Transient separation of multicomponent liquid mixtures in thermogravitational columns

Transient separation of the individual components in a multicomponent liquid mixture in a thermogravitational column can be used to determine the thermal and molecular diffusion coefficients. Two models of the transient behavior are developed. First, a classical model where density only depends on temperature. Second, a general model where the compositional effect on density is also taken into account. Diffusion coefficients can be determined by fitting experimental data to either model. The procedure is demonstrated for a ternary liquid mixture. The results reveal that the classical model is very unreliable even though composition variation only contributes to the total buoyancy by one-third. Diffusion coefficients can be obtained reliably from the general model provided the experimental noise does not exceed +/-1% of steady-state separation. This level of accuracy in composition measurements is achievable.     

On the unsteady-state species separation of a binary liquid mixture in a rectangular thermogravitational column

This paper investigates the unsteady-state species segregation of binary liquid mixtures in rectangular thermogravitational columns. The analysis leads to a procedure to obtain both molecular and thermal diffusion coefficients from transient separation measurements. Two models are presented: first, an ideal model where buoyancy only depends on temperature and second, a general model where buoyancy also varies with composition. Steady-state measurements are not required regardless of which model is chosen. As a result, the new procedure is faster than steady-state procedures. When either the molecular or thermal diffusion coefficient is known a priori, the other can be obtained without knowledge of fluid properties such as density, viscosity, thermal expansion, and compositional coefficients.     

Testing the accuracy of correlations for multicomponent mass transport of adsorbed gases in metal-organic frameworks: diffusion of H2/CH4 mixtures in CuBTC

Mass transport of chemical mixtures in nanoporous materials is important in applications such as membrane separations, but measuring diffusion of mixtures experimentally is challenging. Methods that can predict multicomponent diffusion coefficients from single-component data can be extremely useful if these methods are known to be accurate. We present the first test of a method of this kind for molecules adsorbed in a metal-organic framework (MOF). Specifically, we examine the method proposed by Skoulidas, Sholl, and Krishna (SSK) ( Langmuir, 2003, 19, 7977) by comparing predictions made with this method to molecular simulations of mixture transport of H 2/CH 4 mixtures in CuBTC. These calculations provide the first direct information on mixture transport of any species in a MOF. The predictions of the SSK approach are in good agreement with our direct simulations of binary diffusion, suggesting that this approach may be a powerful one for examining multicomponent diffusion in MOFs. We also use our molecular simulation data to test the ideal adsorbed solution theory method for predicting binary adsorption isotherms and a method for predicting mixture self-diffusion coefficients.     

Column Dynamics of Ternary Ion Exchange Part I: Diffusional and Mass Transfer Relations

The complete multicomponent ion-exchange diffusion equations based on irreversible thermodynamics and their approximations by the Nernst-Planck model or the Fick's law model are all put in the same algebraic form. Their differences occur only in the definition of the diffusion coefficients. Multicomponent diffusion coefficients. Multicomponent diffusion coefficients are related to those in binary systems by either the Nernst-Planck or Fick's law model. Using a linear driving force approximation for the flux equations, similar relationships are developed for estimating multicomponent (ternary) mass transfer coefficients based on the analysis of binary data. Hence from binary data and these relationships, multicomponent effluent concentration histories may be predicted numerically.     

On measurement of molecular and thermal diffusion coefficients in multicomponent mixtures

We have developed the theory for using the deflection of laser beams of various wavelengths to determine molecular and thermal diffusion coefficients in multicomponent mixtures. In the past, simultaneous determination of molecular and thermal diffusion coefficients have only been achieved for binaries. Our procedure is faster and more accurate than the current techniques to determine molecular diffusion coefficients. The analysis for an N-component mixture requires deflections from (N - 1) beams of different wavelengths. We show in an example that the molecular and thermal diffusion coefficients can be determined reliably in a ternary mixture.     

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.     

The transport of adsorbate mixtures in porous materials: Basic equations for pores with simple geometry

The basic equations governing the transport of single and binary adsorbate mixtures through single pores are considered. An irreversible thermodynamic formulation is adopted and both viscous and diffusive terms are incorporated following the earlier work of Mason and co-workers. The links between phenomenological coefficients and molecular properties are demonstrated. For single components, the gas phase and high density limits are considered. By using simple hydrodynamic models it is shown that the phenomenological coefficients in the mixture equations can all be expressed as functions of the coefficients for the individual components in the same pore, and the properties of the component adsorption isotherms. Whilst it is appreciated that the hydrodynamic approach will be of limited value in very small pores, it is argued that useful insights can be gained into the feasibility of membrane separation processes from this method. The general equations can be used in future development of network models for porous materials.     

