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Abstract: Darcy-scale models of flow and transport in porous media often fail to describe experimentally observed phenomena, while their pore-scale counterparts are accurate but can be computationally prohibitive. Most numerical multiscale models, which seek to combine these two descriptions, require empirical closures and/or assumptions about the behavior of pore-scale quantities at the continuum (Darcy) scale. We present a general formulation of an iterative hybrid numerical method that links the pore and continuum scales without resorting to such approximations. The algorithm treats the fluxes exchanged at the internal boundaries between pore- and continuum-scale domains as unknown, and allows for iteratively determined boundary conditions to be applied at the pore-scale in order to guarantee flux continuity. While the algorithm proposed is general, we use it to model transport in a fracture with chemically reactive walls. Results demonstrate significant improvement upon standard continuum-scale formulations. [Copyright &y& Elsevier]

Abstract: The transport of a reactive solute by diffusion and convection in a thin (or long) curved pipe is considered. Using asymptotic analysis with respect to the pipe’s thickness, the effective model for solute concentration is formally derived. A simple approximation is computed, showing explicitly the effects of the pipe’s geometry in nature and magnitude. [Copyright &y& Elsevier]

Abstract: Binary mutual diffusion coefficients (interdiffusion coefficients) of calcium gluconate (C12H22CaO14) in water at 298.15K and at concentrations between 0.001 and 0.0500moldm−3 have been measured, using a Taylor dispersion method. These data are discussed on the basis of the Onsager-Fuoss model. Based on these data, the equivalent conductance at infinitesimal concentration of the gluconate ion in the studied solutions has been estimated. Through the same technique, ternary mutual diffusion coefficients (D 11, D 22, D 12 and D 21) for aqueous solutions containing calcium gluconate and lactose, at T =298.15K, and at different carrier concentrations, were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of calcium gluconate in different media. [ABSTRACT FROM AUTHOR]

Abstract: An asymptotic analysis is presented for the mass transport of a solute due to volume-cycled oscillatory flow in a prestressed and viscoelastic tube with a reactive wall layer (wall retention and absorption). Based on the homogenization technique, the convection–diffusion transport equation is derived for the developed time-mean concentration, containing the effective transport coefficients of advection and dispersion as functions of oscillation frequency, initial stresses, viscoelasticity of the wall, and the two wall reactions. The present model as applied to gas transport in pulmonary airways under high-frequency ventilation is examined in detail, through comparison with a model in the literature. The dispersion coefficient is independent of the wall properties if the tube is tethered. The gas transport rate is found to be enhanced monotonically when either the reversible phase partitioning or its exchange rate increases. [Copyright &y& Elsevier]

Abstract: Binary mutual diffusion coefficients (interdiffusion coefficients) of nickel chloride in water at T =298.15K and T =310.15K, and at concentrations between (0.000 and 0.100)mol·dm−3, using a Taylor dispersion method have been measured. These data are discussed on the basis of the Onsager–Fuoss and Pikal models. The equivalent conductance at infinitesimal concentration of the nickel ion in these solutions at T =310.15K has been estimated using these results. Through the same technique, ternary mutual diffusion coefficients (D 11, D 22, D 12, and D 21) for aqueous solutions containing NiCl2 and lactose, at T =298.15K and T =310.15K, and at different carrier concentrations were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of NiCl2 in different media. [ABSTRACT FROM AUTHOR]

Abstract: The solute transport in a core-annular geometry is studied. A Newtonian or non-Newtonian (i.e., power-law) liquid flows through the core, while the solute can exchange between the liquid and the surrounding tissue. The permeability of the phase interface depends on the nature of the solute, i.e., relatively low for lipids and macromolecules but high for ions and gases. We analyse the moment’s equations of the residence time distribution (RTD). The solution of the equation for the second moment provides the exact formula for the Taylor dispersion coefficient. Unlike previous studies using a perturbation procedure where coefficient of axial dispersion cannot be defined at low permeability, the current study gives Taylor coefficient of dispersion for any value of the permeability. It is found that the coefficient in shear-thinning fluid is lower than in the Newtonian one, although the relative importance of non-Newtonian effects decreases when other factors, e.g. inter-phase transport and solubility, become dominant. The equations for the higher moments are analysed and the general structure of the solution is obtained in the form of integrals, which can be easily evaluated numerically. When the analysis is applied to solute transport between capillaries and surrounding tissues, it is shown that the classic Taylor expression does not describe dispersion of solute, e.g. glucose and albumin, in the capillary, except in situations where the Péclet number is very low. For the range of parameters typical for microvascular circulation in tissues, the higher moments play an important role and need to be considered. [ABSTRACT FROM AUTHOR]

