Taylor Dispersion Coefficient Research Articles

Effect of phase exchange kinetics on Taylor dispersion of chemically reactive solutes in an oscillatory magnetohydrodynamics flow between two parallel plates

The study of kinetic sorptive effects on the transport phenomena of reactive solute has numerous real-world applications, including in the industrial and environmental sectors. These kinds of investigations become more realistic when an oscillatory pressure gradient with both the reversible and irreversible reactions at the channel walls is considered in a magnetohydrodynamics flow. In the past, Ng and Yip [J. Fluid Mech. 446, 321–345 (2001)] studied the effect of sorptive phase exchange at boundaries on the solute transport phenomena in an open-channel flow using Mei's multiple-scale homogenization technique. They considered fluid flows without magnetic field and boundary absorption. This work uses the above-mentioned method to investigate the phase exchange kinetics of Taylor dispersion phenomena in a two-dimensional magnetohydrodynamics fluid flowing through a parallel channel. The paper discusses how various parameters and dimensionless numbers, such as the Hartmann, oscillatory Reynolds, and Damkohler, affect the flow velocity, transport coefficient, multi-dimensional concentration distributions, and transverse variation rate. Due to the strong magnetic field, the flow velocity and Taylor dispersivity are adversely affected and conspicuously reduced. Additionally, for large Damkohler numbers, the total dispersion coefficient and the Taylor dispersion coefficient both decrease. However, the longitudinal concentration distribution rises with the Hartmann number and partition coefficient. It is worth noting that in the presence of unequal boundary absorption, there is no occurrence of transverse symmetry in solute concentration at any given time. Controlling various processes of tracer dispersion in environmental systems, especially water purification and the chemical industry, may benefit from these intriguing findings.

A pore-scale numerical framework for solute transport and dispersion in porous media

Pore-scale modeling plays a crucial role in understanding and upscaling solute transport behavior in porous media. Direct simulation offers the highest fidelity in resolving pore-scale fluid flow and mass transfer, nevertheless, with unacceptable computational costs for practical applications. Pore network models (PNM), on the other hand, provide an efficient alternative but with reduced accuracy in representing transport dynamics. In this study, we propose a new framework of pore network models that ensures both accuracy and efficiency, which reproduces the pore-scale shear dispersion effect by utilizing the pore-scale shear dispersion coefficient to calculate the diffusive mass exchange rate between network elements. The coefficient is determined based on the extension of Taylor-Aris theory that expands the classical Taylor-Aris theory to encompass the pre-asymptotic regime. Additionally, the framework adopts a physically representative pore network, where the conduit length and volume of network elements are determined based on local resistance equivalence. After verifying its accuracy and reliability, we conduct a series of numerical cases on tube networks, sphere packs, and sand packs. The breakthrough curves and concentration profiles obtained from our new model show good agreement with direct simulation results and experimental data, while the simulation outcomes of the models that rely on the molecular diffusion coefficient or Taylor dispersion coefficient for local mass exchange may exhibit significant errors. We finally demonstrate that the significance of pore-scale shear dispersion on solute transport weakens for tube networks with increasing degrees of geometrical disorder. The proposed model provides an accurate and efficient numerical framework for the study of solute transport and dispersion in porous media.

On scalar transport in an oscillatory Couette–Poiseuille flow under the effects of heterogeneous and bulk chemical reactions: A multi-scale approach

This research presents an analytical solution to explore a two-dimensional concentration transport of solute in an oscillatory Couette–Poiseuille flow between two parallel plates in the presence of homogeneous and heterogeneous reactions. Mei's homogenization method up to second order approximation is used to find the multi-dimensional concentration distributions, namely, transverse concentration distribution, longitudinal concentration distribution, mean concentration distribution, Taylor dispersion coefficient, and the transverse uniformity simultaneously for three different flow conditions: steady, periodic, and the joint effect of steady and periodic Couette–Poiseuille flow for the first time. The distribution of transverse concentration of solute is studied due to its importance in oil lubrication and industrial applications. The transverse variation rate shows that the introduction of heterogeneous reactions cause transverse non-uniformity, but it is significant to note that homogeneous reaction has no effect on it. Furthermore, the maximum variation rate of the concentration cloud is obtained along the upstream and downstream directions when the boundary absorption is considered at steady and moving plates, respectively. To validate the present analytical model, a comparison is performed with the numerical solution and has achieved an excellent agreement. The outcomes of the present study may be helpful to develop a better understanding of the process of contamination and to prevent the pollution in the flow.

