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The relationship between the longitudinal dispersion (DL) and Peclet number (Pe) is crucial for predicting and simulating tracer through the variable‐aperture fracture. In this study, the roughness of the self‐affine fracture wall was decomposed into primary roughness (relatively large‐scale waviness) and secondary roughness (relatively small‐scale waviness) by a multiscaled wavelet analysis technique. Based on the complete dispersion mechanism (diffusion, macrodispersion, and Taylor dispersion) in the variable‐aperture fracture, three relationships (second‐order, power‐law, and linear relationships) between the DL and Pe were investigated at large and small scales, respectively. Our results showed that the primary roughness mostly controlled the Taylor dispersion mechanism, whereas the secondary roughness was a dominant factor for the macrodispersion mechanism. Increasing the Hurst exponent and removing the secondary roughness led to the decreasing range of Pe where macrodispersion mechanism dominated the solute transport. It was found that estimating the DL from the power‐law relationship based on Taylor dispersion theory resulted in considerable errors, even in the range of Pe where the Taylor dispersion mechanism dominated. The exponent of the power‐law relationship increased as the secondary roughness was removed. Analysing the linear relationship between the DL and Pe revealed that the longitudinal dispersivity αL increased linearly. However, this linear increase became weak as the Taylor dispersion mechanism dominated. In the range of Pe where the macrodispersion mechanism dominated, increasing the Hurst exponent caused the increase of αL and the secondary roughness played a significant role in enhancing the αL. As the Taylor dispersion mechanism dominated, the αL was insensitive to the influence of multiscale roughness in variable‐aperture fractures.

The critical micelle concentration is a basic characteristic of surfactants. In this article, the process of formation of micelles is studied by Taylor dispersion analysis using capillary electrophoresis instrumentation as a substituent of capillary liquid chromatography. New methods for determination of critical micelle concentration are presented. Sodium octylbenzene sulfonate and sodium dodecylsulfate are used as model compounds with and without chromophore. Two novel approaches based on indirect ultraviolet detection and indirect Taylor dispersion analysis with direct ultraviolet detection are introduced for the determination of critical micelle concentration value of surfactant without any chromophore. The determined critical micelle concentration values are in correspondence with the tabulated values at 95% confidence level.

Determining the charge and the nature (small ion, nanoparticle or polyelectrolyte) of an unknow solute from its electrophoretic characteristics remains a challenging issue. In this work, we demonstrate that, if the knowledge of the effective electrophoretic mobility (μep) at a given ionic strength is not sufficient to characterize a given solute, the combination of this parameter with (i) the relative decrease of the electrophoretic mobility with the ionic strength (S), and (ii) the hydrodynamic radius (Rh), is sufficient (in most cases) to deduce the nature of the solute and its charge. These three parameters are experimentally accessible by capillary zone electrophoresis and Taylor dispersion analysis performed on the same instrumentation. 3D representation of the three aforementioned parameters (μep; S and Rh) is proposed to visualize the differences in the electrophoretic behavior between solutes according to their charge and nature. Surprisingly, such 3D slope plot in the case of small ions and nanoparticles looks like a ‘whale-tail’, while polyelectrolyte contour plot represents a rather simple and monotonous map which is independent of solute size. This work also sets how to estimate the effective charge of a solute from a given experimental (S,Rh,μep5mM) triplet, which is not possible to obtain unambiguously with only Rh,μep5mM) or S,μep5mM) doublet, where μep5mM is the effective electrophoretic mobility at 5 mM ionic strength. This article is protected by copyright. All rights reserved

A 3D analytical solution is presented for the problem of mass transport in a T-sensor by taking the axial diffusion effects into account. The solution methodology is based on an eigenfunction expansion of the solute concentration and enjoys the variational calculus for the solution of the associated eigenvalue problem. The method is capable of handling a mixed electroosmotic and pressure-driven velocity profile and is executed assuming a rectangular channel cross-section although it can be easily extended to more complex geometries. Two simplified models, one based on a uniform velocity profile, valid for the channel half height to Debye length ratios of above 100, and the other based on a depthwise averaging of the species concentration to be used for cases in which the channel width to height ratio is above 5 are also presented. As a part of the latter, expressions are derived for the Taylor dispersion coefficient of the mixed flow in a slit microconduit. The most interesting finding of this study is that, when the diffusion mechanism significantly contributes to the axial movement of the species, the well-known heterogeneous mass transport evolves into a nearly uniform pattern in the depthwise direction and the mixing length noticeably increases. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4119–4130, 2016

Nanocomposite materials benefit from the diverse physicochemical properties featured by nanoparticles, and the presence of nanoparticle concentration gradients can lend functions to macroscopic materials beyond the realm of classical nanocomposites. It is shown here that linearity and time-shift invariance obtained via the synergism of two independent physical phenomena-translational self-diffusion and shear-driven dispersion-may give access to an exceptionally high degree of flexibility in the design of scalable and programmable long-range concentration gradients of nanoparticles in solidifiable liquid matrices.