Measurement of diffusion coefficients in multicomponent gas mixtures by the reversed-flow technique

Summary The reversed-flow method for measurement of gas diffusion coefficients in binary mixtures is now extended to simultaneous determination of effective diffusion coefficients for each substance in a multicomponent gas mixture. The method is applied to six ternary mixtures, each consisting of two gaseous hydrocarbons and H₂, He or N₂. The results are in agreement with a limiting case of the Stefan-Maxwell equations.     

The Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.     

New thermal diffusion coefficient measurements for hydrocarbon binary mixtures: viscosity and composition dependency

New thermal diffusion coefficients of binary mixtures are measured for n-decane-n-alkanes and 1-methylnaphthalene-n-alkanes with 25 and 75 wt % at 25 degrees C and 1 atm using the thermogravitational column technique. The alkanes range from n-pentane to n-eicosane. The new results confirm the recently observed nonmonotonic behavior of thermal diffusion coefficients with molecular weight for binary mixtures of n-decane- n-alkanes at the compositions studied. In this work, the mobility and disparity effects on thermal diffusion coefficients are quantified for binary mixtures. We also show for the binary mixtures studied that the thermal diffusion coefficients and mixture viscosity, both nonequilibrium properties, are closely related.     

The “fast” and “slow” mode theories of interdiffusion in polymer mixtures: Resolution of a controversy

The theory of interdiffusion of a pair of components in multicomponent polymer mixtures is reviewed from a statistical point of view, and the foundation of the “fast” and “slow” mode theories, as well as the more recent “ANK” theory of interdiffusion is critically examined. The ANK theory reproduces the results of the slow and fast mode theories as the two limits when the vacancy concentration is varied from zero to a large value, and shows that the interdiffusion coefficient in a binary compressible mixture at finite vacancy concentrations can not in general be expressed only in terms of the tracer diffusion coefficients of the components, but it involves in addition the cooperative diffusion coefficient which characterizes the relaxation of total density fluctuations. The predictions of the ANK expression for the molecular dependence of the kinetic factor is compared with recent scattering experiments.     

ITQ-3分子筛中二元混合分子扩散性质的模拟

采用平衡分子动力学方法先是模拟研究了纯组分Ar、SF_6以及CF4在ITQ-3分子筛中的扩散行为,结果表明,在窄孔道中Ar的扩散系数随负载的增加呈现先增加再减小的变化趋势,在宽孔道中则随负载逐渐减小。纯组分的大分子SF_6以及CF4只在y方向扩散,扩散系数与小分子在z方向的变化规律一致。随后,又模拟了二元混合组分SF_6和CF4在ITQ-3分子筛中的扩散行为,模拟结果与各自纯组分SF_6和CF4进行了对比,发现二元混合的SF_6和CF4整体变化趋势与其单组分保持一致,在y方向的扩散系数都是随着负载的增加而先增大后减小,但是两者之间还存在一种相互作用,使得在整个负载范围内扩散较快的CF4的扩散系数比纯组分的扩散系数相对小一些,而纯组分时扩散相对缓慢的SF_6在二元混合中的扩散系数则相对增大。     

Low‐bandwidth space/frequency component separation for quantitative imaging

Quantitative MRI is often used to analyse multicomponent systems. The analysis requires the contributions from different species to be isolated. Species with distinct chemical shifts can be separated by using a low acquisition bandwidth, which is easy to achieve in common quantitative imaging protocols. The bandwidth reduction leads to separation of NMR contributions from different species in the image space. This new method was implemented and tested on two multicomponent systems containing several spectrally and spatially unresolved components with both distinctly different and similar diffusion coefficients and relaxation times. Separation was achieved with routine MRI diffusion and relaxation measurement pulse sequences in a microimaging environment for water/polyethylene glycol solution and for chloroform/TMS/polyethylene glycol solution. Conventional monoexponential fitting was used to determine diffusion coefficients and relaxation times from the spectrally separated data, whereas biexponential or triexponential fitting was required in the unseparated reference experiments. In the two‐component sample, the variation in the determined fast diffusing components was on the same order of magnitude for all experiments, while the variation in the slow diffusing polyethylene glycol was larger when no separation was present. The separation technique provided lower variability for all the determined diffusion coefficients and relaxation times in the three‐component sample. The low‐bandwidth separation method can provide separation of multicomponent systems based on the chemical shift difference between the species. The accuracy of the technique is comparable with the commonly used methods for bicomponent system analysis and surpasses those when there are more than two components in the sample. Copyright © 2016 John Wiley & Sons, Ltd.     

