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This article explores how a chemically reactive solute will disperse across mobile to immobile phase when injected into the fluid flowing within a long circular tube. To model this process, we utilized mathematical modeling, including advection-diffusion equations for flow of fluid within the tube and first-order chemical reaction equations to account for reversible and irreversible reactions on the tubes' wall. We proposed a numerical method based on an explicit finite difference scheme to solve the governing equations for the dispersion of a chemically reactive solute. We used an upwind method with a conservative representation in the diffusion component to discretize the advection-diffusion equation. To ensure the stability of our proposed numerical scheme, we computed the time step constraint condition so that the maximum principle for the discrete governing equation holds. We also verified the performance of our proposed scheme through computational results that were compared with previous studies. One of our key findings was that the depletion coefficient D0 achieved a quasi-steady state for larger absorption rates. We also observed that the advection coefficient D1 initially increased with an increasing absorption rate, but eventually declined due to phase exchange kinetics. The dispersion coefficient D2 also decreased with a rising absorption rate due to a low-velocity gradient in the middle region. Our study showed that rapid distributions are possible under certain conditions, such as a high Damköhler number (Da ≥ 10) and a high absorption rate (Γ>5). Computational results show that the proposed scheme can be useful in developing an efficient pulmonary drug delivery system for periodic inhalation of drugs to determine the optimal frequency of injection. [ABSTRACT FROM AUTHOR]

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number $ {{Le}} $ L e and the flow Peclet number $ {{Pe}} $ P e . The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the $ {{Le}} $ L e - $ {{Pe}} $ P e plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for $ {{Le}} \lt 1 $ L e < 1 , exists now for $ {{Le}} \gt 1 $ L e > 1 but is absent when $ {{Le}} \lt 1 $ L e < 1. In fact, the cellular instability identified for $ {{Le}} \gt 1 $ L e > 1 is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I $ _s $ s ) or through a longwave stationary bifurcation (also known as type-II $ _s $ s ). The latter type-II $ _s $ s bifurcation leads in the weakly nonlinear regime to a Kuramoto-Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in $ {{Le}} \gt 1 $ L e > 1 mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions. [ABSTRACT FROM AUTHOR]

In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in three-dimensional infinite pipes. As a byproduct of our analysis, we obtain an enhanced decay for circular flows on a disc of arbitrary radius. [ABSTRACT FROM AUTHOR]

Reactive flow and transport in porous media is topic of intense research since decades. Since dispersion is one of the key parameters in solute transport, its accurate modeling is essential to avoid wrong predictions of flow and transport behavior. In this research, we investigate novel effective dispersion models for reactive transport of electrically charged chemical species in a thin, potentially evolving strip taking into account Taylor–Aris and electroosmotic‐induced dispersion as well as their cross‐coupling effects. We prove positivity of the dispersion coefficient and the existence and uniqueness of strong solutions in the fixed geometry setting. Moreover, we numerically investigate scenarios for both the fixed and evolving geometry situation. The simulation results illustrate the possibility of separating charged species, such that the findings of this study can lead to a better understanding of mixing and separation processes of charged solutes and an improved prediction of breakthrough curves. Finally, we study the limits of vanishing channel width, precipitation layer thickness, and molecular diffusion. We show convergence of the solutions to the corresponding limit cases such as a hyperbolic model or the fixed geometry case. From these results, we can rate the impact of distinct dispersion mechanisms and evaluate the necessity of a detailed modeling for different parameter regimes. [ABSTRACT FROM AUTHOR]

We consider a kinetic model of an active suspension of rodlike microswimmers. In certain regimes, swimming has a stabilizing effect on the suspension. We quantify this effect near homogeneous isotropic equilibria ip = const. Notably, in the absence of particle (translational and orientational) diffusion, swimming is the only stabilizing mechanism. On the torus, in the nondiffusive regime, we demonstrate linear Landau damping up to the stability threshold predicted in the applied literature. With small diffusion, we demonstrate nonlinear stability of arbitrary equilibrium values for pullers (front-actuated swimmers) and enhanced dissipation for both pullers and pushers (rear-actuated swimmers) at small concentrations. On the whole space, we prove nonlinear stability of the vacuum equilibrium due to generalized Taylor dispersion. [ABSTRACT FROM AUTHOR]