In this work, we study mixed layer lateral dispersion that is enhanced by near-inertial internal Poincare waves in the offshore region of a large stratified lake, Lake Michigan. We examine the hypothesis that the vertical shear created by near-inertial internal Poincare waves is not only an energy source for vertical mixing in the thermocline and mixed layer, but also enhances horizontal dispersion via an unsteady shear flow dispersion mechanism. Complex empirical orthogonal function analysis reveals that the dominant shear structure is observed to mirror the thermal structure, with the location of maximum shear gradually lowered as the mixed layer deepens. This changing structure of shear and vertical mixing produces different characteristics in shear flow dispersion between the early and later stratified periods. The estimated depth-averaged surface layer vertical turbulent diffusivity grows from 10−5 m2s−1 to 10−3 m2s−1 over the stratified period, and the associated lateral dispersion coefficients are estimated as 0.1 –40 m2s−1. The Poincare waves are found to enhance greatly lateral dispersion for times less than the inertial period following release. In contrast, sub-inertial shear is the dominant mechanism responsible for shear dispersion for times greater than the inertial period. A simple approximation of the dispersion coefficient for lateral dispersion is developed, which scales as the product of surface current velocity (or wind friction velocity) and mixed layer depth. The calculated dispersion coefficients agree well with Okubo's diffusion diagram for times up to a week, which suggests that unsteady shear dispersion is a plausible mechanism to explain observed dispersion rates in the mixed layer for early times after release.

An effort to analyze the viscoelasticity effects on transverse transport of neutral solutes between two miscible streams in an electrokinetic T-sensor is presented. The analysis is based on an approximate analytical solution for the depthwise averaged concentration, assuming a channel of large width to depth ratio for which a one-dimensional profile is sufficient for describing the velocity field. We show that the solution derived is surprisingly accurate even for very small channel aspect ratios and the maximum error reduces to only about 1% when the aspect ratio is 5. The developed model reveals that the mixing length for a viscoelastic fluid may be by far larger than that for a Newtonian fluid. Moreover, the Taylor dispersion coefficient for electroosmotic flow of viscoelastic fluids, which its determination is a main part of the analysis, is found to be an increasing function of both the elasticity level and the EDL thickness. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4533–4541, 2015

Trichloroethylene (TCE) is a halogenated aliphatic organic compound frequently detected as pollutant in soils and ground water. To study the fate of TCE in water and to devise effective remediation strategies, a series of advection-diffusion (dispersion) models, where the diffusion coefficient of TCE (DTCE) is an important parameter, have been developed. However, DTCE in water has never been experimentally determined and only theoretical values ( ≃1×10−5 cm2 s−1 at 25°C) are present in the literature. A new method based on the Taylor dispersion technique, which allows to measure DTCE in a broad range of temperature and, in principle, in any solvent is presented. At 25°C DTCE = 8.16±0.06×10−6 cm2 s−1 and the value increases almost linearly with the temperature, while, in the limit of the experimental error, is independent from [TCE] for dilute solutions. From the temperature dependence of DTCE, it was possible to calculate the specific TCE fitting constant in the well-known Wilke and Chang theoretical relation and the activation energy of the diffusion process through the Arrhenius plot. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3511–3515, 2015

An analytic expression is presented for the effective dispersion coefficient in the case where a solute is focused in a parabolic flow against a linear gradient in a restoring force. This expression was derived by employing a minor variation on the method of moments used by Aris in his development of the dispersion coefficients for a time-dependent, isocratic system. In the present case, dispersion is controlled by two dimensionless groups, a Peclet number which is proportional to the parabolic component of the flow, and a gradient number which is proportional to the slope of the restoring force. These results confirm that the Aris-Taylor expression for the dispersion coefficient should not be applied in cases where a solute is focused to a stationary steady state.

A novel approach with fewer technical and analytic limitations in liquid solvent-bitumen diffusion studies is used in this article. The Taylor dispersion technique was selected for its convenient short run time experiments and reliable data analysis to find mutual diffusion coefficients in a hexane + bitumen mixture. For the first time, the infinite-dilution molecular diffusion coefficients of bitumen in hexane were measured in both the presence and relative absence of asphaltene particles in the solution at atmospheric pressure and temperatures of 303.15, 310.15, and 317.15 K. The polydisperse nature of bitumen was clearly revealed. Results were compared with common predictive tools. Also, the asphaltene surface charge in the hexane precipitating solvent was demonstrated. Through concentration dependency investigations at atmospheric pressure and 303.15 K, it was determined that the mutual diffusion coefficients monotonically decrease as the viscosity of mixture increases within the studied 0–34% volumetric concentration of bitumen. The Taylor dispersion technique shows great potential for diffusion studies of liquid solvent-bitumen systems. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2670–2682, 2014

A theoretical model for fluid mixing in steady and transient buoyancy-driven flows induced by laminar natural convection in porous layers is presented. This problem follows a highly nonlinear dynamics and its accurate modeling poses numerical challenges. Based on the Taylor dispersion theory, a one-dimensional analytical model is developed for steady and transient velocity fields. To investigate steady-state mixing, a unicellular steady velocity field is established by maintaining a thermal gradient across a porous layer of finite thickness. A passive tracer is then introduced into the flow field and the mixing process is studied. In the case of transient flows, as the convective flow grows and decays with time the behavior of the dispersion coefficient is characterized by a four-parameter Weibull function. The simple analytical model developed here can recover scaling relations that have been reported in the literature to characterize the mixing process in steady and transient buoyancy-driven flows. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1378–1389, 2013