Flame stability under flow-induced anisotropic diffusion and heat loss

A two-dimensional model for premixed flames accounting for flow-enhanced diffusion or Taylor dispersion and heat loss is investigated. This is the first analytical study addressing the effect of Taylor dispersion on the thermo-diffusive instabilities of non-adiabatic flames. It is also the first numerical study coupling flame instability with Taylor dispersion. A linear stability analysis is carried out in the limit of infinite Zeldovich number β. This leads to a dispersion relation, generalising classical relations in the literature, and involving three parameters, l (the reduced Lewis number), p (the Taylor-dispersion coefficient which is proportional to the Peclet number), and κ (the heat loss coefficient). Stability diagrams are determined and their implications on the cellular and oscillatory instabilities are discussed. A Kuramoto–Sivashinsky type equation incorporating the parameters l, p and κ and characterising the flame dynamics in the weakly non-linear regime near the onset of the cellular instability is derived. The theoretical results demonstrate the ability of Taylor dispersion and heat loss to significantly affect the flame stability. In particular, the oscillatory instability is found to be promoted by an increase in κ and hampered by an increase in p. On the other hand, both p and κ have a destabilising effect in connection with the cellular instability. Also, the theory provides a formula predicting the typical size of cells first emerging from the cellular instability which is found to be a decreasing function of p.Numerical simulations are carried out illustrating and significantly extending the analytical findings. Particular attention is devoted to the influence of β. In particular, we reconcile apparent quantitative and sometimes qualitative discrepancies between the numerical and theoretical predictions, which are found to be more pronounced for larger values of p. Luckily, the asymptotic theory is found to be robust in the sense that its predictions are recovered numerically if β is taken large enough, although such predictions may be questionable for realistic values of β. In general, the effect of β on flame stability is found to be opposite to that of p: an increase in p or a decrease in β have a destabilising effect in connection with the cellular instability, and a stabilizing effect in connection with the oscillatory instability; both instabilities are promoted by an increase in κ.

Influence of Shear Displacement on Fluid Flow and Solute Transport in a 3D Rough Fracture

Abstract Fractured rocks in the subsurface are ubiquitous, and the dynamics of mass transfer in fractured rocks plays an important role in understanding the problem in engineering geology and environmental geology. In this study, the influence of shear displacement on fluid flow and solute transport in a 3D rough fracture was investigated. A 3D self-affine rough fracture was generated using the modified successive random addition (SRA) technology, and three sheared fractures with different shear displacements were constructed based on the mechanistic model. A direct numerical model based on the Navier-Stokes equation and the advection-diffusion equation was developed to solve the fluid flow and the solute transport. The results showed that shear displacement had a significant influence not only on the fluid flow but also on the solute transport. A global measure of the spatial variability of the flow velocity showed that the heterogeneity became weaker with decreasing shear displacement. All measured BTCs deviated from the Gaussian profile and exhibited the typical anomalous behaviors, such as the long tail and the early arrival. Although the best-fitted results of the advection-dispersion equation (ADE) model and mobile-immobile model (MIM) were generally consistent with those of the BTCs, the MIM was more capable than the ADE model for characterizing the shear-induced anomalous behavior of the BTCs. It was found that the mass exchange process between the immobile and mobile domains was enhanced in the sheared fractures while the fraction of the advection-dominant mobile domain decreased as the shear displacement increased. Furthermore, the deviation of the Taylor dispersion coefficient from the fitted dispersion coefficient by the ADE model and MIM in the sheared fractures was confirmed due to the influence of shear displacement.

Multi-scale approach to analyze the dispersion of solute under the influence of homogeneous and inhomogeneous reactions through a channel

The present study deduces an analytical solution to explore a two dimensional transport of solute concentration in a fluid flowing between two parallel plates in appearance of a homogeneous and first order inhomogeneous reactions. Mei's homogenization method is used to get the transverse concentration distribution up to third order approximation. Taylor dispersion model can only predict the longitudinal dispersion of mean concentration and this fact mainly focused by many researchers over the last two decades. Nowadays, due to its importance in environmental engineering and industrial applications, the spread of transverse concentration is quite significant. The outcomes of the investigation reveal that the Taylor dispersion coefficient decreases with the enhancement of both the homogeneous and inhomogeneous reactions. It is found that the reaction rates cause transverse non-uniformity of the solute cloud. However, the centroid of the concentration cloud moves when the inhomogeneous reaction is applied at any one or both of the channel plates. Interestingly, the centroid gradually shifts towards the upstream direction whenever reaction is taken at both the walls.