Direct interactions between the flow field and the chemical reaction in premixed flames occur when the reaction zone thickness is comparable to, or greater than flow length scales. To study such interactions, a laminar model is considered that has direct bearings to steadily propagating deflagrations in a Hele-Shaw channel with a background plane Poiseuille flow. The study employs asymptotic analyses, pertaining to large activation energy and lubrication theories and considers a distinguished limit where the channel width is comparable to the reaction zone thickness, with account being taken of thermal-expansion and heat-loss effects. The reaction zone structure and burning rates depend on three parameters, namely, the Peclet number, P , the Lewis number, L e and the ratio of channel half-width to reaction zone thickness, λ ∗ . In particular, when the parameter λ ∗ is small wherein the reaction zone is thick, transport processes are found to be controlled by Taylor's dispersion mechanism and an explicit formula for the effective burning speed S T is obtained. The formula indicates that S T / S L ∝ 1 / L e for P ≫ 1 , which interestingly coincides with a recent experimental prediction of the turbulent flame speed in a highly turbulent jet flame. The results suggest that the role played by differential diffusion effects is significant both in the laminar and turbulent cases. The reason for the peculiar 1 / L e dependence can be attributed, at least in our laminar model, to Taylor dispersion. Presumably, this dependence may be attributed to a similar but more general mechanism in the turbulent distributed reaction zone regime, rather than to diffusive-thermal curvature effects. The latter effects play however an important role in determining the effective propagation speed for thinner reaction zones, in particular, when λ ∗ is large in our model. It is found that the magnitude of heat losses at extinction, which directly affects the mixture flammability limits, is multiplied by a factor 1 / L e 2 in comparison with those corresponding to the no-flow case in narrow channels. [ABSTRACT FROM AUTHOR]

The influence of oligosaccharides (α-cyclodextrin, β-cyclodextrin and γ-cyclodextrin), and a polysaccharide, sodium hyaluronate (NaHy), on the diffusion of aqueous solutions of cobalt and chromium chlorides has been investigated. Cobalt and chromium are constituents of metal alloys for biomedical use, including dental prostheses. Thus, the release of these ions in the human body can lead to harmful biological effects. The interaction of metal ions with saccharides might have information on the role of mouthwashes in preventing these effects. This interaction has been assessed by measuring multicomponent intermolecular diffusion coefficients at 298.15 K. It has been found that β-cyclodextrin has the highest interaction towards cobalt and chromium ions. This work will contribute to unveiling the mechanisms responsible for transport by diffusion in aqueous solutions, and, therefore, mitigating the potential toxicity inherent to those metal ions. [ABSTRACT FROM AUTHOR]

The rich and complex phenomena of the transport of active particles like microorganisms in shear flows are of great significance to various biological and environmental applications. Recent studies have shown that the motility and gyrotaxis of algae could greatly influence their transport in waters. However, little attention has been paid to the initial and transient transport regime when the classical Taylor dispersion model is not applicable. To tackle this problem, we resort to Gill's generalized dispersion model for passive particles like solute, which has the potential for accurately describing the entire transport process. For the first time, we extend Gill's model to the active particles, and the effects of swimming, gyrotaxis, and flow shear on the microorganism dispersion in an open‐channel flow have been thoroughly investigated. We first theoretically solve the transient drift and dispersion coefficients, based on which we obtain analytical solutions for concentration distributions of microorganisms, and further validate these results by numerically solving the governing equation. We find that when there is no flow, the longitudinal dispersion of microorganisms can be weakened by the gravitactic accumulation in the vicinity of water surface, while enhanced by a stronger swimming ability of the microorganisms. The effect of the flow shear does not affect the form of the asymptotic concentration distribution, but can greatly enhance the transient drift velocity and the dispersivity. We further analyze the effect of turbulence on microorganisms' dispersion by combing the direct numerical simulation and the random walk simulation. The increase of turbulence is shown to decrease the vertical non‐uniformity of the concentration distribution, as well as the relative contribution of active behavior to both the drift and Taylor dispersivity during transport. Key Points: For the first time we extend Gill's dispersion model for active particlesThe initial transient transport features can be captured by the new modelThe turbulence is seen to decrease the relative contribution of active motions [ABSTRACT FROM AUTHOR]

We have developed a theoretical framework to characterize the transport and mixing of a passive scalar in a capillary tube. In this configuration, a suspension of magnetic nanoparticles undergoes Poiseuille flow, while a rotating magnetic field is applied around the tube's revolution axis, inducing a secondary flow in the azimuthal direction. This secondary flow facilitates the mitigation of concentration gradients and radial dispersion associated with the axial parabolic Poiseuille profile. The improvement in mixing is emphasized by a new dimensionless parameter, the mixing factor, which is incorporated into the scalar transport equation. Such a factor acts as a quantitative measure of the effect of the tangential motion induced by the spin-up flow on the overall mixing efficiency of the liquid and the observed reduction of the Taylor dispersion in the measured residence time distributions. Recognizing the mixing factor as a crucial parameter advances our understanding of the mechanisms governing scalar transport and provides a valuable tool for predicting and optimizing mixing in laminar capillary flows subjected to spin-up motion. [Display omitted] • New scalar transport model in conjoined Poiseuille/spin-up flows in a capillary. • Spin-up flow improves crosswise mixing, curtailing RTD variance. • Spin-up flow reduces Taylor dispersion, promoting faster nanofluid homogenization. • Nanoparticle cluster regime challenges emphasize the need for a predictive theory. [ABSTRACT FROM AUTHOR]