In this work, transport and thermodynamic properties of mixtures of n-hexane with the aldehydes citral, citronellal and dihydrocitronellal, important to the fine chemicals industry, were determined experimentally and compared to theoretical predictions. Liquid binary diffusion coefficients were measured using the Taylor dispersion technique at various temperatures. The Wilke-Chang correlation gave precise approximations. The second part of this work is concerned with the gas-liquid phase equilibrium of citral/n-hexane. The mixture is slightly nonideal and may be sufficiently described by applying the modified UNIFAC (Dortmund) group contribution method. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2557–2562, 2012

The effect of homogeneous and heterogeneous reactions on the dispersion of a solute in a composite porous medium between two parallel plates is studied. The solution approach suggested by Taylor [2] is generalized for the present model. The Brinkman model is used to define the flow through the porous medium. The fluids in both the regions of the parallel-plate channel are incompressible and transport properties are assumed to be constant. The closed-form solutions are obtained in both the regions of the channel. The results are tabulated for various values of viscosity ratio, pressure gradient, and porous parameter on the volumetric flow rate and the effective Taylor dispersion coefficient. It is found that for a homogeneous chemical reaction, the effective Taylor dispersion coefficient decreases as the reaction rate parameter and porous parameter increase. The validity of the results obtained for a composite porous medium is compared with the available porous medium results for a one-fluid model and the values tallied for the small values of porous parameter. Also a two-fluid model in the absence of a porous matrix is compared with the available one-fluid model and good agreement is found. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res, 40(7), 608–640, 2011; Published online 26 July 2011 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20364

The miscible liquid-liquid two phases based on Taylor flow in microchannels was investigated by high-speed imaging techniques and Villermaux/Dushman reaction. The mixing based on Taylor flow was much better compared with that without introducing gas in microchannels, even the ideal micromixing performance could be obtained under optimized superficial gas and liquid velocities. In the mixing process based on Taylor flow, the superficial gas and liquid velocities affected the lengths and the velocities of Taylor bubble and liquid slug, and finally the micromixing performance. The formation process of Taylor flow in the inlets, the initial uniform distribution of reactants and the internal circulations in the liquid slug, and the thin liquid films all improved the mixing performance. Furthermore, a modified Peclet number that represented the relative importance of diffusion and convection in the mixing process was proposed for explaining and anticipating micromixing efficiency. (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 16601670, 2012

In this work, the applicability of using CE to perform a physicochemical characterization of a PEGylated liposomal drug formulation of the anti-cancer agent oxaliplatin was examined. Characterization of the liposomal drug formulation using CE instrumentation encompassed: determination of the electrophoretic mobilities, size determination by Taylor dispersion analysis and interaction studies. Electrophoretic mobilities determined by CE were compared with the results obtained by laser Doppler electrophoresis, which were found to be subject to larger variation. Average hydrodynamic diameters of the liposome preparations, as determined by Taylor dispersion analysis, were in the range of 61-84 nm and were compared with the results obtained by dynamic light scattering. Interactions between oxaliplatin (and paracetamol) and the PEGylated liposome were non-detectable by CE frontal analysis as well as by liposome electrokinetic chromatography. In contrast, for the more lipophilic compound propranolol, apparent liposome-aqueous phase distribution coefficients (D(lip) ) were successfully determined by both electrokinetic chromatography (log D(lip) =2.10) and by CE frontal analysis (log D(lip) =2.14). It is envisioned that CE and capillary-based techniques, including Taylor dispersion analysis, will be useful tools for the characterization of nanoparticulate (e.g. liposomal) drug formulations.

The gaseous diffusion coefficients of methyl bromide (CH3Br) and methyl iodide (CH3I) into dry air, nitrogen, and oxygen have been measured in the temperature range 303–453 K and at atmospheric pressure via the Taylor dispersion method. Both for methyl bromide and methyl iodide, the diffusion coefficients do not vary in practice on substituting pure nitrogen or oxygen for dry air. The diffusion coefficients for methyl iodide are systematically smaller than those for methyl bromide by about 11%. For the methyl iodide-oxygen system, the effect of the thermal decomposition of methyl iodide has been observed at 453 K. The present results can be reproduced well by the functional form D = ATB, where D (cm2s−1) is the diffusion coefficient at 101 325 Pa (1 atm) and T (K) is the absolute temperature. The constants A and B are as follows: methyl bromide-(air, nitrogen, oxygen), A = 5.57 × 10−6, B = 1.76; methyl iodide-(air, nitrogen, oxygen), A = 5.26 × 10−6, B = 1.75. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20255

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.

