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A theoretical analysis is developed to investigate the effects of gas expansion due to heat release on unsteady diffusion flames evolving in a pipe flow in which the mixing of reactants is controlled by Taylor's dispersion processes thereby extending a previously developed theory based on the thermo-diffusive model. It is first shown that at times larger than radial diffusion times, the pressure gradient induced by the gas expansion is, in the first approximation, small in comparison with the prevailing pressure gradient driving the flow, indicating that corrections to the background velocity profile are small. The corrections to the velocity components along with the leading-order mixing variables such as the concentrations, temperature and density are solved for a Burke–Schumann flame. Due to the dependence of the effective Taylor diffusion coefficients on the gas density, quantitative and sometimes qualitative departures in predictions from the thermo-diffusive model are observed.

We investigate the effect of Taylor dispersion on the thermo-diffusive instabilities of premixed flames. This is a physically interesting and analytically tractable problem within a relatively unex...

The two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube and a concentric circular annulus. Here, we study peristaltic flow in a non-axisymmetric annular tube: in this case, the flow is three-dimensional, with motions in the azimuthal direction. This type of geometry is motivated by experimental observations of the pulsatile flow of cerebrospinal fluid along perivascular spaces surrounding arteries in the brain, which is at least partially driven by peristaltic pumping due to pulsations of the artery. These annular perivascular spaces are often eccentric and the outer boundary is seldom circular: their cross-sections can be well matched by a simple, adjustable model consisting of an inner circle (the outer wall of the artery) and an outer ellipse (the outer edge of the perivascular space), not necessarily concentric. We use this geometric model as a basis for numerical simulations of peristaltic flow: the adjustability of the model makes it suitable for other applications. We concentrate on the general effects of the non-axisymmetric configuration on the flow and do not attempt to specifically model perivascular pumping. We use a finite-element scheme to compute the flow in the annulus driven by a propagating sinusoidal radial displacement of the inner wall. Unlike the peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional: azimuthal pressure variations drive an oscillatory flow in and out of the narrower gaps, inducing an azimuthal wiggle in the streamlines. We examine the dependence of the flow on the elongation of the outer elliptical wall and the eccentricity of the configuration. We find that the time-averaged volumetric flow is always in the same direction as the peristaltic wave and decreases with increasing ellipticity or eccentricity. The additional shearing motion in the azimuthal direction will increase mixing and enhance Taylor dispersion in these flows, effects that might have practical applications.

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.

The Richardson-scaling law states that the mean square separation of a fluid particle pair grows according to t3 within the inertial range and at intermediate times. The theories predicting this scaling regime assume that the pair separation is within the inertial range and that the dispersion is local, which means that only eddies at the scale of the separation contribute. These assumptions ignore the structural organization of the turbulent flow into large-scale shear layers, where the intense small-scale motions are bounded by the large-scale energetic motions. Therefore, the large scales contribute to the velocity difference across the small-scale structures. It is shown that, indeed, the pair dispersion inside these layers is highly non-local and approaches Taylor dispersion in a way that is fundamentally different from the Richardson-scaling law. Also, the layer's contribution to the overall mean square separation remains significant as the Reynolds number increases. This calls into question the validity of the theoretical assumptions. Moreover, a literature survey reveals that, so far, t3 scaling is not observed for initial separations within the inertial range. We propose that the intermediate pair dispersion regime is a transition region that connects the initial Batchelor- with the final Taylor-dispersion regime. Such a simple interpretation is shown to be consistent with observations and is able to explain why t3 scaling is found only for one specific initial separation outside the inertial range. Moreover, the model incorporates the observed non-local contribution to the dispersion, because it requires only small-time-scale properties and large-scale properties.

Passive micromixers are of great importance in biomedical engineering (lab-on-chips) and chemical processing (microreactors) fields. Various hydrodynamic principles such as lamination, flow separation, and chaotic advection were employed previously to improve mixing in passive mixers. However, mixing enhancement due to velocity gradients in the flow, which is known as the Taylor dispersion effect, has been seldom studied. In the present study, thin rectangular slabs oriented in the flow direction are placed in the mixing channel of a T-micromixer. The thin rectangular slabs are referred to as Taylor Dispersion Obstructions (TDOs) as they are designed to create velocity gradients in the flow. The mixing performance of T-micromixer with and without TDOs is estimated in the Re range of 0 to 350. It is observed that there is no effect on mixing in the presence of TDOs in the low Re (0 < Re < 100), as the velocity gradients created in the flow are considerably small. The vortex formed in the flow for Re of 100 to 220 damped the gradients of velocity created in the flow (due to the presence of TDOs) which resulted in negligible improvement in the quality of mixing. However, considerable enhancement in mixing performance is obtained at high Re (250 to 350) with the presence of TDOs in the mixer. The increase in inertial effects at higher Recreated larger gradients of velocity near the walls of TDOs and mixing channel walls and thereby a significant enhancement in mixing performance is obtained due to Taylor dispersion.

Taylor dispersion is used to measure the binary mutual diffusion coefficient (D) of aqueous solutions of sodium salicylate (NaSal), a non-steroidal anti-inflammatory drug (NSAID). The D° value estimated by extrapolation to zero NaSal concentration is used to calculate the limiting mobility of the Sal− ion for comparison with the value determined previously from conductivity data. Salt effects on NSAID diffusion are studied by measuring the ternary mutual diffusion coefficients (Dik) of aqueous NaSal(C1) + NaCl(C2) solutions, including results for the diffusion of NaSal in physiological saline solutions with C2 = 0.15 mol dm−3. As the NaCl:NaSal ratio increases, NaSal diffusion coefficient D11 changes from the binary diffusion coefficient of aqueous NaSal (a weighted average of the Na+ and Sal− diffusion coefficients) to the tracer diffusion coefficient of the Sal− ion in NaCl solutions. Coupled diffusion in the solutions is analysed by using Nernst-Planck equations to calculate the fluxes of ions migrating in the electric field (diffusion potential) generated by NaSal and NaCl concentration gradients.