Diffusion coefficients, D, for ethanol in supercritical carbon dioxide (scCO2) were measured in the temperature range 306.15–331.15 K and along the 10.5 MPa isobar, using the Taylor dispersion technique. The obtained diffusivities ranged from 1.49 × 10−8 to 2.98 × 10−8 m2 s−1, an order of magnitude higher than in usual liquids. The dependence of D on temperature and solvent density was examined. Various correlation models based in the hydrodynamic theory were assessed to estimate the diffusion coefficients, with reasonable results obtained for the Wilke–Chang and Lai–Tan models. [ABSTRACT FROM AUTHOR]

• First study on real tension joint fracture with a characteristic plumose structure, scanned using LiDAR technology. • Hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. • Local variation of heat transport parameters is controlled by fracture roughness. • Different heat transport regimes identified, based on fracture aperture and roughness. The understanding of heat transport in fractures is crucial for mining geothermal systems. Studies of heat transport in natural fractures at scales comprised between those of laboratory experiments and those of field tracer tests are seldom. To bridge the gap, a joint surface with characteristic plumose was scanned in the field using LiDAR technology. The scanned surface was used to build a numerical model of mode 1 fracture. Fluid flow and heat transport were modeled solving the steady-state Stokes equation and assuming Fourier transport, respectively. We considered three different fracture apertures and varied systematically roughness in order to investigate the impact of plumose on fluid and heat transport. The 3D velocity flow fields were characterized by mean hydraulic aperture and by statistics on the directional components of the velocity vector. The method of temporal moments was used to extract first and second moments from temperature breakthrough curves. Heat transport parameters (local and macroscopic) were calculated from first and second moments. We show that hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. The local variation of heat transport parameters is controlled by fracture roughness. For the macroscopic transport parameters, several transport regimes were identified. At low fracture aperture (i.e. 1 mm), conductive regime dominates heat transport in agreement with low Péclet numbers. In this case, fracture roughness affects the transport parameters via the loss of hydraulic aperture. With higher aperture (i.e. 3 mm) geometrical dispersion regime is dominant, roughness controlling the amplitude of transport parameters. At 5 mm aperture, transition from geometrical to Taylor dispersion occurs and the roughness tends to decrease dispersion and dispersivity according to the mean flow velocity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

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 unexplored class of problems pertaining to the interaction between Taylor dispersion (or flow-enhanced diffusion) and Turing-like instabilities in reaction–diffusion systems. The analysis is carried out in the Hele–Shaw burner configuration and adopts a constant density and negligible heat-loss assumptions. These simplifying assumptions allow to isolate the effect of Taylor dispersion on flame stability (by switching off the Darrieus–Landau instability and experimentally challenging extinction phenomena) while keeping the problem analytically tractable. Starting from a 3D formulation, depth-averaged equations are first obtained leading to a 2D model which accounts for enhanced diffusion in the flow direction and shows that diffusion is effectively anisotropic. A linear stability analysis of the travelling wave solutions of the 2D problem leads to a simple dispersion relation which generalises a classical one obtained by Sivashinsky to incorporate the effect of the flow Peclet number coupled to that of the mixture's Lewis number. Based on the new dispersion relation, stability-bifurcation diagrams are drawn in terms of the Peclet and Lewis numbers and their physical implications are discussed. In particular, the study clearly demonstrates the ability of Taylor dispersion to significantly affect the flame thermo-diffusive instabilities, whether these are of the cellular or oscillatory types, with the effect on the latter being more pronounced. It is found that Taylor dispersion typically promotes the cellular instability and hampers the oscillatory instability. This is the first stability analysis accounting for Taylor dispersion in the context of combustion and has thus a fundamental value, both in combustion and in other reaction–diffusion areas, independent of the fact that the phenomena predicted may well be difficult to reproduce experimentally. [ABSTRACT FROM AUTHOR]

We develop a theory of enhanced diffusivity and skewness of the longitudinal distribution of a diffusing tracer advected by a periodic time-varying shear flow in a straight channel. Although applicable to any type of solute and fluid flow, we restrict the examples of our theory to the tracer advected by flows which are induced by a periodically oscillating wall in a Newtonian fluid between two infinite parallel plates as well as flow in an infinitely long duct. These wall motions produce the well-known Stokes layer shear solutions which are exact solutions of the Navier–Stokes equations. With these, we first calculate the second Aris moment for all time and its long-time limiting effective diffusivity as a function of the geometrical parameters, frequency, viscosity, and diffusivity. Using a new formalism based upon the Helmholtz operator, we establish a new single series formula for the variance valid for all time. We show that the viscous dominated limit results in a linear shear layer for which the effective diffusivity is bounded with upper bound κ (1 + A 2 / (2 L 2)) , where κ is the tracer diffusivity, A is the amplitude of oscillation, and L is the gap thickness. Alternatively, for finite viscosities, we show that the enhanced diffusion is unbounded, diverging in the high-frequency limit. Non-dimensionalization and physical arguments are given to explain these striking differences. Asymptotics for the high-frequency behavior as well as the low viscosity limit are computed. We present a study of the effective diffusivity surface as a function of the non-dimensional parameters which shows how a maximum can exists for various parameter sweeps. Physical experiments are performed in water using particle tracking velocimetry to quantitatively measure the fluid flow. Using fluorescein dye as the passive tracer, we document that the theory is quantitatively accurate. Specifically, image analysis suggests that the distribution variance be measured using the full width at half maximum statistic which is robust to noise. Further, we show that the scalar skewness is zero for linear shear flows at all times, whereas for the nonlinear Stokes layer, exact analysis shows that the skewness sign can be controlled through the phase of the oscillating wall. Further, for single-frequency wall modes, we establish that the long-time skewness decays at the faster rate of t - 3 / 2 as compared with steady shear scalar skewness which decays at rate t - 1 / 2 . These results are confirmed using Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