A new methodology based on heart-cutting 2-D CE in a single capillary was developed for the chiral separation of a mixture of 22 underivatized amino acids. The first dimension is performed in an achiral BGE (2.3 M acetic acid, pH 2.1) allowing the separation of the analytes as a function of their charge-to-radius ratio. A selected fraction from the first dimension is then separated in the second dimension in the presence of a chiral selector (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid. Since the introduction of the second electrolyte is performed by pressure mobilization, capillaries with small id of 10 microm are used to limit the peak broadening due to Taylor dispersion. Double capacitively coupled contactless conductivity detector is used for monitoring the selection and the isolation of the fraction at the different steps of the analysis (voltage and pressure mobilization steps). This double detection allows calculating the voltage and pressure stop times in real-time analysis. This new methodology is applied with success for the chiral separation of different amino acids (D,L-Tyr, D,L-Trp and D,L-Thr) contained in a mixture of 22 native amino acids.

The purpose of this note is to present new evidence of diameter-dependent dispersion in solute flowing through packed cylinders. Hydrodynamic dispersion was simulated at the pore scale in cylinders packed with spheres of diameter d, with cylinder radii ranging from R 1⁄4 5d to R 1⁄4 25d. The time-dependent, axial dispersion coefficient, DL(t), was plotted for different cylinder radii. These plots cross over, implying diameter-dependent dispersion. Comparisons with periodic sphere packs suggest the cylinder wall introduces new scales of length and time for dispersion. These results were obtained from threedimensional, pore-scale simulations of flow and transport in packed cylinders. The simulations are computationally demanding and we have been limited to relatively short durations. However, we were recently able to extend the duration enough to reveal the cross-over dynamics. We begin by describing the background for the new results. Taylor dispersion of a solute flowing in a tube illustrates the phenomenon of diameter-dependent dispersion. Taylor observed that radial variation in fluid velocity leads to an axial dispersion coefficient greater than the bulk molecular diffusivity, DM, of the solute, and he showed that this coefficient develops over a time and distance that depend on the tube diameter and average velocity, v. Indeed, this result is general for arbitrary velocity profiles, as shown by Aris. The packed column is similar, but requires the additional consideration of the characteristic length scale of the porous medium. It is generally accepted that the asymptotic axial dispersion coefficient in a packed cylinder depends on the ratio of cylinder diameter to particle diameter, b 1⁄4 2R/d because of nearwall packing effects on the velocity profile. Delgado reviews experimental investigations, dating to at least 1958, that discuss the effects of radial variations in porosity and velocity on dispersion. However, the consensus among these investigations is that dispersion is independent of the ratio for b . k, where k is a number in the range from 10 to 15. Gunn, for example, makes a case for diameter independence based on a mathematical model and earlier experimental results. De Ligny was perhaps the first to propose a correlation for the dispersion coefficient that explicitly accounts for both particle and cylinder diameters. The correlation predicts the effective dispersion coefficient in a packed cylinder from these two parameters and from the effective radial dispersion coefficient. The radial coefficient is assumed to be only weakly dependent on b. A number of authors have developed models of radial variations in porosity and velocity and used them to predict concentration distributions and mass transfer zones in packed cylinders. Perhaps the simplest illustration is given by Rudraiah et al. for a rectangular packed duct; they assume Brinkman’s equation to describe the near-wall velocity profile and further assume the value of a bulk dispersion coefficient that is characteristic of the ! 2007 American Institute of Chemical Engineers *This article ia a U.S. Government work and, as such, is in the public domain in the United States of America.

The Taylor dispersion of a solute is studied in a core–annular geometry. The fluid flows only through the core, but the solute can diffuse into the solid annulus. The long time limit of the dispersion coefficient D* is derived by a regular expansion in the aspect ratio for two different scalings of the Biot number (Bi), which is the dimensionless interfacial mass-transfer resistance. The results for the case of O(1) Bi match those obtained by Aris and a number of other researchers. In the case of O(e) Bi, where e is the aspect ratio, the average mass-transfer equations for the core and the annulus are coupled and do not simplify to a simple convection–dispersion form. The average mass-transfer equations are derived for two velocity profiles: Poiseuille flow and plug flow. The dispersion coefficient for the limiting case when both the core and the annulus are radially well mixed at all times is also determined for the case of O(1) Bi. For O(1) Bi, the dispersion of the solute arises as a result of molecular diffusion, interfacial mass-transfer resistance, and convective flow, and the contribution from interfacial mass-transfer resistance is independent of the velocity profile. This dispersion coefficient reduces to the classical result of fluid flow through a tube in the limit of vanishing annulus thickness and also for the case when the solute has zero solubility in the solid. The core–annular geometry mimics the Krogh cylinder, which is a model used for analyzing mass transfer from capillaries into surrounding tissue. The model predictions for the dispersion coefficients in different tissues agree reasonably with the experimentally reported values, and the agreement is the best for muscles, where the Krogh cylinder model is expected to most closely resemble the actual physiology. © 2005 American Institute of Chemical Engineers AIChE J, 2005

The class of equilibrium gradient methods utilizes the opposition of two forces, at least one of which changes in magnitude with position, to separate and concentrate analytes. The drawback of many methods of this type is that the production of two opposing forces requires in comparison to standard methods, such as capillary electrophoresis, a relatively complex apparatus. In addition, for techniques such as electric field gradient focusing, hydrodynamic flow leads to Taylor dispersion, which limits the attainable concentration factor. We propose a new method, gradient field electrophoresis, which achieves analyte separation and focusing with only one spatially varying force, an electric field gradient. A model for the method is developed and used to analyze peak capacity. Experimental results for a protein (R-phycoerythrin) are given and compared to the model.