Using perdeuterated surfactant micelles to resolve mixture components in diffusion‐ordered NMR spectroscopy

Diffusion‐ordered NMR spectroscopy resolves mixture components on the basis of differences in their respective diffusion coefficients or molecular sizes. However, when components have near‐identical diffusion coefficients, they are not resolved in the diffusion dimension of a diffusion‐ordered spectroscopy (DOSY) spectrum. Adding surfactant micelles to these mixtures has been shown to enhance resolution when the component molecules interact differentially with the micelles. This approach is similar to that used in electrokinetic chromatography (EKC) where modifiers like micelles or polymers are used to enhance the separation of mixture components. In this study, perdeuterated surfactants are added to analyte mixtures studied with the DOSY technique. Since no micelle resonances appear in the mixture spectra, the difficulty associated with performing biexponential analyses in spectral regions where analyte and surfactant resonances overlap is avoided. The approach is demonstrated using mixtures of peptides with near‐identical diffusion coefficients. Copyright © 2008 John Wiley & Sons, Ltd.     

On the separation factor of binary gaseous mixtures in two-layer nanoporous membranes

The separation factor is calculated for a binary gaseous mixture in two-layer membranes composed of nano- and microporous layers. The transfer in nanosized pores is described with regard to the diffusion in an adsorption layer. The mutual influence of components when they pass through the fine-pore layer is taken into account. The dependence of the diffusion coefficients in the adsorption layer on the degree of surface coverage is taken into account. It is shown that the mutual influence of the components on the transfer in the adsorption layer substantially affects the separation factor and its dependence on process parameters. The problem concerning the asymmetry of the separation factor at different membrane orientations with respect to the flow is discussed.     

Large distinct diffusivity in binary mixtures confined to zeolite Nay

Mutual diffusion coefficients have been computed from molecular dynamics simulation of two different binary mixtures confined to zeolite NaY. In one of these mixtures, where one component is from the linear regime and the other from the anomalous regime of the levitation effect [S. Yashonath, P. Santikary, J. Phys. Chem., 1994, 98, 6368], the magnitude of distinct diffusivity, Dd, is unusually large and comparable to the mixture self-diffusivity Ds. Distinct van Hove correlations suggest that the large Dd seems to arise from the presence of distinct physisorption sites for the two components. The contribution from Dd might be important for achieving good separation of mixtures, for which zeolites are used extensively.     

Equations for the evolution of a growing or evaporating free microdroplet under nonstationary conditions of diffusion and heat transfer in a multicomponent vapor–gas medium

A set of equations has been derived for the nonstationary composition, size, and temperature of a growing or evaporating multicomponent microdroplet of a nonideal solution under arbitrary initial conditions. Equations for local nonstationary diffusion molecular and heat fluxes in a mixture of a multicomponent vapor with a noncondensable carrier gas have been obtained within the framework of nonequilibrium thermodynamics with allowance for hydrodynamic flow of the medium. The derived closed set of equations takes into account the nonstationarity of the diffusion and heat transfer, effect of thermodiffusion and other cross effects in the multicomponent vapor–gas medium, the Stefan flow, and droplet boundary motion, as well as the nonideality of the solution in the droplet. The general approach has been illustrated by the consideration of the multicomponent medium at low concentrations of vapors taking into account its thermal expansion due to the Stefan flow in the case of a nonstationary diffusion regime of the nonisothermal condensation growth of a one-component droplet.     

The effect of corrugation of pore wall on the thermal diffusion in nanopores by molecular dynamics simulations

In this work we have studied the effect of corrugation on the thermal diffusion (soret effect) in isotopic and non-isotopic fluid mixtures confined in a slit pore. We used a boundary driven non-equilibrium molecular dynamics to simulate thermal diffusion in Lennard–Jones (LJ) binary mixtures confined in structureless Steele 10-4-3 and atomistic Lennard–Jones pore walls. The results showed that for the isotopic mixture thermal diffusion factor for both wall types agrees and the corrugation of the LJ wall has no effect in isotopic mixture. However, for non-isotopic mixture confined in atomistic LJ pore the component with stronger attraction adsorbs more to the wall than the structureless Steele wall. The effect of corrugation of pore wall on the thermal diffusion is noticeable in narrow slit pore and mixture with large difference in molecular attraction parameter of components.     

Separation of mixtures at nano length scales: blow torch and levitation effect

A new conceptual basis for the separation of multicomponent molecular mixtures is proposed. A separation method where different components of the mixtures are driven in opposite directions is realized by a judicious combination of two effects, viz., levitation and blow torch effects. Monte Carlo simulations of two Lennard-Jones binary mixtures with different-sized components are shown to be separated well if at least one of the components lies in the anomalous regime and the others lie in the linear regime. A separation factor of 10(8) is obtained on nano length scales as compared to 10(3), obtainable through conventional methods of separation on macrolength scales.