Laminar dispersion at low and high Peclet numbers in a sinusoidal microtube: Point-size versus finite-size particles

This paper adopts Brenner’s homogenization theory to investigate dispersion properties, over a wide range of Peclet values, of point-size and finite-size particles in sinusoidal cylindrical microchannels in the presence of a pressure-driven Stokes flow field. The periodic alternation of entropic barriers/traps can unexpectedly increase the effective finite-size particle velocity as well as decrease the effective dispersion coefficient for both point-size and finite-size particles, for large values of the radial Peclet number. While this phenomenon has a simple explanation for tracer particles, its understanding for finite-size particles is not trivial and goes through the analysis of the localization feature of the equilibrium unit-cell particle density w0(x) and how this spatial nonuniformity impacts upon the effective particle velocity and on the solution of the so-called b field, controlling the large scale axial dispersion coefficient. Unfortunately, dispersion reduction cannot be exploited for the sake of the separation of particles having different radii because the separation performance of a hydrodynamic sinusoidal column turns out to be worse than that of a standard straight column for experimentally feasible Peclet values. Interesting analytical results for long-wavelength sinusoidal channels are obtained by a long-wave asymptotic expansion. Both zero-order and first-order terms for the asymptotic expansion of the w0(x) measure and of the b field are obtained, thus exploring a wide range of Peclet values and deriving an analytical expression for the Taylor dispersion coefficient.

When can the local advection–dispersion equation simulate non-Fickian transport through rough fractures?

Non-Fickian solute transport is observed across many scales, which has motivated development of numerous non-Fickian-based models. Assuming that local fluid flow was estimable from the Modified Local Cubic Law, this study determined whether the local ADE better simulated non-Fickian transport through rough (3-D) fractures when local dispersion was described using either the Taylor dispersion coefficient (DTaylor) or the molecular diffusion coefficient (Dm). The assessment was based on how well the local ADE compared to particle-tracking solutions for solute transport across a range of Peclet numbers (Pe) through two simulated fractures. Even though the local ADE is based on local Fickian transport processes, it was able to reproduce non-Fickian transport characteristics through these heterogeneous fractures. When supplying DTaylor to the local ADE, it extended the applicability of the local ADE to a threshold of Pe < 450; using Dm, the local ADE was only accurate when Pe < 70. No differences were observed for small Pe. Therefore, our recommendation is to always use DTaylor in the local ADE to capture non-Fickian transport so long as the Pe threshold is not exceeded.

Dispersion in steady and time-oscillatory two-dimensional flows through a parallel-plate channel

A multiple-scale perturbation theory is developed to analyze the advection-diffusion transport of a passive solute through a parallel-plate channel. The fluid velocity comprises a steady and a time-oscillatory component, which may vary spatially in the transverse and streamwise directions, and temporally on the fast transverse diffusion timescale. A long-time asymptotic equation governing the evolution of the transverse averaged solute concentration is derived, complemented with Taylor dispersion coefficients and advection speed corrections that are functions of the streamwise coordinate. We demonstrate the theory with a two-dimensional flow in a channel comprising alternating shear-free and no-slip regions. For a steady flow, the dispersion coefficient changes from zero to a finite value when the flow transitions from plug-like in the shear-free section to parabolic in the no-slip region. For an oscillatory flow, the dispersion coefficient due to an oscillatory flow can be negative and two orders of magnitude larger than that due to a steady flow of the same amplitude. This motivates us to quantify the relative magnitude of the steady and oscillatory flow such that there is an overall positive dispersion coefficient necessary for an averaged (macrotransport) equation. We further substitute the transport coefficients into the averaged equation to compute the evolution of the concentration profile, which agrees well with that obtained by solving the full two-dimensional advection-diffusion equation. In a steady flow, we find that while the shear-free section suppresses band broadening, the following no-slip section may lead to a wider band compared with the dispersion driven by the same pressure gradient in an otherwise homogeneously no-slip channel. In an unsteady flow, we demonstrate that a naive implementation of the macrotransport theory with a (localized) negative dispersion coefficient will result in an aphysical finite time singularity (or “blow-up solution”), in contrast to the well-behaved solution of the full advection-diffusion equation.