As an extension of the modelling on environmental dispersion in a single zone wetland [Zeng, L., Chen, G.Q., 2009. Ecological degradation and hydraulic dispersion of contaminant in wetland. Ecol. Model., 222, 293–300], the typical case of a pulsed contaminant emission into a steady flow through a distinctively vegetated two-zone shallow wetland channel is analytically explored in this paper in terms of the longitudinal evolution of the lateral mean concentration under environmental dispersion. The velocity profile of a fully developed flow through the wetland is derived, with that for a single zone wetland flow included as a special case. Taylor’s classical analysis and Aris’s method of concentration moments for solute dispersion in a single phase fluid flow are rigorously generalized for the two-zone case of a wetland flow to develop the dispersion model and to determine the dispersivity, which is illustrated with an asymptotic time variation characterized by stem dominated, transitional, and width-stem dominated stages. For typical contaminant constituents of chemical oxygen demand, biochemical oxygen demand, total phosphorus, total nitrogen and heavy metal, the evolution of contaminant cloud is illustrated with the critical length and duration of the contaminant cloud with constituent concentration beyond some given environmental standard level. [Copyright &y& Elsevier]

How hydrodynamic dispersion is affected by wall slip remains to be fully understood. An attempt is made in this article looking into this issue for dispersion in some elementary pressure-driven flows. Both the long-time Taylor-Aris dispersion and the early-phase convection-dominated dispersion are investigated, analytically and numerically, respectively. The mean and the variance of the residence time distribution are also examined. In the basic case where the walls of a parallel-plate channel have equal slip lengths, the slip is in general to reduce the spread of a solute cloud in a finite channel by either increasing the convection speed or decreasing the dispersivity. However, the decreasing effect of slip on dispersion can be diminished or even reversed by unequal slip lengths and/or phase exchange with the wall. The convection-dominated regime is investigated, following a recently proposed transport-based method, to determine how the mean residence time and variance of elution profiles may change with axial positions depending on the slip. [ABSTRACT FROM AUTHOR]

Abstract: Infinite dilution binary diffusion coefficients, D 12, of ferrocene, 1,1′-dimethylferrocene and ethylferrocene in hexane, cyclohexane and ethanol at 313.2K and pressures from 0.2 to 19MPa, in acetonitrile at 298.2–333.2K and 0.2MPa, and various metallic acetylacetonate, acac, complexes such as Co(acac)3, Ru(acac)3, Rh(acac)3, Pd(acac)2 and Pt(acac)2 mainly in ethanol at 313.2K and 0.2MPa were measured by the Taylor dispersion method. The D 12 values in m2 s−1 for the three ferrocenes in the present study and those of ferrocene and 1,1′-dimethylferrocene in supercritical carbon dioxide in our previous studies were represented by the modified hydrodynamic equation over a wide range of viscosity: M 0.5 D 12/T =1.435×10−13 η −0.8446 with average absolute relative deviation of 2.40% for 316 data points, where M is the solute molecular weight, T is the temperature in K, η is the solvent viscosity in Pas. Although the D 12 values for the acac complexes were roughly represented by the above hydrodynamic equation, the accuracies were lower because they were dependent on not solute molecular weight but the number of acac ligand in the complex molecules. [ABSTRACT FROM AUTHOR]

Abstract: Taylor dispersion is used in this study to measure ternary mutual diffusion coefficients (D ik ) for aqueous solutions of Triton X-100+Brij 35 mixed nonionic surfactants. The dispersion profiles appeared to be measured precisely, but they could not be analyzed by using established techniques. Least-squares procedures, for example, failed to converge. These difficulties appeared to be caused by nearly identical eigenvalues of the D ik matrix and the resulting numerical ill conditioning of the fitting equations. Yet Brij 35 diffuses significantly more slowly than Triton X-100, as indicated by the broader profiles generated by Brij 35 concentration gradients. The puzzling diffusion behavior is investigated by using theory to estimate D ik coefficients for solutions of mixed nonionic surfactants. At compositions well above the critical micelle concentration, where the diffusion of free surfactant monomers is negligible, the predicted eigenvalues approach the mixed-micelle diffusion coefficient and become identical within the precision of the Taylor measurements (about ±2%). Techniques for measuring multicomponent mutual diffusion have relied on the assumption of distinct eigenvalues of the D ik matrix. Prompted by the evidence that common surfactants provide exceptions to this longstanding rule, equations derived for equal-eigenvalue dispersion profiles are used to evaluate D ik coefficients for aqueous Triton X-100+Brij 35 solutions. Results are also reported for aqueous tetradecylsulfobetaine+hexadecylsulfobetaine solutions. The physical significance of mutual diffusion with equal eigenvalues is discussed in terms of the loss of a degree of freedom when associating solute components A and B diffuse together A n B m complexes. [ABSTRACT FROM AUTHOR]