We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the walls become important. We provide a simple and general formula for the effective diffusion constant along the channel as well as the first non-trivial finite time correction for arbitrary flows along the channel, arbitrary interaction potentials with the walls and arbitrary expressions for the diffusion tensor. The formula are in particular amenable to a straightforward numerical implementation, rendering them extremely useful for comparison with experiments. We present a number of applications, notably for systems which have parabolically varying diffusivity profiles, to systems with attractive interactions with the walls as well as electroosmotic flows between plates with differing surface charges within the Debye-H\"uckel approximation., Comment: 33 pages, 7 figures

Modeling contaminant transport in fractured-rock matrix systems often approximates the effect of the parabolic flow field in the fractures (i.e., Poiseuille flow) on transport by adding a dispersion term to the uniform flow field. In this study, an analytical solution is derived to model contaminant transport in a parallel-plate fractured-rock matrix that explicitly simulates Poiseuille flow in the fractures, eliminating the need for the dispersion approximation. In addition to simulating Poiseuille flow in the fracture, the contaminant transport model developed here includes: (1) two-dimensional contaminant diffusion in the fractures and matrix, (2) first-order decay in the aqueous phase, and (3) rate-limited sorption onto matrix solids. It should be noted, however, that this model, much like the commonly employed Taylor dispersion approximation, neglects macro dispersion, thereby limiting the model’s applicability to systems having wide fracture apertures with extremely high flow velocities ( P e > 104). Model equations are analytically solved in the Laplace domain and numerically inverted. In addition, analytical expressions for the zeroth, first, and second spatial moments of the concentration profiles along the fractures are derived for both the new Poiseuille flow model as well as a model that approximates the effect of Poiseuille flow on transport by using a dispersion term. The first and second moment expressions are used to quantify how well the dispersion term approximates the effect of Poiseuille flow. Simulations confirm that the dispersion approximation will be adequate for natural fractures at long times. However, if a modeler is concerned with short-time transport behavior or transport behavior in systems with relatively wide-aperture fractures and high groundwater velocities where macro dispersion can be ignored, such as may be found at engineered geothermal systems and carbon capture and storage sites, there may be significant differences between model simulations that explicitly incorporate Poiseuille flow and those that approximate Poiseuille flow with a dispersion term. The model presented here allows the modeler to analytically quantify these differences, which, depending on the modeling objective, may cause the dispersion approximation to be inadequate. Simulations were also run to examine the effect of adsorption rate on remediation of fractured-rock matrix systems. It was shown that moderate adsorption rate constants could lead to very long remediation times, if remediation success is quantified by achieving low concentrations within the fracture.

Transport of micro-organisms in confined flows can be characterized by a one-dimensional overall dispersion mechanism, of importance to various biotechnological applications. Based on Brenner’s generalized Taylor dispersion theory, an overall dispersion model is analytically studied in the present work for a dilute suspension of active particles in confined unidirectional flows. With the confined section of the channel and the swimming orientation space taken together as the local space and the longitudinal coordinate standing for the one-dimensional global space, this model is analytically accurate and possessed of wide adaptability in terms of the swimming Péclet number. The Robin boundary condition is introduced to account for wall accumulation of active particles, and compared with a typical reflection boundary condition. Complications associated with the boundary conditions for analytical derivation are removed respectively by a decomposition of the distribution function and an extension of the flow field. Interesting solutions are concretely found and intensively illustrated. Detailed case studies on the transport of spherical and rod-like particles to illustrate the dispersion mechanism are presented with respect to a Couette flow and a plane Poiseuille flow. Associated with the local distribution of particles, extensive descriptions are given for the dynamical system behaviours such as accumulation near both stable points/lines and boundaries, symmetric polarization structure, closed orbits, trapping effect, nematic alignments and bimodalization of swimming direction. For spherical particles, the accumulation is shown leading to a reduction of the overall dispersivity in both of the flows, while for rod-like active particles in the Couette flow, the accumulation can result in an enhancement of dispersion, due to the nematic alignments of particles towards streamlines.

Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to $1/\nu$, which is much faster than what would be produced by the static fluid if its viscosity is $0 < \nu \ll 1$. This phenomenon is analyzed rigorously using the linear PDE governing the evolution of the solute. It is shown that the solution can be split into two pieces, an approximate solution and a remainder term. The approximate solution is governed by an infinite-dimensional system of ODEs that possesses a finite-dimensional center manifold, on which the dynamics correspond to diffusion at a rate proportional to $1/\nu$. The remainder term is shown to decay at a rate that is much faster than the leading order behavior of the approximate solution. This is proven using a spectral decomposition in Fourier space and a hypocoercive estimate to control the intermediate Fourier modes., Comment: 37 pages, 0 figures

Fully resolved simulations of flow and mass transfer in a unit cell of structured open-cell foam catalysts are presented. Numerical studies are conducted on a uniform three-dimensional Cartesian grid where the fluid-solid interface coupling is enforced via a sharp interface Immersed Boundary technique. Several validation cases for the numerical method are presented followed by extensive calculations to quantify hydrodynamic dispersion in open-cell foams. In our study five different porosities of the idealized foam structure, represented by the spatially periodic Kelvin’s unit cell, were considered. Dimensionless dispersion coefficients were calculated for varying Peclet numbers and flow directions using volume-averaging theory. Our numerical studies indicate that Taylor dispersion is the dominant mechanism for structured porous media in the Darcy-Brinkman flow regime.