The effect of shear thinning on the stability of the Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional non-linear coupling in the velocity components through the viscosity

Peak dispersion effects in nonaqueous capillary electrophoretic separations of aromatic anionic analytes were investigated in a propanolic background electrolyte solution. Poly(glycidylmethacrylate-co-N-vinylpyrrolidone) coating was applied to the capillary to suppress the electroosmotic flow and to improve the repeatability of the migration times. Electrical field strengths up to 2000 Vcm - 1 were applied in separations and the separation efficiencies were compared with theoretical values calculated on the basis of plate height theory. The contributions to the total plate height were calculated for injection plug length, diffusion, Joule heating, electromigration dispersion, analyte adsorption to the capillary wall, and detector slit aperture length. Analyte diffusion coefficients were measured by Taylor dispersion method, while distribution constants were measured chromatographically. Agreement between the calculated and empirical results was fairly good even though some approximations were required. In most cases the longitudinal diffusion contribution governed the total plate height, while the contribution of Joule heating was insignificant even at exceptionally high field strengths used. The relatively long detection slit aperture was found to influence the separation efficiency strongly, while the other dispersion sources that were investigated were of minor importance, except for adsorption in the case of one analyte. With all analytes, the dispersive effect of longitudinal diffusion was reduced as the field strength was increased, leading to enhanced migration velocities and faster separations.

We present a systematic, experimentally validated method of designing electrokinetic injections for on-chip capillary electrophoresis applications. This method can be used to predict point-wise and charge-coupled device (CCD)-imaged electropherograms using estimates of species mobilities, diffusivities and initial sample plug parameters. A simple Taylor dispersion model is used to characterize electrophoretic separations in terms of resolution and signal-to-noise ratio (SNR). Detection convolutions using Gaussian and Boxcar detector response functions are used to relate optimal conditions for resolution and signal as a function of relevant system parameters including electroosmotic mobility, sample injection length, detector length scale, and the length-to-detector. Analytical solutions show a tradeoff between signal-to-noise ratio and resolution with respect to dimensionless injection width and length to the detector. In contrast, there is no tradeoff with respect to the Peclet number as increases in Peclet number favor both SNR and separation solution (R). We validate our model with quantitative epifluorescence visualizations of electrophoretic separation experiments in a simple cross channel microchip. For the pure advection regime of dispersion, we use numerical simulations of the transient convective diffusion processes associated with electrokinetics together with an optimization algorithm to design a voltage control scheme which produces an injection plug that has minimal advective dispersion. We also validate this optimal injection scheme using fluorescence visualizations. These validations show that optimized voltage scheme produces injections with a standard deviation less than one-fifth of the width of the microchannel.

Mutual diffusion coefficients of hydrogen gas (H2) into air and its component gases (N2 and O2) have been measured in the temperature range of 30 to 180°C and at atmospheric pressure via the Taylor dispersion method. For a H2–N2 system, the composition dependence of the mutual diffusion coefficient has been studied with both H2 and N2 as the carrier gas. The mutual diffusion coefficients for the H2–air and H2–N2 systems are almost the same and smaller than that for the H2–O2 system by about 5%. The present data for the H2–N2 system, corrected to an equimolar composition, agree well with the accurate data reported by the groups of P. J. Dunlop and of R. J. J. Van Heijningen. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 182–193, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10025

A comparison between various methods to determine diffusion coefficients of polymers in dilute solutions has been made. It is shown that Taylor dispersion analysis (TDA), dynamic light scattering (DLS), hydrodynamic chromatography (HDC), and size exclusion chromatography (SEC) can all be used to accurately determine diffusion coefficients when the polymer samples have low polydispersities. By the analysis of a series of practically representative styrene acrylonitrile copolymer (SAN) samples, it is shown that polydispersity of the samples and the presence of low-molecular-mass material cause considerable differences between the methods. It was found that TDA is mostly disturbed by the presence of low-molecular-mass material, whereas DLS is more sensitive to the polydispersity of the polymer. With broad samples, DLS gives the Z-average diffusion coefficient. SEC can be used to obtain a diffusion coefficient distribution as well as an average diffusion coefficient of a polydisperse sample. Although, the same was expected for HDC, it was found that this method could only be successfully used for polymer samples having low polydispersities. Deviations between SEC, HDC, and TDA found for narrow samples were not related to the chemical composition of the samples.

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

An analysis and applications of the wave model for longitudinal dispersion are pre-sented. Asymptotic forms of the wave model are considered and analytical solutions of typical linear stationary and nonstationary problems of chemical reactor engineering interest are obtained and compared to those for the Fickian dispersion model. The wave model leads to efficient analytical solutions for linear problems, which in principle differ from the solutions of the Fickian dispersion model; only for slowly varying concentration fields do the soluctions of both models approach each other. Spatial and time moments of the concentration distribution are obtained for pulse-dispersion problems; the first three spatial moments of the mean, variance, and skewness have exact, large-time asymptotic forms in the case of Taylor dispersion. Old experiments that could not be explained with the standard dispersion model are reconsidered and explained: the change with time of the variance of a concentration pulse when the flow direction is reversed and the difference in values of the apparent axial dispersion coefficient and the backmixing coefficient in a rotating disk contactor. The experimental determination of model parameters is discussed.