The article discusses a study on how dispersion can be suppressed through a properly designed mixer element and how the effect on the resulting chemical reactions occurring in the flow can be controlled. It presents the Taylor dispersion or residence time distribution (RTD) phenomena where a viscous liquid spends more time in a microfluidic device and describes the effect of the dispersion on the outcome of chemical reactions. It suggests that a pressure driven micromixer design with characteristics similar to the ideal plug-flow reactor can be achieved.

Abstract: Ternary mutual diffusion coefficients measured by Taylor dispersion method (D 11, D 22, D 12, and D 21) are reported for aqueous solutions containing isoniazid and different electrolytes (NaCl, NaOH, or HCl) at T =298.15K at different carrier concentrations. These diffusion coefficients have been measured having in mind a better understanding of the structure of these systems and the thermodynamic behaviour of isoniazid in different media. For example, it is possible to make conclusions about the influence of these electrolytes in diffusion of isoniazid, and to obtain information concerning the number of moles of each component transported per mole of the other component driven by its own concentration gradient. [Copyright &y& Elsevier]

Abstract: The supercritical fluid (SCF) chromatographic technique based on the Taylor dispersion theory has been widely applied in determination of diffusion coefficients of various organic compounds in SCFs. This study was aimed to understand impacts of mobile phase mean velocity (MPMV) and column orientation on diffusion coefficient measurements. The benzene/SCCO2 system was investigated. Experiments were carried out at 40 and 60°C and 9–15MPa over a wide range of CO2 densities at varying MPMV and repeated in two column orientations, vertical and horizontal. It was found that both MPMV and column orientation significantly affected measurements of diffusion coefficients in SCFs. When the column was installed vertically, apparent diffusion coefficients obtained at relatively low CO2 density (<580kg/m3) increased with increasing MPMV over the entire velocity ranges. This results in a conclusion that diffusion coefficients cannot be accurately determined under these conditions using a vertically installed column. Under all other conditions, as MPMV increased, apparent diffusion coefficients initially increased, then remained constant, and finally increased again. The initial increase of apparent diffusion coefficients was associated with significant decline of curve-fitting errors, which indicates that the buoyancy effects are non-negligible and will cause larger errors. Accordingly, a new generalized D 12–U diagram comprised of three regions is proposed. Column orientation affected diffusion coefficient measurements mainly by enhancing or weakening the buoyancy effects. When the column was installed vertically, the buoyancy effects were enhanced, leading to lower apparent diffusion coefficients, especially when CO2 density was relatively low. In addition, it was found that when CO2 density was below ∼580kg/m3, diffusion coefficients obtained when the column was horizontally installed were higher than those obtained when the same column was vertically installed. When CO2 density was above that value, opposite outcomes resulted. Finally, the horizontal orientation of a diffusion column is recommended for diffusion coefficient measurements by the SCF chromatographic technique, especially when densities of SCFs are relatively low. [Copyright &y& Elsevier]

Abstract: The dispersion issue of a solute in a pulsating flow through a tube is the topic of different studies both in chemical engineering and biomechanics. In hydrogeology and for aquifer gas storages, oscillations of water in piezometers and control-wells can exhibit amplitude of several tens of meters within annual cycles. Owing to water–air interface in wells, the effective dispersion coefficients defined by Taylor (1953, 1954), Aris (1956, 1960), and later Watson (1983) are not suitable. To address this issue, the phenomena are numerically modeled. Results allow to adapt the expression of the Taylor''s effective dispersion coefficient by introducing an effective velocity. In a second step, the coupling between the well model and an aquifer model, provides the downhole solute propagation. For a 450m deep well with interface oscillations of 80m, it is shown that 35years are needed to reach a solute concentration at the strainers equal to 10− 3 times the concentration at the interface, which is constant. The goal of this study was to investigate a non-expensive and easy to implement technique in order to introduce a tracer from a control-well using the energy related to the air/water oscillating interface. The introduction of such tracer in the storage aquifer is useful to understand the dispersion phenomena at the edge of the gas saturated area. [Copyright &y& Elsevier]