The integration of Taylor dispersion analysis (TDA) into mobility capillary electrophoresis allows protein separation, effective charge and hydrodynamic radius measurements., Measuring the conformations and effective charges of proteins in solution is critical for investigating protein bioactivity, but their rapid analysis remains a challenging problem. Here we report a mobility capillary electrophoresis (MCE) based method for the rapid analysis of protein stereo-structures and effective charges in different solution environments. With the capability of mixture separation, MCE measures the hydrodynamic radius of a protein through Taylor dispersion analysis and its effective charge through ion mobility analysis. The experimental results acquired from MCE are then utilized to restrain molecular dynamics simulations, so that the most probable conformation of that protein can be obtained. As proof-of-concept demonstrations, the charge states and structures of five proteins were analyzed under close to native environments. The conformation transitions and charge state variations of bovine serum albumin and lysozyme under different pH conditions were also investigated. This method is promising for high-throughput protein analysis, which could potentially be coupled with mass spectrometry for investigating protein stereo-structures and functions in top-down proteomics.

Associated with Taylor dispersion, in this paper we analyze how the vertical position of a point-source solute release will affect the transport process in laminar open channel flow, through obtaining and applying analytical solution by the two-scale perturbation analysis (Wu and Chen, 2014, J. Fluid Mech., 740, 196–213), which is verified and supported by results from numerical simulations. Based on multi-dimensional spatial concentration distribution of the solute plume, we resort to the previously proposed criterion for identifying the stage of solute transport characterized by the dispersion-dominated (Taylor dispersion) regime, focusing on the relative uniformity of concentration distribution across a given family of curved surfaces (Wu et al., 2016, Sci. Rep., 6, 20556). The most important finding is that for the solute transport transition into the dispersion-dominated regime, the necessary time is about 50% more for the case of solute release at free water surface compared with that at the channel bed, which is substantial under typical physical parameters. Other effects of release position include affecting the displacement of the solute plume centroid, the value of the maximum mean concentration, and non-Gaussian properties regarding the form of the streamwise distribution of the mean concentration.

The present article discusses the solute transport process in unsteady laminar blood flow through\ud a non-Darcy porous medium, as a model for drug movement in blood vessels containing deposits.\ud The Darcy-Brinkman-Forchheimer drag force formulation is adopted to mimic a sparsely packed\ud porous domain, and the vessel is approximated as an impermeable cylindrical conduit. The\ud conservation equations are implemented in an axisymmetric system (R,Z) with suitable boundary\ud conditions, assuming constant tortuosity and porosity of the medium. Newtonian flow is assumed,\ud which is physically realistic for large vessels at high shear rates. The velocity field is expanded\ud asymptotically, and the concentration field decomposed. Advection and dispersion coefficient\ud expressions are rigorously derived. Extensive visualization of the influence of effective Péclet\ud number, Forchheimer number, reaction parameter on velocity, asymptotic dispersion coefficient,\ud mean concentration, and transverse concentration at different axial locations and times are\ud provided. Increasing reaction parameter and Forchheimer number both decrease the dispersion\ud coefficient, although the latter exhibits a linear decay. The maximum mean concentration is\ud enhanced with greater Forchheimer numbers, although the centre of the solute cloud is displaced\ud in the backward direction. Peak mean concentration is suppressed with the reaction parameter,\ud although the centroid of the solute cloud remains unchanged. Peak mean concentration\ud deteriorates over time since the dispersion process is largely controlled by diffusion at the large\ud time, and therefore the breakthrough curve is more dispersed. A similar trend is computed with\ud increasing Péclet number (large Péclet numbers imply diffusion-controlled transport). The\ud computations provide some insight into a drug (pharmacological agents) reacting linearly with\ud blood.

Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For active dispersion process in confined flows, previous analytical studies focused on the long-time asymptotic values of dispersion characteristics. Only several numerical studies preliminarily investigated the temporal evolution. Extending recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1--34; J. Fluid Mech., vol. 899, 2020, A18), this work makes the first analytical attempt to investigate the transient process. The temporal evolution of the local distribution in the confined-section--orientation space, drift, dispersivity and skewness, is explored based on moments of distributions. We introduce the biorthogonal expansion method for solutions because the classic integral transform method for passive transport problems is not applicable due to the self-propulsion effect. Two types of boundary condition, the reflective condition and the Robin condition for wall accumulation, are imposed respectively. A detailed study on spherical and ellipsoidal swimmers dispersing in a plane Poiseuille flow demonstrates the influences of the swimming, shear flow, wall accumulation and particle shape on the transient dispersion process after a point-source release. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Though the wall accumulation significantly affects the evolution of the local distribution and the drift, the time scale to reach the Taylor regime is not obviously changed. The shear-induced alignment of ellipsoidal particles can enlarge the dispersivity but has less influence on the drift and the skewness., 34 pages,21 figures

The effect of traces of ethanol in supercritical carbon dioxide on the mixture's thermodynamic properties is studied by molecular simulations and Taylor dispersion measurements. This mixture is investigated along the isobar p = 10 MPa in the temperature range between T = 304 and 343 K. Along this path, the mixture undergoes two transitions: First, the Widom line is crossed, marking the transition from liquid-like to gas-like conditions. A second transition occurs from the supercritical gas-like domain to a subcritical gas. The Widom line crossover entails inflection points for most of the studied properties, i.e. density, enthalpy, shear viscosity, Maxwell–Stefan and intradiffusion coefficients. On the other hand, the transition between the super- and subcritical regions is found to be generally smooth, an observation that is qualitatively confirmed by experimental Taylor dispersion measurements. Dedicated atomistic simulations show the presence of microheterogeneities due to ethanol self-association along the investigated path, which lead to the mixture's anomalous behavior in its extended critical region.