Upscaling of Mixing‐Limited Bimolecular Chemical Reactions in Poiseuille Flow

AbstractWe consider the fast irreversible bimolecular chemical reaction in the Poiseuille flow through a channel, in which A displaces B. This system allows to systematically study the impact of the interaction of interface deformation and diffusion on mixing and reactive transport. At early times, the reaction is diffusion controlled. With increasing time, advection begins to dominate and we find enhanced reaction efficiency due to the deformation of the interface between the two reactants. For times larger than the characteristic diffusion time across the channel, mixing and reaction are quantified by the Taylor dispersion coefficient. Predictions based on Taylor dispersion may significantly overestimate the reaction efficiency at preasymptotic times, when the system is characterized by incomplete mixing. This type of behaviors of incomplete mixing and reaction have been observed in heterogeneous systems across different scales. Channel flow allows to study them in detail for a well‐controlled system. We propose a dispersive lamella approach based on the concept of effective dispersion which accurately predicts the full evolution of the product mass. Specifically, this approach captures the impact of interface deformation and diffusive coalescence, which marks the transition to the Taylor regime. It gives insight into the mechanism of incomplete mixing and its consequences for reactive transport in more general porous media flows.

Indicators for evaluating uncertainties of solute concentration prediction in wetland flows

Abstract Solute transport in wetland flows is an important process to understand for agricultural practices, providing essential information to assist in decision making and regulation for both cases of agricultural water contamination and agricultural pollution. Recent study has suggested that in the application of the one-dimensional Taylor dispersion model for solute concentration distribution in wetlands, uncertainties can arise even when contaminants are initially released at the same streamwise location. In this paper, we present an analytical study of instantaneous point-source release of solute in a wetland flow dominated by bank wall effects. The movement of the solute centroid and the long-term asymptotic Taylor dispersion coefficient are determined by the Aris concentration moment method, which are required for quantifying the streamwise distribution of the mean concentration and the transverse concentration distribution profiles. It is shown that the additional longitudinal displacement serves as a key indicator revealing the uncertainties of concentration distribution caused by different lateral positions of the contaminant release. More indicators including the lateral concentration distribution and the relative difference of the concentration are analyzed in detail. With given physical parameters, simple applications are provided to illustrate the streamwise transport of the solute plume centroid and the evolution of the additional longitudinal displacement affected by the bank wall effects.

Simulation of solute transport through heterogeneous networks: analysis using the method of moments and the statistics of local transport characteristics

We used a time domain random walk approach to simulate passive solute transport in networks. In individual pores, solute transport was modeled as a combination of Poiseuille flow and Taylor dispersion. The solute plume data were interpreted via the method of moments. Analysis of the first and second moments showed that the longitudinal dispersivity increased with increasing coefficient of variation of the pore radii CV and decreasing pore coordination number Z. The third moment was negative and its magnitude grew linearly with time, meaning that the simulated dispersion was intrinsically non-Fickian. The statistics of the Eulerian mean fluid velocities {hat{{boldsymbol{u}}}}_{{boldsymbol{i}}}, the Taylor dispersion coefficients {hat{{boldsymbol{D}}}}_{{boldsymbol{i}}} and the transit times {hat{{boldsymbol{tau }}}}_{{boldsymbol{i}}} were very complex and strongly affected by CV and Z. In particular, the probability of occurrence of negative velocities grew with increasing CV and decreasing Z. Hence, backward and forward transit times had to be distinguished. The high-τ branch of the transit-times probability curves had a power law form associated to non-Fickian behavior. However, the exponent was insensitive to pore connectivity, although variations of Z affected the third moment growth. Thus, we conclude that both the low- and high-τ branches played a role in generating the observed non-Fickian behavior.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme.

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Effect of Electric Field on Dispersion of a Solute in an MHD Flow through a Vertical Channel With and Without Chemical Reaction

The longitudinal dispersion of a solute between two parallel plates filled with two immiscible electrically conducting fluids is analyzed using Taylor’s model. The fluids in both the regions are incompressible and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions are matched at the interface using suitable matching conditions. The flow is accompanied by an irreversible first-order chemical reaction. The effects of the viscosity ratio, pressure gradient and Hartman number on the effective Taylor dispersion coefficient and volumetric flow rate for an open and short circuit are drawn in the absence and in the presence of chemical reactions. As the Hartman number increases the effective Taylor diffusion coefficient decreases for both open and short circuits. When the magnetic field remains constant, the numerical results show that for homogeneous and heterogeneous reactions, the effective Taylor diffusion coefficient decreases with an increase in the reaction rate constant for both open and short circuits.