Abstract: Binary mutual diffusion coefficient data for aqueous solutions of propylene and dipropylene glycols were measured using the Taylor dispersion technique for each aqueous binary system at different concentrations (x 1 =0.2–0.80) and temperatures (303.2–323.2K). The measured data were fit to different empirical and semi-theoretical models and compared with the values predicted from such models. The measured mutual diffusion coefficient data are well represented by either rough hard-sphere or UNIDIF model. On the side, the infinite dilution diffusion coefficient has been found greater at lower glycol molecular weight, an observation that corroborates with the property''s dependence on free volume. [Copyright &y& Elsevier]

Abstract: The present study is concerned with broadening of neutral solute band in electrically driven flow through a straight channel with longitudinally varying zeta potential. The present analysis takes into account effects that are important for submicron channels, namely, variation of the excess conductivity in the diffuse part of the electric Double Layer and the non-uniformity of the velocity profile within the Double Layer. Initially, the combined, electroosmotic and pressure driven flow through a straight channel is addressed for the case of longitudinal variation of zeta potential. Using the obtained distribution of the hydrodynamic velocity, the plate height for a non-electrolyte neutral solute is interrelated with the longitudinal distribution of the electrokinetic potential. Several examples of cross-section geometry and electrolyte composition are discussed. [Copyright &y& Elsevier]

Abstract: Facilitating a new concept of clean diesel combustion using supercritical fluids requires a better understanding of thermophysical properties of the diesel fuel/diluent system. Mass diffusivity is one such property that is important to understand diesel fuel/diluent mixing and spray and combustion of supercritical fuel mixtures. In this work, diffusion coefficients of diesel fuel and surrogate compounds in supercritical carbon dioxide were experimentally determined by the Taylor dispersion method at temperatures from 313.15 to 373.15K and pressures up to 30MPa. Difficulties were encountered to measure diffusion coefficients using the Taylor dispersion method near the critical region of CO2 which resulted in curve-fitting errors greater than 5%. Predictive correlations including Wilke–Chang, Scheibel, and He–Yu were examined. Diffusivity data were also fitted by D 12/T − η and correlations. Results showed that the He–Yu correlation has the best prediction performance while the D 12/T − η correlation best fits the data with AAD%<8%. [Copyright &y& Elsevier]

Abstract: Ternary mutual diffusion coefficients measured by Taylor dispersion method (D 11, D 22, D 12, and D 21) are reported for aqueous solutions of 2-hydroxypropyl-β-cyclodextrin (HP-β-CD)+caffeine at T =298.15K at carrier concentrations from (0.000 to 0.010)mol·dm−3, for each solute, respectively. These diffusion coefficients have been measured having in mind a better understanding of the structure of these systems and thermodynamic behaviour of caffeine and 2-hydroxypropyl-β-cyclodextrin in solution. For example, from these data it will be possible to estimate some parameters, such as the fraction of associated species HP-β-CD (X 1) and caffeine (X 2) in this complex, the monomer and dimer fractions, and , respectively, and the limiting diffusion coefficients of the HP-β-CD, , of the dimers caffeine entities, , and of those complexes (1:1), . [Copyright &y& Elsevier]

Abstract: Residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. Through mathematical modeling the relationship between the operating parameters of the heat pump and the piping length of the geothermal system, which is directly correlated to the cost of the system is investigated. The effect of Taylor dispersion of heat in the fluid which is not yet addressed in the literature with respect to geothermal systems is included. A model of a simple configuration of a single pipe surrounded concentrically by grout and then by soil is considered, where the soil region has a constant ambient temperature. The conduction between the two regions is modeled with a classical thermal resistance. Taylor dispersion effects are significant at higher Peclet numbers associated with this system, and Taylor dispersion in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. We consider both steady state and transient (cyclic operation) analyses and find that the axial dispersion increases linearly in the cycle rate for large flow rates. We find that the estimated tubing length for complete energy transport is increased when Taylor dispersion is included, but that this effect can be mitigated with an appropriate choice of the borehole radius. [Copyright &y& Elsevier]