While near-surface geothermal energy applications for the heating and cooling of buildings have been in use for decades, their practical adoption is limited by the energy transport rates through soils. Aquifers provide a means to use convective heat transport to improve heat transfer between the building and the aquifer. However, the solid matrix in the aquifer is carbonaceous in nature, and calcification prevention techniques in the heat exchangers for the building also lead to dissolution of the aquifer matrix. Due to the Arrhenius nature of the reaction, dissolution rates may decrease with increasing temperature. An effective medium model is derived for the energy, calcium species, and fluid transport through a dynamic calcite porous medium which undergoes a reaction between the matrix and fluid. To better discern how these competing phenomena affect thermal transport in the aquifer, a two-dimensional Cartesian system is considered, where the vertical axis is parallel to the borehole axis, and flow is in the horizontal direction. An effective medium model is derived for the energy, calcium species, and fluid transport through a dynamic calcite porous medium which undergoes a reaction between the matrix and fluid. Since the fluid velocity decays algebraically with radial distance from the borehole axis, two flow regimes are considered. In one regime, far from the borehole where flow rates are small, conductive thermal transport acts faster than the species transport, leading to a case where precipitation dominates and regions of the smallest porosity contract to limit energy recovery. In regions with larger porosity, moderate advection of the species is sufficient to prevent significant pore closures over the time scale of exploration. The second regime, closer to the borehole, larger flow rates reduce species concentrations sufficiently to dissolve the solid phase between pores. In this second regime, Taylor dispersion effects in both energy and species transport compete, but thermal conduction acts more slowly than advection, promoting dissolution. The critical limitation in modeling the long-term evolution of the aquifer structure is the in situ dissolution rate.

In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218-220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe. Such a plume is prone to an instability to form blips. This work models the gyrotactic plume as a steady parallel basic state and its subsequent breakdown into blips as an instability, employing both the Generalised Taylor Dispersion (GTD) theory and the Fokker-Planck model for comparison. Upon solving for the basic state, it is discovered that the steady plume solution undergoes sophisticated bifurcations. When there is no net flow, there exists a non-trivial solution of the plume structure other than the stationary uniform suspension, stemming from a transcritical bifurcation with the average cell concentration. When a net downflow is prescribed, there exists a cusp bifurcation. Furthermore, there is a critical concentration, at which the cell concentration at the centre would blow up for the GTD model. The subsequent stability analysis using the steady plume solution shows that the Fokker-Planck model is inconsistent with what was experimentally observed, as it predicts stabilisation of axisymmetric blips at high concentration of the plume and destabilisation of the first non-axisymmetric mode at low flow rates.

We consider the injection of a buoyant low viscosity fluid into an aquifer saturated with a higher viscosity fluid. The nose region of the flow, where the thickness of the injected fluid is less than the thickness of the aquifer, grows in proportion to time and as a result fluid continually migrates further into the nose where it has a progressively smaller vertical extent. We explore how the flow in the nose influences the migration of a pulse of tracer. The growth of the nose stretches a pulse of tracer of initial length, , longitudinally to have a length proportional to , where is the nose entry time. Diffusion acts at the same rate and the combination of the two processes results in an tracer spreading longitudinally with a length proportional to at long times after entering the nose, where D is the coefficient of diffusion. The results are generalised to consider the case in which the permeability in the aquifer varies with depth. At early times, the tracer is sheared. As the tracer migrates into continually thinner regions of the growing nose, the permeability contrast sampled by the tracer rapidly decays. The role of the shear becomes dominated by the stretching of the nose and ultimately the late-time behaviour is as in a uniform aquifer. However, the effective pulse length of the tracer upon asymptoting to the stretching regime is now given by , where is the magnitude of the shear. The spreading in the stretching regime then has a length scale of , which may be much faster than in the case of a uniform aquifer. If the diffusion is sufficiently fast, there may be an intermediate regime in which Taylor dispersion is important prior to the stretching dominating.

The extended method of moments (EMM) is elaborated in recursive algorithmic form for the prediction of the effective diffusivity, the Taylor dispersion dyadic and the associated longitudinal high-order coefficients in mean-concentration profiles and residence-time distributions. The method applies in any streamwise-periodic stationary d-dimensional velocity field resolved in the piecewise continuous heterogeneous porosity field. It is demonstrated that EMM reduces to the method of moments and the volume-averaging formulation in microscopic velocity field and homogeneous soil, respectively. The EMM simultaneously constructs two systems of moments, the spatial and the temporal, without resorting to solving of the high-order upscaled PDE. At the same time, the EMM is supported with the reconstruction of distribution from its moments, allowing to visualize the deviation from the classical ADE solution. The EMM can be handled by any linear advection-diffusion solver with explicit mass-source and diffusive-flux jump condition on the solid boundary and permeable interface. The prediction of the first four moments is decisive in the optimization of the dispersion, asymmetry, peakedness and heavy-tails of the solute distributions, through an adequate design of the composite materials, wetlands, chemical devices or oil recovery. The symbolic solutions for dispersion, skewness and kurtosis are constructed in basic configurations: diffusion process and Darcy flow through two porous blocks in “series”, straight and radial Poiseuille flow, porous flow governed by the Stokes–Brinkman–Darcy channel equation and a fracture surrounded by penetrable diffusive matrix or embedded in porous flow. We examine the moments dependency upon porosity contrast, aspect ratio, Peclet and Darcy numbers, but also for their response on the effective Brinkman viscosity applied in flow modeling. Two numerical Lattice Boltzmann algorithms, a direct solver of the microscopic ADE in heterogeneous structure and a novel scheme for EMM numerical formulation, are called for validation of the constructed analytical predictions.