Tracer dispersion in polysaccaride (scleroglucan) solution flowing through 0.56-mm-ID capillary tubes was studied experimentally. In contrast with experiments modeling enhanced recovery processes, the polymer concertration remains constant during a given experiment, while the tracer concerntration varies. A preparation procedure giving stable rheological characteristics is described, as well as their dependence on the polymer concentration Cp (100 mg/L ≤ Cp ≤ 2,000 mg/L). Dispersion measurements are performed with ionic tracers at Peclet numbers between, showing that the Taylor dispersion mechanism remains dominant. At a constant flow velocity, K decreases by about 75% when Cp increases from 0 to 2,000 mg/L. This variation is related to the flattening of the velocity profile and can be predicted both with a power-law rheological model and Monte Carlo simulations. The extension of these measurements to heterogeneous porous media is discussed.

The International Symposium on Environmental Hydraulics was held in Hong Kong in December 1991 and produced a two volume proceedings.1 The proceedings include over 200 papers, most related to mixing and transport. Conference sessions cov ered such topics as jets and plumes, ocean outfalls, turbulent mixing, dispersion, sediment transport, stratified flow, and modeling. The annual American Society of Civil Engineers National Conference on Hydraulic Engineering was held in Nashville, Tennessee, in July and August 1991 ? Sessions pertinent to mix ing and transport addressed field measurements of dispersion in rivers, water-sediment interface processes, thermal discharges, estuary modeling, oil spills, sediment transport, and water quality hydraulics. Frankel and Brenner3 extended generalized Taylor dispersion theory to unbounded homogeneous shear flow. Using a coor dinate system that deforms with the shear flow, they derived a convective-dispersion type solution for solute transport. Smith4 analyzed the influence of wind mixing on buoyant and slightly dense particles in shallow water. He found that the concentrating action of downwind movement of buoyant particles was coun teracted by increased mixing, thus explaining the lack of cor relation between onshore winds and shoreline pollution. Komori et al5 considered the mixing dynamics of two reacting species injected at separate points to a turbulent flow field. They used the model to evaluate the "unmixedness" parameter, a measure of the effects of mixing on the mean chemical reaction rate. Borgas and Sawford6 revised previously derived formulations of the statistical properties of oneand two-particle turbulent dis persion. New relations for the one-particle Lagrangian acceler ation correlation and two-particle acceleration covariance were derived for the inertial subrange. Squires and Eaton7 evaluated the dispersion of heavy particles in turbulent flow. Through numerical simulations, they deter mined how drift due to body forces and inertia changes diffusion of a heavy particle from that of a neutral particle. Mei et al* mathematically analyzed the influence of Basset and gravitational forces on dispersion of particles. Basset forces were found to affect the particle movement but not the structure of the fluid velocity fluctuations. Yang et al9 presented a new higher-order numerical technique for solution of the advection-diffusion equation. The method tracked advection by the method of characteristics and inter polated the concentration and its derivatives using higher-order polynomials. Kerstein10 reported on the linear-eddy approach for modeling turbulent diffusion over a wide range of length scales. He modeled molecular diffusion deterministically but su perimposed a stochastic model of turbulence-induced diffusive movements. Pai and Tsang11 proposed a second-order closure turbulence model solved by finite elements. They tested their model against laboratory, wind-tunnel, and large-eddy simula tions and reported on the model's parameter sensitivity. Li12 developed a model to solve the two-dimensional advection-dis persion equations using a split-operator scheme. The advective step was solved by minimizing error in a characteristics solution; the dispersion step was solved by an alternating direction explicit method. Ernest et al13 developed a parameter estimation algorithm for advection-dispersion particle transport. The theory was tested against dye clouds and particles in mixed laboratory columns.

The concentration dependence of mutual diffusion coefficients in four binary systems N,N-dimethylformamide-toluene, dimethylsulfoxide-toluene, sulfolane—toluene and n-heptane—toluene is determined at 298.15 K using the Taylor dispersion method. To detect the dispersion of the injected sample a flow-through differential refractometer is applied. The refractometer output signals are recorded at constant time intervalls and a five parameter working equation is fitted to the concentration profile of the sample by a nonlinear least-square procedure. Diffusion coefficients at infinite dilution were obtained and five empirical correlations for estimating diffusivities at infinite dilution are tested against our results.

We discuss the possibility of designing a pressure-driven single-phase microreactor with characteristics similar to that in an ideal plug-flow reactor. We consider equations for the moments of the residence time distribution and investigate the behavior of the solution in long spatially-periodic channels. If the microreactor consists of a large number of folding flow elements, the chaotic advection plays a double role: it mixes the chemical species and suppresses the axial dispersion. It is shown using analytical estimates and numerical modeling that chemical reactions have different sensitivity to the axial dispersion and for some reactions the effect of dispersion can be successfully eliminated. © 2009 American Institute of Chemical Engineers AIChE J, 2010

The Taylor dispersion technique is modified to measure the concentration-dependent mutual diffusion coefficient D of cetylpyridinium chloride (CPC) + water at 25°C near the critical micelle concentration. The solution flowing into the dispersion tube is changed from a solution of CPC concentration C− to a solution of concentration C− + ΔC, forming an initially-sharp moving boundary at the tube inlet. The broadened concentration profile across the eluted boundary is followed by using a flow-through differential refractometer at the tube outlet. A numerical procedure similar to the Boltzmann-Matano procedure for the analysis of free diffusion profiles yields the values of D at the concentrations between C− and C− + ΔC, from a single dispersion run. D for aqueous CPC is found to drop very sharply as the concentration is raised through the critical micelle concentration.