Intrinsic viscosity is a key hydrodynamic parameter to understand molecular structure and hydration, as well as intramolecular interactions. Commercially available instruments measure intrinsic viscosity by recording the macromolecular mobility in a capillary. These instruments monitor Taylor dispersion using an absorbance or fluorescence detector. By design, these instruments behave like U-tube viscometers. To our knowledge, there are no studies to date showing that the Viscosizer TD instrument (Malvern-Panalytical) is able to measure the intrinsic viscosity of macromolecules. In this study, we then performed our assays on the Poly(ethylene oxide) polymer (PEO), used classically as a standard for viscometry measurements and on three model proteins: the bovine serum albumin (BSA), the bevacizumab monoclonal antibody, and the RTX Repeat Domain (RD) of the adenylate cyclase toxin of Bordetella pertussis (CyaA). The presence of P20 in the samples is critical to get reliable results. The data obtained with our in-house protocol show a strong correlation with intrinsic viscosity values obtained using conventional techniques. However, with respect to them, our measurements could be performed at relatively low concentrations, between 2 and 5 mg/ml, using only 7 µL per injection. Altogether, our results show that the Viscosizer TD instrument is able to measure intrinsic viscosities in a straightforward manner. This simple and innovative approach should give a new boost to intrinsic viscosity measurements and should reignite the interest of biophysicists, immunologists, structural biologists and other researchers for this key physicochemical parameter. [ABSTRACT FROM AUTHOR]

In fully-developed pressure-driven flow, the spreading of a dissolved solute is enhanced in the flow direction due to transverse velocity variations in a phenomenon now commonly referred to as Taylor–Aris dispersion. It is well understood that the characteristics of the dispersion are sensitive to the channel's cross-sectional geometry. Here we demonstrate a method for manipulation of dispersion in a single rectangular microchannel via controlled deformation of its upper wall. Using a rapidly prototyped multi-layer microchip, the channel wall is deformed by a controlled pressure source allowing us to characterize the dependence of the dispersion on the deflection of the channel wall and overall channel aspect ratio. For a given channel aspect ratio, an optimal deformation to minimize dispersion is found, consistent with prior numerical and theoretical predictions. Our experimental measurements are also compared directly to numerical predictions using an idealized geometry. [ABSTRACT FROM AUTHOR]

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

Researches on the solute dispersion with boundary adsorption and desorption are common in various fields, such as chemistry, biology, and hydraulics. However, the Laplace transform, as a method available for the transient transport with coupled processes of adsorption–desorption at boundaries, is complicated to apply. Recently, Jiang et al. (2022) proposed a much simpler analytical method by extending the classic framework of separation of variables to derive solutions of concentration moments for tube flows, which is valid for the entire range of the reactive transport process. Here we apply this simple approach to solute transport in open-channel flows with bed adsorption and desorption. We obtain analytical solutions capturing exactly the transient statistics for the solute cloud as compared to the numerical simulations, regarding the variation of the cloud mass, the motions of the centroid of the cloud, and the scattering of the cloud, respectively. We further investigate the effect of adsorption–desorption on the dispersion process and the influence of initial conditions on the non-uniformity of dispersion characteristics over the cross-section before the Taylor dispersion regime. Through comparisons with that of tube flows, we find that the distribution of solute mass, the drift, and the dispersivity for open channel flows change more slowly with time and the response time is longer. • Separation of variables method is used to study solute transport in open channels. • The obtained analytical solutions capture the transient dispersion process. • Response time for dispersion is longer in open channels than in tubes. [ABSTRACT FROM AUTHOR]