The Taylor dispersion of a solute for composite porous medium between two parallel plates with first-order chemical reaction is studied analytically. The fluids in both the regions are incompressible and the transport properties are assumed to be constant. The results are shown graphically for various values of viscosity ratio, pressure gradient and porous parameter on the effective dispersion coefficient and volumetric flow rate. It is found that for both homogeneous and heterogeneous chemical reactions, the effective dispersion coefficient decreases as porous parameter increases. The validity of the results obtained for composite porous media is verified by comparison with the available porous medium results for one fluid model and good agreement is found. Also two fluid model in the absence of porous matrix is compared with the available one fluid model results and the values tally very well.Keywords: Taylor dispersion, immiscible fluids, horizontal channel, porous medium, chemical reaction.

We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse components of this tensor with respect to the direction of averaged bubble rise velocity in a zero mixture velocity frame of reference, we focus on the convective contribution thereof, this being expected to be dominant in commonly encountered bubbly flows. We first extend the theory of Kochet al.(J. Fluid Mech., vol. 200, 1989, pp. 173–188) (which is for dispersion in fixed beds of solid particles under Stokes flow) to account for weak inertial effects in the case of ordered suspensions. In the limits of low and of high Péclet number, including the inertial effect of the flow does not affect the scaling of the effective diffusivity with respect to the Péclet number. These results are confirmed by direct numerical simulations performed in different flow regimes, for spherical or very deformed bubbles and from vanishingly small to moderate values of the Reynolds number. Scalar transport in arrays of freely rising bubbles is considered by us subsequently, using numerical simulations. In this case, the dispersion is found to be convectively enhanced at low Péclet number, like in ordered arrays. At high Péclet number, the Taylor dispersion scaling obtained for ordered configurations is replaced by one characterizing a purely mechanical dispersion, as in random media, even if the level of disorder is very low.

The liquid-gas and liquid-liquid Taylor flows in circular capillary tubes are numerically studied using a mathematical model developed in the frame of Arbitrary-Lagrangian–Eulerian (ALE), where the interface is tracked so that the important interfacial curvature and forces for Taylor flow can be accurately estimated. It is found that for liquid-gas Taylor flow, thin film thickness predicted by the present numerical model agrees very well with the benchmark experimental data both in visco-capillary and visco-inertia flow regimes. Thin film thicknesses decreases first and then increases as Reynolds number ( Re ) increases at relatively large capillary numbers ( Ca ). With the increase of Ca , classical pressure drop correlations become inaccurate, because of strong internal circulation inside liquid slug, the appearance of waves at rear meniscus, as well as the deviation from semi-spherical shape of head meniscus. For liquid-liquid flow, when Ca is small, thin film thickness correlations for liquid-gas flow can be used since the disperse phase has negligible effects, while when Ca is relatively large, the viscosity ratio and density ratio of continuous phase to disperse phase become two additional influencing factors. The larger are the viscosity ratio and the density ratio, the thicker is the film thickness. Different from stagnant thin film in liquid-gas flow, the flow in thin film of liquid-liquid flow is not stagnant and has a large contribution to pressure drop. The numerical model developed in this study is shown to be a powerful and accurate tool to study both the liquid-gas and liquid-liquid Taylor flows.

Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

We present a detailed derivation of a practical two-dimensional model for turbulent and mixed regimes in narrow annular displacement flows, such as are found during the primary cementing of oil and gas wells. Such mixed cross regimes, including those in which different regimes exist in the same annular cross section, are relatively common in primary cementing. The modelling approach considers scaling based on the disparity of length-scales, which allows a narrow-gap averaging approach to be effective. With respect to the momentum equations, the leading-order equations correspond to a turbulent shear flow in the direction of the modified pressure gradient. This leads to a nonlinear elliptic problem that is the natural extension of the laminar displacement model in Bittleston et al. (J Eng Math 43:229–253, 2002). The mass transport equations that model the miscible displacement are however quite different. To leading-order turbulence effectively mixes the fluids. Changes in concentrations within the annular gap arise due to the combined effects of advection with the mean flow, anisotropic Taylor dispersion (along the streamlines) and turbulent diffusivity. The diffusive and dispersive effects are modelled for fully turbulent and transitional flows following Maleki and Frigaard (J Non-Newt Fluid Mech 235:1–19, 2016). The model derived allows the investigation of different well geometries and inclinations, pumping sequences and fluid rheologies, all of which can have importance. A number of computed examples are presented with the aim of demonstrating the complexity of turbulent displacements.

An experimental electrodiffusional technique with eight double probes is used to detect perturbation of the wall shear stress by a single bubble in laminar upward tube flow. Small almost spherical and long Taylor bubbles are tested. The wall shear stress perturbations by bubbles have a complex structure. It is possible to define three components of perturbation caused by a small bubble. The perturbation by Taylor bubble contains only two components due to the main flow symmetry around the bubble. An unexpectedly long shear stress pulsations zone is registered behind the Taylor bubbles.

Taylor dispersion with wall absorption in a laminar tube flow is analytically studied in this work by Aris’s method of concentration moments. The difficulty associated with the conventional approach initiated by Sankarasubramanian and Gill is completely avoided. All the basic characteristic properties governing the dispersion process, including the exchange rate, advection velocity, dispersivity, skewness and kurtosis, are analytically determined in their full time dependance for the first time. Detailed parametrical analysis is performed for the properties. Mean concentration distribution is concretely characterized.