A physical theory explaining the anisotropic dispersion of water and solutes in biological tissues is introduced based on the phenomena of Taylor dispersion, in which highly diffusive solutes cycle between flowing and stagnant regions in the tissue, enhancing dispersion in the direction of microvascular flow. An effective diffusion equation is derived, for which the coefficient of dispersion in the axial direction (direction of capillary orientation) depends on the molecular diffusion coefficient, tissue perfusion, and vessel density. This analysis provides a homogenization that represents three-dimensional transport in capillary beds as an effectively one-dimensional phenomenon. The derived dispersion equation may be used to simulate the transport of solutes in tissues, such as in pharmacokinetic modeling. In addition, the analysis provides a physically based hypothesis for explaining dispersion anisotropy observed in diffusion-weighted imaging (DWI) and diffusion-tensor magnetic resonance imaging (DTMRI) and suggests the means of obtaining quantitative functional information on capillary vessel density from measurements of dispersion coefficients. It is shown that a failure to account for flow-mediated dispersion in vascular tissues may lead to misinterpretations of imaging data and significant overestimates of directional bias in molecular diffusivity in biological tissues. Measurement of the ratio of axial to transverse diffusivity may be combined with an independent measurement of perfusion to provide an estimate of capillary vessel density in the tissue. [ABSTRACT FROM AUTHOR]

Abstract: In this study we show how methods from the theory of stochastic processes can be applied to problems in dispersion theory. First, we show that Taylor dispersion with adsorbing boundaries is easily transformed into a new Taylor dispersion problem without adsorbing boundaries. The transformed problem can then be solved using any of the traditional methods used for Taylor dispersion. Secondly, we consider the dispersion of particles in a channel (between parallel plates) with one partially adsorbing surface and one perfectly reflecting boundary. We determine the exact law of the position of adsorption for an arbitrary channel flow in terms of an infinite series of iterated integrals of the flow field, which is assumed to be a function of the cross-channel coordinate only. We also consider the case of shear flow over an adsorbing plane, by taking the limit where one of the boundaries is taken to infinity [Copyright &y& Elsevier]

We consider the axial dispersion of a liquid flowing through a micro-channel, which has a slender shallow cross-section. A lubrication approximation allows for an analytical analysis of the effect of cross-section and aspect ratio on the dispersion process. Numerical simulations are performed in order to verify the approximate solution. [ABSTRACT FROM AUTHOR]

Many biomolecular assays involve the capture of an analyte by ligands that are attached or immobilized upon a solid surface. Often the binding kinetics of the ligand and analyte are fast enough that the capture step is limited by diffusion or mass transfer of the analyte from the bulk fluid phase onto the surface. In this contribution, after a brief survey of various mathematical models for mass transfer–limited analyte capture, we analyze one model problem. The model involves the capture of analytes by suspended solid spherical beads on whose surface many ligands are attached. The rate of association of the ligand and analyte molecules is taken to be high enough that the overall rate of the capture process is limited by diffusion. Two distinct limits are examined analytically. In early times, when the analytes near a bead are being captured and the depletion layers in the neighborhood of the individual beads are nonoverlapping, the problem is modeled as a diffusion/surface reaction problem about a single bead, and analytical results are obtained that describe the amount of analyte captured as a function of time. At later times, when the depletion layers from neighboring beads begin to overlap, the problem is modeled by means of generalized Taylor dispersion or macrotransport theory. In each case, scaling laws are derived that characterize the capture efficiency as a function of number density, volume fraction, and radius of beads. [ABSTRACT FROM AUTHOR]

The wave-induced Stokes drift plays a significant role on mass/tracer transport in the ocean and the evolution of coastal morphology. The tracer advection diffusion equation needs to be modified for Eulerian ocean models to properly account for the surface wave effects. The Eulerian description of Stokes drift effect on the tracer transport is derived in this study to show that this effect can be accounted for automatically in the wave-averaged advection-diffusion equation. The advection term in this equation is the wave-averaged concentration flux produced by the interaction between fluctuations of linear wave orbital velocity and tracer concentration, and the advection velocity is the same as the Stokes drift velocity. Thus, the effective dispersion of tracers by surface gravity waves is calculated due to the Stokes drift effect and the corresponding dispersion coefficient in the depth-integrated equation is then derived. The Eulerian description of Stokes drift effect of tracer concentration is illustrated by the direct numerical simulation of the advection–diffusion equation under simple linear waves. The equivalence between both the Eulerian and Lagrangian descriptions is also verified by particle tracking method. The theoretical analysis is found to agree well with the wave-induced dye drift velocity observed outside the surf zone in a longshore current experiment. [ABSTRACT FROM AUTHOR]