The Taylor dispersion (peak-broadening) technique is used to measure the quaternary interdiffusion coefficients of the four-component systems sucrose + LiCl + KCl + water and tetra-n-butylammonium bromide + LiBr + KBr + water at 25°C. The dispersion of the eluted solutes is followed by differential refractometry. Direct least-squares analysis of the measured peak shapes is used to calculate the interdiffusion coefficients. Equations are developed to describe dispersion in multicomponent systems containing arbitrary numbers of components.

In 1954, G. I. Taylor derived an expression for an apparent axial dispersion coefficient for mass transfer in turbulent flow under the assumption of no mass transport between the tube wall and the fluid inside the tube. Taylor's expression has been verified in a number of experimental efforts for both mass and heat transfer. This work extends the results of Taylor to the case where there is a significant transport of heat from the tube wall to the fluid in the tube, such as in a double-pipe heat exchanger. Using an analysis similar to Taylor's, it is shown that the apparent axial dispersion coefficient is about one order of magnitude larger when a large radial gradient is present. Experimental data on a double-pipe heat exchanger show significantly improved correspondence with a dispersion-based model of the system when the larger dispersion coefficients are used.

The diffusion coefficients of benzene, naphthalene, anthracene, phenanthrene, and diphenyl at infinite dilution in heptane and in octane in the temperature range 303.2 to 333.2 K were determined by the Taylor dispersion technique. Two empirical estimation methods for diffusion coefficient were tested against our experimental data and a free-volume-type expression was used to correlate the diffusion coefficients.

Transport phenomena for different boundary conditions in finite and effectively semi-infinite domains were successfully simulated using the lattice Boltzmann method (LBM). We verified an LBM solute transport algorithm and its boundary conditions by comparing simulation results with analytical solutions for four different one-dimensional solute transport problems. Zero-diffusion analytical breakthrough curves were derived for parallel plate and pipe flow, and LBM simulations with small diffusion coefficients matched these well. Simulations of solute transport in one-dimensional finite and semi-infinite domains were performed at a low column Peclet number (Pe = 1) for first- and third-type inlet boundary conditions; these followed the analytical solutions closely. A series of transport simulations were performed to demonstrate the impact of diffusion and dispersion on the solute front. Taylor dispersion coefficients for the simulated range of Peclet numbers were estimated using moment analysis of the concentration obtained from transport simulation by the LBM. The simulation results showed good agreement with theoretical predictions and thus verified the robustness of LBM-based transport models.

The diffusion coefficients for an homologous series of ca. 20 n-alkanes from ethane to octacosane have been measured in dilute solution in propan-2-ol and tetrahydrofuran at 300 K and atmospheric pressure using the Taylor dispersion technique with an accuracy of 3–5 % for most systems. The diffusion results are discussed in terms of the hydrodynamic theory of diffusion, in view of the relevance to diffusion-controlled reactions in polymerisation kinetics.

The infinite dilution diffusion coefficients of methane, ethane, n-propane, n-pentane, n-heptane, n-decane, n-dodecane, and n-tetradecane have been measured in n-octane using the Taylor dispersion technique in the temperature range 304-435 at 1.72 x 10/sup 6/ N/m/sup 2/. Using the framework of the rough hard sphere theory, the values of the translational-rotational coupling parameter have been determined for each solute-solvent pair at each temperature. The coupling parameter was found to be independent of temperature over the entire temperature range of the experiments performed and it has the same value for solutes ranging from n-pentane to n-tetradecane. A calculation scheme is presented for accurate determination of infinite dilution diffusion coefficients for a wide range of solutes in n-octane at a wide temperature range.

Tracer diffusion coefficients in liquid cyclohexane of benzene, toluene, p-xylene, mesitylene, naphthalene, and phenanthrene have been determined from 298.2 to 523.2 K (TR = 0.54 ∼ 0.95) using the Taylor dispersion method. Positive deviations from the Arrhenius relationship are observed as the critical temperature is approached, but a rough-hard-sphere theory is found to be adequate for describing the data across the entire temperature range. On the basis of the computer simulation results for hard-sphere fluids, correlations involving solute and solvent critical volumes and their molecular weights have also been developed for practical applications. Tracer diffusivities in supercritical carbon dioxide are also adequately represented by the proposed correlation, as the fluid density is not far removed from that of liquid carbon dioxide.