Molecular tagging velocimetry is a little-intrusive technique based on the properties of specific molecules able to emit luminescence once properly excited. Several variants of this technique have been successfully developed for analyzing external gas flows or internal gas flows in large systems. There is, however, very few experimental data on molecular tagging velocimetry for gas flows in mini or microsystems, and these data are strongly affected by the molecular diffusion of the tracer molecules. In the present paper, it is demonstrated that the velocity field in gas microflows cannot be directly deduced from the measured displacement field without taking into account Taylor dispersion effects. For that purpose, the benchmark case of a Poiseuille gas flow through a rectangular channel 960 μm in depth is experimentally investigated by micro molecular tagging velocimetry using acetone vapor as a molecular tracer. An appropriate reconstruction method based on the advection diffusion equation is used to process the data and to correctly extract the velocity profiles. The comparison of measured velocities with flowrate data and with theoretical velocity profiles shows a good agreement, whereas when the reconstruction method is not implemented, the extracted velocity field exhibits qualitative and quantitative anomalies, such as a non-physical slip at the walls. The robustness of the reconstruction method is demonstrated on flows with light and heavy molecular species, namely helium and argon, at atmospheric as well as at lower pressure conditions, for which diffusion effects are stronger. The obtained results represent an encouraging step for future analysis of rarefied gas microflows.

Suspensions of microswimmers are a rich source of fascinating new fluid mechanics. Recently we predicted the active pipe flow dispersion of gyrotactic microalgae, whose orientation is biased by gravity and flow shear. Analytical theory predicts that these active swimmers disperse in a markedly distinct manner from passive tracers (Taylor dispersion). Dispersing swimmers display nonzero drift and effective diffusivity that is non-monotonic with P$\'e$clet number. Such predictions agree with numerical simulations, but hitherto have not been tested experimentally. Here, to facilitate comparison, we obtain new solutions of the axial dispersion theory accounting both for swimmer negative buoyancy and a local nonlinear response of swimmers to shear, provided by two alternative microscopic stochastic descriptions. We obtain new predictions for suspensions of the model swimming alga $\it Dunaliella\,salina$, whose motility and buoyant mass we parametrise using tracking video microscopy. We then present a new experimental method to measure gyrotactic dispersion using fluorescently stained $\it D. salina$ and provide a preliminary comparison with predictions of a nonzero drift above the mean flow for each microscopic stochastic description. Finally, we propose further experiments for a full experimental characterisation of gyrotactic dispersion measures and discuss implications of our results for algal dispersion in industrial photobioreactors., Comment: 24 pages, 5 figures

The two-phase Taylor flow pattern has been studied extensively. However, limited information is available for flows in intermediate diameter channels ( 5 ≲ Bo ≲ 40 , or 6 mm ≲ D ≲ 27 mm for ambient gas–water flows), as found in air-lift and bubble pumps. Previous investigations have primarily evaluated Taylor flow models in terms of overall pressure drop, which incorporates hydrostatic and multiple hydrodynamic components. Thus, individual sub-models and sources of error could not be directly assessed. In this investigation, volume-of-fluid (VOF) based Taylor flow simulations are performed over a wide range of laminar and turbulent conditions in the intermediate Bond number regime (5

The chemical, temporal, and spatial resolution of chemical signals that are sampled and transported with continuous flow is limited because of Taylor dispersion. Droplets have been used to solve this problem by digitizing chemical signals into discrete segments that can be transported for a long distance or a long time without loss of chemical, temporal or spatial precision. In this review, we describe Taylor dispersion, sampling theory, and Laplace pressure, and give examples of sampling probes that have used droplets to sample or/and transport fluid from a continuous medium, such as cell culture or nerve tissue, for external analysis. The examples are categorized, as follows: (1) Aqueous-phase sampling with downstream droplet formation; (2) preformed droplets for sampling; and (3) droplets formed near the analyte source. Finally, strategies for downstream sample recovery for conventional analysis are described.

To monitor neurochemicals while minimizing brain damage, a microdialysis system is developed with fluidic channels scaled to 5 μm-radius to fit into 15x50 μm2 silicon neural probe. Droplet generation is utilized to halt Taylor dispersion to achieve high temporal resolution. To extend the stability region for monodisperse droplet generation in such a space-limited probe at ultra-low nL/min flow rates, we varied the T-junction angle, parameter that is typically omitted from consideration for larger channels. In a series of experiments, we found that increase of the T-junction angle increases the critical capillary number separating squeezing and jetting segmentation regimes. With optimized geometry, we demonstrated generation of monodisperse pL-volume droplets in silicon nanofluidic channels. Finite element analysis indicated that these effects are due to interplay between differential pressure and viscous shear forces.

A solute flowing in a pressure-driven channel flow experiences an enhanced effective axial dispersion coefficient due to the transverse velocity gradients. An investigation shows how this phenomenon, known as Taylor dispersion, is affected by cross flow and mass transfer at the wall.

The effective diffusivity of a Brownian tracer in unidirectional flow is well known to be enhanced due to shear by the classic phenomenon of Taylor dispersion. At long times, the average concentration of the tracer follows a simplified advection–diffusion equation with an effective shear-dependent dispersivity. In this work, we make use of the generalized Taylor dispersion theory for periodic domains to analyze tracer dispersion by peristaltic pumping. In channels with small aspect ratios, asymptotic expansions in the lubrication limit are employed to obtain analytical expressions for the dispersion coefficient at both small and high Peclet numbers. Channels of arbitrary aspect ratios are also considered using a boundary integral formulation for the fluid flow coupled to a conservation equation for the effective dispersivity, which is solved using the finite-volume method. Our theoretical calculations, which compare well with results from Brownian dynamics simulations, elucidate the effects of channel geometry and pumping strength on shear-induced dispersion. We further discuss the connection between the present problem and dispersion due to Taylor’s swimming sheet and interpret our results in the purely diffusive regime in the context of Fick–Jacobs theory. Our results provide the theoretical basis for understanding passive scalar transport in peristaltic flow, for instance, in the ureter or in microfluidic peristaltic pumps.