Mass transfer in tissues is typically studied by multiple indicator dilution (MID) studies. Several of these studies have shown that drug concentrations can be modelled by axially distributed models. In this paper, we determine the Taylor dispersion coefficient that describes the degree of axial mixing for the MID models, while accounting for the presence of red blood cells in the capillaries. The capillaries are treated as well mixed with no radial concentration gradients. The concentration in tissue is treated as position and time dependent and the partial differential equations for mass transport are averaged using the method of multiple timescales. The calculated values of the dispersion coefficient are in reasonable agreement with the values reported in literature, suggesting that Taylor dispersion is an important contributor to dispersion in tissues. We also show that the average equations for the barrier-limited drugs reduce to the commonly used Sangren–Sheppard model. In this case, Taylor dispersion is not significant in comparison to the dispersion caused by drug exchange between the capillary and the tissue. Additionally, we utilize the average equations for both flow-limited and barrier-limited drugs in pharmacokinetic models. These simulations show that neglecting the dispersion coefficient could cause significant effects in the dynamic drug concentration profiles and thus lead to incorrect estimation of parameters if the experimental data from MID studies are fitted to a model that neglects Taylor dispersion. [ABSTRACT FROM PUBLISHER]

Abstract: In this work, we presented new experimental data of diffusion coefficients of four [Bmim (1-butyl-3-methylimidazolium)]-based ionic liquids in water at infinite dilution for temperatures ranging from 303.2 to 323.2K using Taylor dispersion technique. The investigated ILs were [Bmim][BF4 (tetrafluoroborate)], [Bmim][MeSO4 (methylsulfate)], [Bmim][PF6 (hexafluorophosphate)], and [Bmim][CF3SO3 (trifluoromethanesulfonate)]. The molar conductivities of these ionic liquids were also measured and the infinite dilution conductances were determined. The present experimental diffusion coefficients were represented using three correlations; namely, Wilke–Chang, modified Wilke–Chang, and Nernst–Haskell equation. The Wilke–Chang equation underestimated the diffusion coefficient while the Nernst–Haskell equation overestimated the diffusion coefficient. Only the modified Wilke–Chang equation satisfactorily represented the present experimental data. [Copyright &y& Elsevier]

Abstract: Here, we presented new experimental data of diffusion coefficients of five [Emim, (1-ethyl-3-methylimidazolium)]-based ionic liquids in water at infinite dilution for temperatures ranging from 303.2 to 323.2K using Taylor dispersion method. The investigated ILs were [Emim][C2N3 (dicyanamide)], [Emim][BF4 (tetrafluoroborate)], [Emim][C2H5SO4 (ethylsulfate)], [Emim][CF3SO3 (trifluoromethanesulfonate)], and [Emim][MDEGSO4 (2-(2-methoxyethoxy) ethylsulfate)]. The molar conductivities of these ionic liquids were also measured and the infinite dilution conductances were calculated. The temperature dependency of the present experimental diffusion coefficients of the studied ionic liquids in water at infinite dilution were correlated using three equations; namely, Wilke–Chang, empirical (linear), and Nernst–Haskell equation. The Wilke–Chang equation underestimated the diffusion coefficient. The empirical, a typical linear fit, satisfactory represented the present measurements of all the studied systems. The Nernst–Haskell equation satisfactory predicted the diffusion coefficients of most of the ionic liquids under investigation. The self-diffusion coefficients of the studied ions at infinite dilution were also evaluated and briefly discussed. The present results could be very essential to the assessment of the impact of ionic liquid in the waste water stream since it is the most likely pollution it would contribute to the environment. [Copyright &y& Elsevier]