Axial dispersion in weakly turbulent flows of yield stress fluids

We analyze turbulent flows of shear-thinning yield stress fluids in both pipe and channel geometries. We lay down a consistent procedure for hydraulic calculation of Herschel-Bulkley fluids; i.e. finding the relationship between the mean velocity and the wall shear stress. We show that for weakly turbulent flows it is necessary to include an analysis of wall layers in studying dispersion. In pipe flows, we observe an O(10) increase in Taylor dispersion coefficients, compared to highly turbulent values. This arises from a combination of large velocity and small turbulent dispersivity, acting over a wall layer that can represent ≳ 20% of the pipe area. In channel flows the wall layer effect is more modest, but still represents an O(1) increase in Taylor dispersion coefficient. The preceding effects are negated for small power law index, due to rapid reduction of the wall layer, and are observed to reduce modestly as the yield stress increases.

Analytical solutions for species transport in a T‐sensor at low peclet numbers

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

Analytical and numerical investigation of the advective and dispersive transport in Herschel–Bulkley fluids by means of a Lattice–Boltzmann Two-Relaxation-Time scheme

Dispersion of a passive tracer in a tube has been extensively studied in the case of Newtonian fluids since the pioneer work of Taylor (1953). However, the influence of more complex rheological behavior on the transport has only be scarcely investigated. Non-Newtonian fluids are increasingly used in the industry and transport in this type of fluid merits therefore thorough investigations. An example of industrial application is Enhanced Oil Recovery, that is based on the injection of non-Newtonian fluids as polymers or surfactant solutions in porous media, which are then submitted to dispersion phenomena.This work deals with transport of a passive tracer in shear thinning fluids with and without yield stress whose constitutive behaviors are representative of a large number of industrial fluids. We focus on transport in capillary tubes, essential for the understanding of dispersion in porous media. Transport is investigated at different time scales by solving the advection–diffusion equation using a Two-Relaxation-Time Lattice–Boltzmann method. We also derived an analytical expression of the Taylor dispersion coefficient for a large range of fluid rheologies. Dispersion coefficients of all fluids described by the Herschel–Bulkley model can now be determined. Analytical and numerical results are compared and very good accordance is obtained.We discuss the characteristic time scales of the transport before reaching steady state as a function of fluid rheology and Péclet number. We show that the time to reach the dispersive regime is nearly independent of the fluid rheology whereas the effective dispersion coefficient is a function of the rheological parameters.We also present the displacement distribution of the tracer molecules (propagators) as a function of time and show that they are strongly conditioned by the fluid rheology. Indeed, propagators give valuable information on the temporal evolution of the concentration profile towards the stationary Taylor regime.

Depletion of cross‐stream diffusion in the presence of viscoelasticity

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

Taylor dispersion of colloidal particles in narrow channels

We use a mesoscopic particle-based simulation technique to study the classic convection-diffusion problem of Taylor dispersion for colloidal discs in confined flow. When the disc diameter becomes non-negligible compared to the diameter of the pipe, there are important corrections to the original Taylor picture. For example, the colloids can flow more rapidly than the underlying fluid, and their Taylor dispersion coefficient is decreased. For narrow pipes, there are also further hydrodynamic wall effects. The long-time tails in the velocity autocorrelation functions are altered by the Poiseuille flow.

Axial diffusion effect on concentration dispersion

This work presents an analytical attempt to illustrate the effect of axial diffusion on concentration dispersion in packed tube flows. The concentration moment method is applied to derive the analytical solution for time-dependent Taylor dispersion coefficient. With the increase in the packing parameter α as a damping factor, the concentration dispersion is characterized by three modes: (I) the shear-induced dispersion dominated mode, with dispersion coefficient determined by α; (II) the transition mode; and (III) the diffusion dominated mode, with dispersion coefficient determined by Péclet number Pe. In contrast to the usually negligible effects of axial diffusion for dispersion in pure fluid flows even at a relatively small Pe, axial diffusion with typical α plays an important role for packed media flows even with large Pe.