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

An analysis is presented for the Burke–Schumann flame established when a fuel tank discharges with mean velocity U along a circular duct of radius a filled initially with air. Attention is focused on effects of interactions of shear with transverse diffusion resulting in enhanced longitudinal dispersion. The analysis accounts for preferential-diffusion effects arising for non-unity values of the fuel Lewis number L F , with the Peclet number P e = U a / D o based on the thermal diffusivity D o taken to be of order unity for generality. The solution to the associated Taylor-dispersion problem is described for times t ′ much larger than the characteristic diffusion time across the pipe a 2 / D o , when the flame is embedded in a mixing region of increasing longitudinal extent moving with the mean velocity. At leading order in the limit t ′ ≫ a 2 / D o , the longitudinal flame location, the burning rate, and the peak temperature are found to be a function of the effective Lewis number L e f f = L F (1 + P e 2 / 48) / (1 + L F 2 P e 2 / 48) , whose value changes from L e f f = L F for P e ≪ 1 to L e f f = 1 / L F for P e ≫ 1. As a result of this variation, the flame exhibits preferential-diffusion effects that depend fundamentally on P e , with important implications in designs of microcombustion devices employing narrow channels and pipes. [ABSTRACT FROM AUTHOR]

Since dispersion is one of the key parameters in solute transport, its accurate modeling is essential to avoid wrong predictions of flow and transport behavior. In this research, we derive new effective dispersion models which are valid also in evolving geometries. To this end, we consider reactive ion transport under dominate flow conditions (i.e. for high Peclet number) in a thin, potentially evolving strip. Electric charges and the induced electric potential (the zeta potential) give rise to electro-osmotic flow in addition to pressure-driven flow. At the pore-scale a mathematical model in terms of coupled partial differential equations is introduced. If applicable, the free boundary, i.e. the interface between an attached layer of immobile chemical species and the fluid is taken into account via the thickness of the layer. To this model, a formal limiting procedure is applied and the resulting upscaled models are investigated for dispersive effects. In doing so, we emphasize the cross-coupling effects of hydrodynamic dispersion (Taylor–Aris dispersion) and dispersion created by electro-osmotic flow. Moreover, we study the limit of small and large Debye length. Our results improve the understanding of fundamentals of flow and transport processes, since we can now explicitly calculate the dispersion coefficient even in evolving geometries. Further research may certainly address the situation of clogging by means of numerical studies. Finally, improved predictions of breakthrough curves as well as facilitated modeling of mixing and separation processes are possible. [ABSTRACT FROM AUTHOR]

Scalar transport in an open channel with irreversible first-order absorption boundaries is investigated through random walk particle tracking method (RWPT). We provide the pre-asymptotic behavior of scalar transport as well as a comparison with existing asymptotic formulations. The RWPT method is based on the development of the probability that a particle is absorbed at the boundary. The random walk model is applied to simulate three main parameters of the scalar transport in the laminar flow with sorption boundaries. The three parameters are (1) the attenuation coefficient reflecting the depletion rate of the total mass; (2) the effective velocity coefficient representing the effective advection of the total mass; and (3) the effective longitudinal dispersion coefficient expressing the effective spreading rate of the solute plume. When the Peclet number is large, numerical results agree well with previous theoretical solutions. Results show that (1) the three coefficients reach their asymptotic values when the dimensionless time τ (= Dt/H2) is about 0.5, where t is the time, H is the water depth, and D is the molecular diffusion coefficient and (2) when the Damkohler number reaches a value around 100, the boundary can be treated as a totally absorptive boundary. [ABSTRACT FROM AUTHOR]

A variation potential (VP) is an electrical signal unique to plants that occurs in response to wounding or flaming. The propagation mechanism itself, however, is known not to be electrical. Here we examine the hypothesis that VP transmission occurs via the transport of a chemical agent in the xylem. We assume the electrical signal is generated locally by the activation of an ion channel at the plasma membrane of cells adjacent to the xylem. We work on the assumption that the ion channels are triggered when the chemical concentration exceeds a threshold value. We use numerical computations to demonstrate the combined effect of advection and diffusion on chemical transport in a tube flow, and propose shear-enhanced Taylor-Aris dispersion as a candidate mechanism to explain VP rates observed in experiments. [ABSTRACT FROM AUTHOR]

• Binary mutual diffusion coefficients of sodium salicylate solutions at 25 °C. • Ternary mutual diffusion coefficients of aqueous NaSal + NaCl solutions at 25 °C. • Coupled diffusion in aqueous NaSal + NaCl solutions analysed by using Nernst-Planck equations. 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 (D ik) of aqueous NaSal(C 1) + NaCl(C 2) solutions, including results for the diffusion of NaSal in physiological saline solutions with C 2 = 0.15 mol dm−3. As the NaCl:NaSal ratio increases, NaSal diffusion coefficient D 11 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. [ABSTRACT FROM AUTHOR]

• Contaminant concentration distribution uncertainties are studied. • Additional longitudinal displacement is a key indicator. • Concentration distribution is affected by the lateral position of initial release. 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. [ABSTRACT FROM AUTHOR]