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.

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.

This study investigated the variations of Taylor flow and particle residence time in a Taylor reactor according to the changes of angular velocity and inlet velocity using computational fluid dynamics technique. The results showed that the fluid in a reactor became unstable with an increase of angular velocity. The flow moved to the regions of CCF, TVF, WVF and MWVF resulting in an increase of Reynolds number. Accordingly, the flow characteristics were different for each regions. We confirmed that the inlet velocity influences the Taylor flow. The particle residence time and standard deviation increased with an increase of angular velocity and a decrease of inlet velocity.

Motivated by rock-fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a thin strip consisting of void space and grains, with fluid flow through the void space. Ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, taking into account the possible change in the aperture of the strip that these two processes cause. Temperature variations and possible effects of the temperature in both fluid density and viscosity and in the mineral precipitation and dissolution reactions are included. For the pore scale model equations, we investigate the limit as the width of the strip approaches zero, deriving one-dimensional effective equations. We assume that the convection is dominating over diffusion in the system, resulting in Taylor dispersion in the upscaled equations and a Forchheimer-type term in Darcy's law. Some numerical results where we compare the upscaled model with three simpler versions are presented: two still honoring the changing aperture of the strip but not including Taylor dispersion, and one where the aperture of the strip is fixed but contains dispersive terms. The research of the first and second authors was supported by Research Council of Norway (grant 228832). The research of the fourth author was supported by the Meltzer foundation at the University of Bergen and by the Dutch Research Council (Visitor grant 040.11.499). The third and fourth authors would like to acknowledge the support from Statoil through the Akademia agreement.

A parametrical analysis on solute transport in a packed pipe with first-order wall reaction based on the method of Gill’s series solution is presented. The main contribution of this work is to demonstrate the dispersion of solute cloud in different superficial flow in porous media, in particular, the evolution of the solute cloud in large times. The results show the dependence of some characteristic coefficients of the dispersion process on both the damping factor of the porous media flow and wall reaction rate. This work offers an insight into the effect of porous media on solute migration with wall reaction, the effect turns out to be of monotonous regularity.

We present a matched asymptotic analysis of the fluid flow and solute transport in a small aspect ratio hollow fibre membrane bioreactor. A two-dimensional domain is assumed for simplicity, enabling greater understanding of the typical behaviours of the system in a setup which is analytically tractable. The model permits analysis related to Taylor dispersion problems, and allows us to predict the dependence of the mean solute uptake and solute exposure time on key parameters such as the inlet fluid fluxes, porous membrane porosity and cell layer porosity and width, which could be controlled or measured experimentally.

Using a high-speed video-camera system, the hydrodynamics of gas–liquid two-phase slug flow in a vertical narrow rectangular channel with the cross section of 2.2 mm × 43 mm is investigated for laminar and turbulent regimes in the main flow and turbulent regime in the wake region of the Taylor bubble. The Taylor bubble velocity is the function of the liquid slug length ahead of it, and the interaction of Taylor bubbles for turbulent flow in main flow is weaker than that for laminar flow. Thus, two correlations are proposed for laminar and turbulent flows, respectively. The distributions of Taylor bubble velocity, lengths of liquid slug and Taylor bubble are all positively skewed. The lengths of Taylor bubble and the liquid slug decrease with the liquid flow rate. The Taylor bubble length increases with the gas flow rate, whereas the influence of the gas flow rate on the liquid slug length is insignificant.

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.

The fate of fluid-borne entities depends on flow and transport processes in geological environments. The classical theories for describing flow (Cubic Law) and transport (Taylor dispersion theory) processes within single fractures are based on the Poiseuille flow model (i.e., flow through the parallel plates) and its modifications with more complex surfaces. Nonetheless, the Poiseuille flow model assumes no-slip boundary condition while some natural environments show the otherwise, e.g., fracture walls are slippery with non-zero flow velocity. To better understand the effects of slippery boundaries on transport within Poiseuille flow, we develop a closed-form expression for the longitudinal dispersion coefficient (DL) based on the corrected flow field that considers homogeneous slip boundary condition. Moreover, the reliable direct numerical simulations were implemented to further validate our proposed theory on DL. Both theory and numerical experiments suggest that homogeneous slip boundary condition unsignificantly alters DL, although slippery boundaries can significantly change the mean velocity of Poiseuille flow. Our theory based on mechanistic, albeit simplified, model might shed light on predicting the fate of fluid-borne entities in complex geological environments.

The transport of self-propelled particles such as bacteria and phoretic swimmers through crowded heterogeneous environments is relevant to many natural and engineering processes, from biofilm formation and contamination processes to transport in soils and biomedical devices. While there has been experimental progress, a theoretical understanding of mean transport properties in these systems has been lacking. In this work, we apply generalized Taylor dispersion theory to analyze the long-time statistics of an active self-propelled Brownian particle transported under an applied flow through the interstices of a periodic lattice that serves as an idealization of a porous medium. Our theoretical model, which we validate against Brownian dynamics simulations, is applied to unravel the roles of motility, fluid flow, and lattice geometry on asymptotic mean velocity and dispersivity. In weak flows, transport is dominated by active dispersion, which results from self-propulsion in the presence of noise and is hindered by the obstacles that act as entropic barriers. In strong flows, shear-induced Taylor dispersion becomes the dominant mechanism for spreading, with pillars now acting as regions of shear production that enhance dispersion. The interplay of these two effects leads to complex and unexpected trends, such as a non-monotonic dependence of axial dispersivity on flow strength and a reduction in dispersion due to swimming activity in strong flows. Brownian dynamics are used to cast light on the pre-asymptotic regime, where tailed distributions are observed in agreement with recent experiments on motile micro-organisms. Our results also highlight the subtle effects of pillar shape, which can be used to control the magnitude of dispersion and to drive a net particle migration in quiescent systems., 21 pages, 12 figures