Abstract: Two kinds of tracer response measurements, by the Taylor dispersion method using a stainless-steel diffusion column and the chromatographic impulse response (CIR) method using a polymer-coated diffusion column, were carried out by using the curve fitting to determine infinite-dilution binary diffusion coefficients of vitamin K3 (2-methylnaphthalene-1,4-dione), as a medium polar compound, in supercritical CO2 at 308.2K and pressures from 7.75 to 31.00MPa. The response curves in the Taylor dispersion method showed more significantly tailing closer to the critical point, whereas those did not at conditions away from the critical point. However, the CIR method provided the response curves almost without tailing over an entire range of pressure studied. Consequently, in the CIR method the response curves were accurately reproduced with the determined values of two parameters, binary diffusion coefficient and retention factor. The determined values of diffusion coefficients showed a little slow-down in the near critical region. In the Taylor dispersion method, however, the response curves with tailing were poorly reproduced with the determined values of diffusion coefficients, which apparently led to a steep-down in the near critical region. [Copyright &y& Elsevier]

Abstract: Taylor dispersion in a two-dimensional (2D) stratified velocity field describes a transition, called relaxation, from convective behaviour for short times, towards Fickian behaviour for large times and is partially reversible upon reversal of the flow direction. In 2D the physics are assumed to be governed by the unidirectional convection diffusion equation (2D uCDE). The approximate height-averaged 1D Generalised Telegraph Equation (GTE) catches an essential part of the longitudinal spreading. Contrary to the 1D Fickian approach, it explicitly accounts for the transient reversible nature [Camacho J. Purely global model for Taylor dispersion. Phys Rev E 1993/2;48(1); Berentsen CWJ, Verlaan ML, van Kruijsdijk CPJW. Upscaling and reversibility of Taylor dispersion in heterogeneous porous media. Phys Rev E 2005;71:046308]. Here we approach Taylor dispersion from a Lagrangian–Markovian point of view. In the redistribution model (RM) that we present, the Euler forward method accounts for convection and a probability redistribution matrix generates the transverse movement by diffusion over time. We consider two redistribution matrices. The first results from the direct discretisation of the Gaussian distribution function associated with the transverse mixing of the 2D uCDE. The resulting Gaussian redistribution model (GRM) is able to capture the multi-scale relaxation and reversibility behaviour of the full 2D uCDE. The correlated redistribution model (CRM) is the RM model with a redistribution matrix based on auto-correlation. The CRM is a generalisation of the correlated random walk model of [Scheidegger AE. The random walk model with auto-correlation of flow through porous media, Can J Phys 1958;36]. For uniform auto-correlation, the CRM model approximates the multi-scale relaxation nature of the 2D uCDE as a single scale relaxation process similar to the GTE. Moreover, it has the same variance as the GTE in the limit of the time step over relaxation time ratio to zero. For specific conditions the equality of the CRM model and the GTE is proven up to Δt 2 order accuracy. [Copyright &y& Elsevier]

Abstract: Binary diffusion coefficients, D 12, of α-amino acids with hydroxyl groups, e.g., serine, threonine, allothreonine and homoserine, in dilute aqueous solutions were measured at six different temperatures from 293.2 to 333.2K by the Taylor dispersion method. The determined D 12 values of serine and threonine at 298.2K were in good agreement with the published data, whereas no data for allothreonine and homoserine is available in the literature. The D 12 values for each amino acid were well represented with the Stokes–Einstein equation by adjusting the molecular diameter. The D 12 values for amino acids containing hydroxyl groups, except for homoserine, were lower by approximately 5%, on the basis of the same solute molar volume, than those from the corresponding amino acids without hydroxyl groups. [Copyright &y& Elsevier]

Abstract: The method of operator splitting is applied to an advection–diffusion model as it occurs in a pulse tube. Firstly, the governing equations of the simplified model are studied and the mathematical description is derived. Then the splitting approach is used to separate the advection and the diffusion part. Now it turns out that the advective part can be solved analytically and therefore the computational cost are reduced and the accuracy is increased. It is shown that the method can model an effect called Taylor dispersion. Applying a domain decomposition strategy, the solution process can be decoupled, reducing the numerical cost even more. This procedure allows to study the relevant parameters within the model with the goal to maximize the amount of energy stored within the tube wall. As a measure of efficiency, the amount of energy transferred between the fluid phase and the wall is chosen. [Copyright &y& Elsevier]

Purpose: The degree of tear mixing in various parts of eyes plays an important role in determining some important aspects of tear dynamics. This study develops a mathematical model of tear mixing in the lower conjunctival sac. Method: Tear mixing in the lower conjunctival sac is modeled using Taylor dispersion. The concentration of instilled solutes is obtained numerically from an equation set that integrates the mass balance of solutes in the lower conjunctival sac and the exposed tear film. Results: The time for dye to appear in the exposed tear film and the time for maximal dye concentration after instillation into the lower conjunctival sac vary for different amplitudes and frequencies of lid motion. The time scales for mixing are in qualitative agreement with experiments reported in the literature. Conclusion: This study supports the hypothesis that the tear mixing in the lower conjunctival sac is driven by Taylor dispersion caused by lid/globe movements during blinking. [ABSTRACT FROM AUTHOR]