Diffusion flame streets, observed in non-premixed micro-combustion devices, align parallel to a shear flow. They are observed to occur in mixtures with high Lewis number (Le) fuels, provided that the flow Reynolds number, or the Peclet number Pe , exceeds a critical value. The underlying mechanisms behind these observations have not yet been fully understood. In the present paper, we identify the coupling between diffusive-thermal instabilities and Taylor dispersion as a mechanism which is able to explain the experimental observations above. The explanation is largely based on the fact that Taylor dispersion enhances all diffusion processes in the flow direction, leading effectively to anisotropic diffusion with an effective (flow-dependent) Lewis number in the flow direction which is proportional to 1 / Le for Pe ≫ 1. Validation of the identified mechanism is demonstrated within a simple model by investigating the stability of a planar diffusion flame established parallel to a plane Poiseuille flow in a narrow channel. A linear stability analysis, leading to an eigenvalue problem solved numerically, shows that cellular (or finite wavelength) instabilities emerge for high Lewis number fuels when the Peclet number exceeds a critical value. Furthermore, for Peclet numbers below this critical value, longwave instabilities with or without time oscillations are obtained. Stability regime diagrams are presented for illustrative cases in a Le − Pe plane where various instability domains are identified. Finally, the linear analysis is supported and complemented by time dependent numerical simulations, describing the evolution of unstable diffusion flames. The simulations demonstrate the existence of stable cellular structures and show that the longwave instabilities are conducive to flame extinction. [ABSTRACT FROM AUTHOR]

Recent extensive and important studies have provided detailed information and compelling evidence on how the presence of waves influences the vertical diffusivity/dispersivity in the coastal environment, which can affect various water quality considerations such as the distribution of suspended sediments in the water column as well as the potential of eutrophication. Comparatively, how the presence of waves influences the horizontal diffusivity/dispersivity has received only scant attention in the literature. Our previous works investigated the role played by the Taylor mechanism due to the wave-induced drift profile which leads to the longitudinal dispersion of contaminants in the horizontal direction, under regular sinusoidal waves and random waves with single-peak spectra. Natural waves in the coastal environment, however, often possess dual-peak spectra, comprising both higher frequency wind waves and lower frequency swells. In this study, the Taylor dispersion of contaminants under random waves with dual-peak spectra is examined through analytical derivation and numerical calculations. The effects of various dual-peak spectral parameters on the horizontal dispersion, including the proportion of lower frequency energy, peak frequency ratio and spectral shape parameter, are investigated. The results show that the relative energy distribution between the dual peaks has the most significant effect. Compared with single-peak spectra with equivalent energy, the Taylor dispersion with dual-peak spectra is stronger when the lower frequency is close to the peak frequency of the single-peak spectrum, and weaker with the higher frequency instead. Thus, it can be concluded that with a dual-peak wave spectrum, wind-dominated seas with higher frequency lead to stronger dispersion in the horizontal direction than swell-dominated seas with lower frequency. [ABSTRACT FROM AUTHOR]

The present investigation deals with Taylor dispersion of reactive species in Casson liquid in an oscillatory flow because of the pulsatile pressure gradient. The solute is considered to be chemically active at the boundary and also participate a first order reaction within the bulk flow. To evaluate transport coefficients, Aris-Barton moment technique is considered. The solute transport process is discoursed in detailed with respect to yield stress, chemical reaction parameter, Womersly number etc. The study reveals that both wall absorption and bulk flow reaction have a significant response on dispersion phenomena. Both the chemical reactions agree to diminish the negative exchange coefficient and the apparent dispersion coefficient, however, increases the negative convection coefficient. The negative exchange coefficient is independent of yield stress but a significant variation is observed due to yield stress in the cases of negative convection coefficient and the apparent dispersion coefficient. The axial distribution of mean concentration is approximated by using the Hermite polynomial representation of central moments as a function of reaction rate parameters, wall absorbing parameter, yield stress etc. The present article may be useful for the studies related to physiological blood flow analysis. [ABSTRACT FROM AUTHOR]

Highlights • Binary mutual diffusion coefficients of alkyl substituted sulfonated resorcinarenes solutions. • Conductivities of alkyl substituted sulfonated resorcinarenes solutions. • Limiting mobilities of the ETRA4− and PRRA4− ions derived independently from the diffusion and conductivity measurements. Abstract Resorcinarenes are macrocyclic compounds that form supramolecular complexes with a wide range of applications. In this paper, mutual diffusion coefficients and molar ionic conductivities are reported for aqueous solutions of the sodium salts of sulfonated resorcinarenes with two different alkyl groups: sodium C-tetraethyl-resorcin[4]arene sulfonate (Na 4 ETRA) and sodium C-tetrapropyl-resorcin[4]arene sulfonate (Na 4 PRRA). The diffusion coefficients and conductivities were measured at 25 °C for dilute solutions of the resorcinarenes (concentration < 0.010 mol·dm−3). The concentration dependence of the conductivities is accurately represented by equations for solutions of strong electrolytes, suggesting that association of the ETRA4− and PRRA4− ions with the Na+ counterions is negligible at the concentrations that were used. Furthermore, the limiting mobilities of the ETRA4− and PRRA4− ions derived independently from the diffusion and conductivity measurements are in good agreement. The change in the hydrodynamic radius of sulfonated resorcinarene caused by increasing the length of alky substituents is discussed. [ABSTRACT FROM AUTHOR]