An automated Taylor dispersion apparatus, designed to operate from 298 to 573 K and 101 to 3,450 kPa (14.7 to 500 psia), was used to measure diffusion coefficients at infinite dilution for the solutes n-octane, n-decane, n-dodecane, n-tetradecane, and n-hexadecane in the solvents n-heptane and n-dodecane. Dodecane viscosity and density also were measured at all conditions. Various predictive theories are tested in light of the new data, and a correlation based on the data at high temperature and pressure is presented. The data are well represented by a free-volume expression of the form . The data given here extend the available data base for alkane/alkane diffusion by 100 to 200 K, and allow evaluation of predictive theory over an extended range of temperatures.

The diffusion coefficient of benzoic acid in water at 25°C has been measured as a function of concentration using the Taylor dispersion technique. The diffusion coefficient was found to decrease from 1.25 × 10−9 m2/s to 1.07 × 10−9 m2/s when the concentration increased from 0.27 mol/m3 to 5.44 mol/m3. Two different models describing the concentration dependence of the diffusion coefficient have been developed. They are fitted to the measured data and experimental data from literature at infinite dilution (D = 1.57 × 10−9 m2/s) and at higher concentrations up to 20 mol/m1 (D = 0.75 × 10−9 m2/s). The significance of the concentration dependence is evaluated by measurement and by computer simulations of liquid–solid mass transfer in a tube. The simulations show that 0.80 × 10−9 m2/s is the constant diffusivity that gives the best approximation in dissolution studies. On a mesure le coefficient de diffusion de l'acide benzoique dans l'eau a 25°C en fonction de la concentration en utilisant la technique de dispersion de Taylor. On a trouve que le coefficient de diffusion diminue de 1,25 × 10−9 m2/s a 1,07 × 10−9 m2/s quand la concentration augmente de 0,27 mol/m3 a 5,44 mol/m3. Deux modeles differents decrivant la variation avec concentration du coefficient de diffusion ont ete etablis. Les parametres des modeles ont ete a justes par rapports aux donnees mesurees ainsi que par rapport a des donnees experimentales publiees a dilution infinie (D = 1,57 × 10−9 m2/s) et a des concentrations superieures jusqu'a 20 mol/m3 (D = 0,75 × 10−9 m2/s). L'importance de la variation avec la concentration est evaluee par des mesures et des simulations par ordinateur du transfert de matiere liquide–solide dans un tube. Les simulations montrent que la diffusivite constante qui donne la meilleure approximation des resultats sur la dissolution est de 0,80 × 10−9 m2/s.

A compartmental dispersion model of longitudinal mixing in tube networks has been developed. The ability of this model to predict the impulse response of helium, benzene vapor, and sulfur hexafluride tracer gases in two and in five generation symmetric network models of the large airway system of the lung has been tested over an air flow range of 1 to 400 ml/s. The results imply that velocity profile distortion and secondary flows in branching regions have only a small effect upon the overall longitudinal mixing when flow is directed toward the higher-order generations. On the other hand, accurate prediction of the data requires adequate treatment of the finite rate of evolution of the Taylor dispersion occurring in these tube networks.

Tracer diffusivities measured with the Taylor dispersion technique are reported for carbon tetrachloride, s-trioxane, 12-crown-4, 15-crown-5, and 18-crown-6 in acetonitrile, benzene, and chlorobenzene across ranges of temperature. It is demonstrated that Stokes' law corrected with a microfriction factor successfully accounts for the diffusion behavior of even disk-shaped crown ethers. Solute and solvent molecules being effectively spherical in the context of Stokes' law, the tracer diffusion of crown ethers is found to be satisfactorily represented by a rough-hard-sphere model for molecular diffusion. The degree of success increases with decreasing solvent polarity. The diffusion data for carbon tetrachloride are also used to extend the basis of the recently developed reduced equation for the tracer diffusion of nonelectrolytes in liquids over wide temperature ranges.

The extended Taylor dispersion method was used to determine the translational diffusion coefficients of a series of polystyrene standards in 1,4-dioxane at infinite dilution at temperatures from 323.2 to 378.2 K. The experimental data suggest that in the context of Kirkwood's theory the Monte Carlo chain represents real polystyrene molecules better than does the Guassian chain with physically reasonable values for the hydrodynamic interaction parameter h*. The feasibility and accuracy of the simultaneous determination of the diffusivities of several polystyrene standards from a single dispersion measurement were also analyzed using a binary mixture of polystyrenes with molecular weights of 2000 and 100,000 as an example.

Generalized Taylor dispersion theory for nonreactive solutes (Brenner 1980a; 1982) undergoing convection and diffusion is extended to include irreversible first-order volumetric and surface chemical reactions possessing position-dependent reactivity coefficients at the microscale. For sufficiently long times the equivalent chemical kinetic description of the rate of solute depletion at the macroscale is shown to manifest itself as a single constant reactivity coefficient K* characterizing an apparent first-order irreversible volumetric reaction. Subtraction of this gross solute depletion rate from the original microscale transport equation permits the resulting Taylor dispersionlike problem to be resolved by a solution scheme closely paralleling that for the comparable nonreactive case. This allows a straightforward determination of the mean global solute velocity vector Ū* and dispersivity dyadic D* appearing in the macroscale convection-diffusion-reaction equation describing the local-space averaged mean transport process. By way of example, these three coefficients are explicitly calculated for reacting and diffusing solute particles sedimenting from a solvent flow occurring between two parallel plates onto the reactive surface of one of these plates.