of 13 000–290 000 have been studied. Interfacial transfer coefficients and the corresponding values of free energy of activation have been determined. The results indicate that the rate of interfacial diffusion is a function of the partition coefficient as wella as the size of the diffusing molecule.

Diffusion of Salts across a Butanol-Water Interface

Diffusion of the chloride salts of Li, Na, K, Rb, and Cs from water into 1-butanol and from 1-butanol into water was examined at temperatures from 13-40 degrees C. Distribution coefficients, interfacial transfer coefficients, Arrhenius activation energy, free energy of activation, enthalpy, and entropy of activation were determined for the diffusion of these salts across the alcohol-water interface. The results indicate that the entropy decrease made the major contribution to the change in the free energy of activation.

Interfacial resistance in the absorption of oxygen by water

AbstractTransient absorption rates of oxygen into water have been measured by passing a laminar jet through the pure gas for contact times varying from 0.8 to 11.8 msec. The absorption rate is significantly lower than the theoretical value corresponding to no interfacial resistance, if a diffusivity of 2.20 × 10−5sq. cm./sec. at 22.2°C. is used for comparison. The available evidence indicates that this diffusivity is about correct and that the lowered rate may be caused by an interfacial resistance described by an interfacial transfer coefficient equal to 0.6 cm./sec. This resistance is small enough to be neglected in most gas absorbers.

Diffusion through an Interface—Binary System

Diffusion measurements have been made between saturated layers in the system SO2—n-heptane, using S35 tagged SO2 as a radioactive tracer. The results are evaluated in terms of the interfacial transfer coefficient α introduced in a previous paper. The resistance in the interface is significant compared with the resistance to ordinary diffusion, even within 4°C of the critical solution temperature.