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 Péclét 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. [ABSTRACT FROM AUTHOR]

Abstract Interdiffusion coefficients and molar conductivities of the macrocycle tetrasodium 5,11,17,23-tetrakissulfonatemethylen-2,8,14,20-tetra(2(methylthio)ethyl)resorcinarene (H 8 Na 4 RSTio) in non-buffered aqueous solutions at 25.00 °C and at concentrations from (0.001 to 0.020 mol·dm−3) have been measured. The concentration dependence of the conductivities is accurately represented by equations for solutions of strong electrolytes, suggesting that there are no association between anionic species from macrocyclic molecule and Na+ counterions at the concentrations that were used. Furthermore, the limiting conductivities of the H 8 RSTio4− ions derived independently from the diffusion and conductivity measurements, as well as the Nernst diffusion coefficients derived from diffusion (1.296 × 10−9) m2·s−1 and from conductance (1.298 × 10−9) m2·s−1, are in good agreement. Limiting diffusion coefficient of H 8 RSTio4− anion was used, together with the Stokes–Einstein equation, to determine the equivalent hydrodynamic radius. Highlights • Transport properties of a methylsulfonate resorcinarene have been measured. • Mutual diffusion coefficients were measured using the Taylor technique. • Hydration radii of the resorcinarene were estimated. • Ionic conductivities are justified on the basis of Quint-Viallard theory. • Limiting diffusion coefficients are in agreement with conductivity data. [ABSTRACT FROM AUTHOR]

Highlights • To obtain the time-dependent dispersion coefficients of Gill’s model. • To show the relation between the coefficients of dispersion model and cumulants of concentration distribution. • To solve the Taylor-Gill expansion equation of mean concentration distribution up to the fourth order to account for the asymmetry (skewness) and heavy tails (kurtosis). Abstract Previous applications of Gill’s generalized dispersion model in the description of solute transport in Poiseuille flow with wall absorption used only the long-time asymptotic values of dispersion coefficients. They are also limited to the simplest second order equation, which resembles Taylor’s classic model with a Gaussian distribution for cross-sectional mean concentration. To obtain the time-dependent dispersion coefficients, in this work the coefficients of dispersion model are concretely related to the moments of concentration distribution. With the readily obtained higher order dispersion coefficients, solution of the Taylor-Gill expansion equation is presented up to the fourth order, accounting for the asymmetry (skewness) and heavy tails (kurtosis) of the cross-sectional mean concentration distribution. [ABSTRACT FROM AUTHOR]

Highlights • Analytical solutions are deduced by two-scale perturbation analysis and moment method. • Dispersion-dominated transport is identified by 2-D concentration distribution patterns. • Remarkable difference in times exists for release at different depths to enter dispersion-dominated regime. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • The aspect ratio and damping factor on the dispersion process are characterized. • The lateral-sidewall-effect in a thin wetland channel at large time is dominated. • Skewness of the transverse mean concentration distribution is presented. Abstract Predicting the evolution of concentration distribution of environmental transport in wetland flows has a broad range of applications in ecological engineering practice. By extending a previous study, the spatial concentration distribution of solute transport due to an instantaneous environmental emission in a wetland channel with rectangular cross-section is presented in this work by means of Chatwin's long-time asymptotic technique. To account for the effect of high order moment, skewness of the transverse mean concentration distribution is analyzed. Two important parameters, i.e., aspect ratio (depth to width) and damping factor, on the dispersion process are discussed. Four studied cases illustrated that the transverse concentration distribution is nonuniform even at large time and the aspect ratio can affect the transverse concentration distribution greatly. The cross-sectional mean concentration distribution is asymmetrical in the initial stage and shows an asymptotic Gaussian distribution at large time. The dispersion process in a thick (width equals depth) wetland channel is quicker than that in a thin wetland channel. The spatial concentration distribution is dominated by the lateral-sidewall-effect on a large time scale for environmental transport in a thin wetland channel. [ABSTRACT FROM AUTHOR]

This study aims at contributing to quinine extraction using supercritical CO2 and ethanol as a co-solvent. The diffusion coefficients of quinine in supercritical CO2 are measured using the Taylor dispersion technique when quinine is pre-dissolved in ethanol. First, the diffusion coefficients of pure ethanol in the supercritical state of CO2 were investigated in order to get a basis for seeing a relative change in the diffusion coefficient with the addition of quinine. We report measurements of the diffusion coefficients of ethanol in scCO2 in the temperature range from 304.3 to 343 K and pressures of 9.5, 10 and 12 MPa. Next, the diffusion coefficients of different amounts of quinine dissolved in ethanol and injected into supercritical CO2 were measured in the same range of temperatures at p = 12 Mpa. At the pressure p = 9.5 MPa, which is close to the critical pressure, the diffusion coefficients were measured at the temperature, T = 343 K, far from the critical value. It was found that the diffusion coefficients are significantly dependent on the amount of quinine in a small range of its content, less than 0.1%. It is quite likely that this behavior is associated with a change in the spatial structure, that is, the formation of clusters or compounds, and a subsequent increase in the molecular weight of the diffusive substance.