International audience; The extended method of moments (EMM) is elaborated in recursive algorithmic form for the prediction of the effective diffusivity, the Taylor dispersion dyadic and the associated longitudinal high-order coefficients in mean-concentration profiles and residence-time distributions. The method applies in any streamwise-periodic stationary d-dimensional velocity field resolved in the piecewise continuous heterogeneous porosity field. It is demonstrated that EMM reduces to the method of moments and the volume-averaging formulation in microscopic velocity field and homogeneous soil, respectively. The EMM simultaneously constructs two systems of moments, the spatial and the temporal, without resorting to solving of the high-order upscaled PDE. At the same time, the EMM is supported with the reconstruction of distribution from its moments, allowing to visualize the deviation from the classical ADE solution. The EMM can be handled by any linear advection-diffusion solver with explicit mass-source and diffusive- flux jump condition on the solid boundary and permeable interface. The prediction of the first four moments is decisive in the optimization of the dispersion, asymmetry, peakedness and heavy-tails of the solute distributions, through an adequate design of the composite materials, wetlands, chemical devices or oil recovery. The symbolic solutions for dispersion, skewness and kurtosis are constructed in basic con figurations: diffusion process and Darcy flow through two porous blocks in " series " , straight and radial Poiseuille fl ow, porous f ow governed by the Stokes - Brinkman - Darcy channel equation and a fracture sur- rounded by penetrable diffusive matrix or embedded in porous flow. We examine the moments dependency upon porosity contrast, aspect ratio, Péclet and Darcy numbers, but also for their response on the effective Brinkman viscosity applied in flow modeling. Two numerical Lattice Boltzmann algorithms, a direct solver of the microscopic ADE in heterogeneous structure and a novel scheme for EMM numerical formulation, are called for validation of the constructed analytical predictions.

The biofluids being manipulated in lab-on-a-chip devices usually contain elastic macromolecules. Accordingly, for an accurate modeling of the relevant flow physics one should invoke viscoelastic constitutive equations. In this paper, attention is paid toward the hydrodynamic dispersion by the fully developed electroosmotic flow of PTT viscoelastic fluids in slit microchannels of low zeta potential. Adopting the Taylor–Aris approach, analytical solutions are derived for late-time solute concentration and effective dispersion coefficient. Finite element-based numerical simulations are also conducted to monitor the broadening of an analyte band from the moment of injection. Both approaches are found to be in a good agreement with an average error of below 8% in the calculated dispersion coefficients. It is observed that, for given zeta potential and electrolyte type, the hydrodynamic dispersion is severely pronounced by increasing the level of elasticity in the fluid. The variations are reversed and less pronounced when the analysis is made for a fixed mean flow rate. Moreover, the effective dispersivity grows by thickening the EDL when it is sufficiently thin, whereas the opposite is true for thick EDLs. Finally, an inspection of the average concentration reveals the formation of tails for thick EDLs that may reduce the resolution in sensing applications.

We investigate the transport of a passive scalar in a fully developed turbulent axisymmetric jet at a Reynolds number of $\mathit{Re}=4815$ using data from direct numerical simulation. In particular, we simulate the response of the concentration field to an instantaneous variation of the scalar flux at the source. To analyse the time evolution of this statistically unsteady process we take an ensemble average over 16 independent simulations. We find that the evolution of $C_{m}(z,t)$, the radial integral of the ensemble-averaged concentration, is a self-similar process, with the front position and spread both scaling as $\sqrt{t}$. The longitudinal mixing of $C_{m}$ is shown to be primarily caused by shear-flow dispersion. Using the approach developed by Craske & van Reeuwijk (J. Fluid Mech., vol. 763, 2014, pp. 538–566), the classical theory for shear-flow dispersion is applied to turbulent jets to obtain a closure that couples the integral scalar flux to the integral concentration $C_{m}$. Model predictions using the dispersion closure are in good agreement with the simulation data. Application of the dispersion closure to a two-dimensional jet results in an integral transport equation that is fully consistent with that of Landel et al. (J. Fluid Mech., vol. 711, 2012, pp. 212–258).

The effect of axial flow variation on the hydrodynamic (Taylor–Aris) dispersion in a patterned microchannel consisting of periodic pillars and gaps is characterized for limiting Cassie–Baxter and Wenzel state configurations. The entry effects of flow for subsequent gaps and pillars are crucial as the flow tends towards plug flow over the gaps due to free slip at the air–liquid interface for the Cassie state or increased cross section for the Wenzel state and fully-developed parabolic flow over the pillars. The study includes analyzing the solute concentration distribution as a function of Peclet number based on the gap length, using CFD simulation and quantifying the dispersion based on Aris method of moments. For the Cassie State, simulations predict a narrower solute concentration distribution compared to flow in smooth channels. Detailed analysis reveal varied dispersion characteristics with Peclet number: similar dispersion with a time lag for low Peclet numbers and a reduced dispersion for high Peclet Number due to enhanced effect of slip. For the Wenzel state, a considerable loss of solute occurs due to the presence of dead zones within the gaps resulting in a significant increase in dispersion. The changed dispersion characteristics may have profound implications in microfluidic applications involving mixing and separation e.g., in liquid chromatography.

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