Abstract: Fractures have been recently identified in potential host rock for high level nuclear waste disposal, like indurated argilite formations. These fractures appear as potential rapid pathways for radionuclides transport and hydrodynamic properties of the transport inside these systems must thus be characterized. Miscible non-sorbing and sorbing tracers displacements were performed on a 2-D model derived from a real fracture geometry observed in the Tournemire argilite formation with a lattice-gas cellular automaton (LGA). LGA was shown to easily handle the complex geometry of such a fracture. The numerical breakthrough curves obtained were inverted with the 1-D CDE and MIM transport models. Two main conclusions were drawn: (i) at the length scale of the study, the non-sorbing tracer transport in our fracture geometry was more accurately interpreted in terms of the MIM model rather than in terms of the classical CDE model; (ii) in order to correctly model the sorbing tracers migration, the hydrodynamic dispersion coefficient value was found to increase with the increase of the retardation factor. A semi-empirical relation based on the Taylor–Aris theory was then used to describe this dependency. [Copyright &y& Elsevier]

We consider the long-time asymptotic transport of a small Brownian sphere that is sedimenting through a viscous fluid within an infinite vertical cylinder whose radius changes periodically and abruptly between two values. Use of generalized Taylor dispersion theory gives rise to a set of steady-state differential equations that govern the long-time mean velocity. We prove that these equations possess a unique solution. Finite difference discretization of all governing equations and boundary conditions, except for the normalization condition, leads to a homogeneous system of equations that possesses an infinite number of solutions. Application of the normalization condition selects the particular solution of the set that satisfies all conditions. Despite the absence of classical wall effects, the long-time mean velocity of the particle through the pore is generally less than the Stokes sedimentation velocity that applies at every point within the fluid. This anomalous behavior could be used to enhance force-driven separation of Brownian particles that possess identical Stokes velocities but different diffusivities. Furthermore, this numerical approach may be applied to similar problems. [ABSTRACT FROM AUTHOR]

Abstract: Dr. Aydin Akgerman greatly contributed to studies on diffusion in liquids and supercritical fluids, in particular, measurements by the Taylor dispersion method. Based on his work, this article describes recent progress in measurements for binary diffusion coefficients in supercritical fluids by using the chromatographic impulse response technique as well as the Taylor dispersion method, and in the predictive empirical correlations. The data reported in the literature and the proposed correlations are also briefly reviewed together with the research subjects to be investigated in future. [Copyright &y& Elsevier]

ABSTRACT: An analytical study is presented of dispersion in steady and oscillatory open-channel flow under the combined effects due to reversible sorptive phase exchange with the bed and irreversible air-Cwater exchange on the free surface. The free-surface reaction is assumed to be so weak that the asymptotic mean concentration can be developed well before undue substantial loss to the air occurs. The effective advection-Cdispersion transport equation, which is derived using a multiple-scale homogenization technique, contains formal expressions for the various components of the dispersion coefficient arising from the two chemical effects. Numerical calculations demonstrate that, as long as the bed is sorbing, the kinetics of the sorptive exchange plays a key role in controlling the overall dispersion mechanism. The otherwise weak effects of the free-surface loss can be significantly enhanced by the presence of kinetic phase exchange on the bottom. [Copyright &y& Elsevier]

Abstract: An analytical study is presented of dispersion in steady and oscillatory open-channel flows under the combined effects due to reversible sorptive phase exchange with the bed and irreversible air–water reaction on the free surface. The free-surface reaction is assumed to be so weak that the asymptotic mean concentration can be developed well before undue substantial loss to the air occurs. The effective advection–dispersion transport equation, which is derived using a multiple-scale homogenization technique, contains formal expressions for the various components of the dispersion coefficient arising from the two chemical effects. Numerical calculations demonstrate that, as long as the bed is sorbing, the kinetics of the sorptive exchange plays a key role in controlling the overall dispersion mechanism. The otherwise weak effects of the free-surface loss can be significantly enhanced by the presence of kinetic phase exchange on the bottom. [Copyright &y& Elsevier]