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.

Mutual diffusion coefficients, D, were determined for aqueous solutions of sodium hyaluronate (NaHy) at 25 °C and concentrations ranging from 0.00 to 1.00 g·dm−3 using the Taylor dispersion technique. From these experimental data, it was possible to estimate some parameters, such as the hydrodynamic radius Rh, and the diffusion coefficient at infinitesimal concentration, D0, of hyaluronate ion, permitting us to have a better understanding of the structure of these systems of sodium hyaluronate in aqueous solutions. The additional viscosity measurements were done and Huggins constant, kH, and limiting viscosity number, [η], were computed for interaction NaHy/water and NaHy/NaHy determination.

A simple local two-relaxation-time Lattice Boltzmann numerical formulation (TRT-EMM) of the extended method of moments (EMM) is proposed for analysis of the spatial and temporal Taylor dispersion in d -dimensional streamwise-periodic stationary mesoscopic velocity field resolved in a piecewise-continuous porous media. The method provides an effective diffusivity, dispersion, skewness and kurtosis of the mean concentration profile and residence time distribution. The TRT-EMM solves a chain of steady-state heterogeneous advection–diffusion equations with the pre-computed space-variable mass-source and automatically undergoes diffusion-flux jump on the abrupt-porosity streamwise-normal interface. The temporal and spatial systems of moments are computed within the same run; the symmetric dispersion tensor can be restored from independent computations performed for each periodic mean-velocity axis; the numerical algorithm recursively extends for any order moment. We derive an exact form of the bulk equation and implicit closure relations, construct symbolic TRT-EMM solutions and determine specific relation between the equilibrium and the collision degrees of freedom viewing an exact parameterization by the physical non-dimensional numbers in two alternate situations: “parallel” fracture/matrix flow and “perpendicular” Darcy flow through porous blocks in “series”. Two-dimensional simulations in linear Brinkman flow around solid and through porous obstacles validate the method in comparison with the two heterogeneous direct LBM-ADE schemes with different anti-numerical-diffusion treatment which are proposed and examined in parallel. On the coarse grid, accuracy of the three moments is essentially determined by the free-tunable collision rate in all schemes, and especially TRT-EMM. However, operated within a single periodic cell, the TRT-EMM is many orders of magnitude faster than the direct solvers, numerical-diffusion free, more robust and much more capable for accuracy improving, high Péclet range and free-parameter influence reduction with the mesh refinement. The method is an efficient predicting tool for the Taylor dispersion, asymmetry and peakedness; moreover, it allows for an optimal analysis between the mutual effect of the flow regime, Péclet number, porosity, permeability and obstruction geometry. [ABSTRACT FROM AUTHOR]

As an extension of our recent study (Li et al. Taylor dispersion in wind-driven current. Journal of Hydrology 555, 697–707), an analytical study based on spatial concentration moments is performed on contaminant transport in a gravity induced open channel flow under wind effect. The zeroth to the fourth order spatial concentration moments are derived to describe the temporal evolution of spatial concentration distribution, fitted by the fourth order Hermite polynomials. In initial stage, convection dominates the contaminant transport, leading to a large non-uniformity of vertical concentration. As time passes, the contaminant transport gradually evolves to an asymptotic pattern following a diffusion-like model of Taylor dispersion. The combined influence of gravity and wind effect on contaminant transport is investigated: the tailwind effect will accelerate the development of Taylor dispersion as well as the transport of contaminant, while the conveyance capacity is weakened in a headwind circumstance. [ABSTRACT FROM AUTHOR]

Studying solute dispersion in channel flows is of significance for environmental and industrial applications. Two-dimensional concentration distribution for a most typical case of a point source release on the free water surface in a channel flow with bed absorption is presented by means of Chatwin’s long-time asymptotic technique. Five basic characteristics of Taylor dispersion and vertical mean concentration distribution with skewness and kurtosis modifications are also analyzed. The results reveal that bed absorption affects both the longitudinal and vertical concentration distributions and causes the contaminant cloud to concentrate in the upper layer. Additionally, the cross-sectional concentration distribution shows an asymptotic Gaussian distribution at large time which is unaffected by the bed absorption. The vertical concentration distribution is found to be nonuniform even at large time. The obtained results are essential for practical implements with strict environmental standards. [ABSTRACT FROM AUTHOR]

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