Hydrodynamic Dispersion Research Articles

Asymptotic study of unsteady mass transfer through a rigid artery with multiple irregular stenoses

The present article examines the transport of species in streaming blood through a rigid artery in the presence of multi-irregular stenosis. The carrier fluid i.e., blood is assumed to be non-Newtonian fluid (Cassons viscoplastic model is used) and the arterial wall is considered to be rigid. A robust model is developed for non-Newtonian flow and hydrodynamic dispersion with the first-order chemical reaction on the arterial boundary in multiple irregular stenosed arterial geometries. Multiple scale solutions of the non dimensional boundary value problem are presented. Asymptotic expressions are developed for velocity and shear stress. Extensive visualization of velocity, concentration, and other flow characteristics is included for various stenotic scenarios, Péclet numbers, and Damköhler numbers. Significant modification in hemodynamic characteristics is computed with viscoplasticity. Mean concentration is also dramatically modified with yield stress and Péclet and Damköhler numbers. The study is relevant to arterial disease simulation.

Hydrodynamic dispersion relations at finite coupling

By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the mathcal{N} = 4 supersymmetric Yang-Mills theory at infinite ’t Hooft coupling and infinite number of colours. Here, we extend this analysis to the domain of large but finite ’t Hooft coupling. To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations. However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease. The piecewise nature of the dependence is related to the dynamics of branch point singularities of the energy-momentum tensor finite-temperature two-point functions in the complex plane of spatial momentum squared. We repeat the study using the Einstein-Gauss-Bonnet gravity as a model where the equations can be solved fully non-perturbatively, and find the expected decrease of the radii of convergence with the effective inverse coupling which is also piecewise continuous. Finally, we provide arguments in favour of the non-perturbative approach and show that the presence of non-perturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.

Enhancement of T2* Weighted MRI Imaging Sensitivity of U87MG Glioblastoma Cells Using γ-Ray Irradiated Low Molecular Weight Hyaluronic Acid-Conjugated Iron Nanoparticles.

IntroductionIt has been reported that low-molecular-weight hyaluronic acid (LMWHA) exhibits a potentially beneficial effect on cancer therapy through targeting of CD44 receptors on tumor cell surfaces. However, its applicability towards tumor detection is still unclear. In this regard, LMWHA-conjugated iron (Fe3O4) nanoparticles (LMWHA-IONPs) were prepared in order to evaluate its application for enhancing the T2* weighted MRI imaging sensitivity for tumor detection.MethodsLMWHA and Fe3O4 NPs were produced using γ-ray irradiation and chemical co-precipitation methods, respectively. First, LMWHA-conjugated FITC was prepared to confirm the ability of LMWHA to target U87MG cells using fluorescence microscopy. The hydrodynamic size distribution and dispersion of the IONPs and prepared LMWHA-IONPs were analyzed using dynamic light scattering (DLS). In addition, cell viability assays were performed to examine the biocompatibility of LMWHA and LMWHA-IONPs toward U87MG human glioblastoma and NIH3T3 fibroblast cell lines. The ability of LMWHA-IONPs to target tumor cells was confirmed by detecting iron (Fe) ion content using the thiocyanate method. Finally, time-of-flight secondary ion mass spectrometry (TOF-SIMS) imaging and in vitro magnetic resonance imaging (MRI) were performed to confirm the contrast enhancement effect of LMWHA-IONPs.ResultsFlorescence analysis results showed that LMWHA-FITC successfully targeted the surfaces of both tested cell types. The ability of LMWHA to target U87MG cells was higher than for NIH3T3 cells. Cell viability experiments showed that the fabricated LMWHA-IONPs possessed good biocompatibility for both cell lines. After co-culturing test cells with the LMWHA-IONPs, detected Fe ion content in the U87MG cells was much higher than that of the NIH3T3 cells in both thiocyanate assays and TOF-SIMs images. Finally, the addition of LMWHA-IONPs to the U87MG cells resulted in an obvious improvement in T2* weighted MR image contrast compared to control NIH3T3 cells.DiscussionOverall, the present results suggest that LMWHA-IONPs fabricated in this study provide an effective MRI contrast agent for improving the diagnosis of early stage glioblastoma in MRI examinations.

Convergence of hydrodynamic modes: insights from kinetic theory and holography

We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a quali\-tatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.

Effects of Wastewater Treatment Plant’s Discharges on a Freshwater Ecosystem—a Case Study on the Ramalhoso River (Portugal)

Sewage discharges constitute severe stress in freshwater ecosystems. The Ramalhoso River belongs to the Tagus River watershed and was chosen for a pilot study on the impact of wastewaters discharges in a freshwater ecosystem and its ability for self-depuration. Twelve water samples were collected along the river and were georeferenced. The first point is located upstream of the first discharge point, the second one corresponding to the discharge flow, and all the other samples located downstream of secondary inflows at approximately equal distances. Three sampling campaigns were conducted during the rainy winter (January), the intermediate conditions (March), and the dry season (June). The following chemical parameters were analyzed: biochemical oxygen demand for 5 days (BOD5), dissolved oxygen concentration (DO), total phosphorus (Ptotal), total nitrogen (Ntotal), pH, temperature, total suspended solids (TSS), microbiological parameters (MP), and flow determination. Dissolved oxygen, BOD5, and TSS were used as indicators of environmental pollution. A coupled hydrodynamic and water dispersion model simulated different pollution scenarios using the QUAL2kw software to construct a water quality model. The simulation results are consistent with field observations and demonstrate that the model has been correctly calibrated, allowing feasibility studies of different treatment schemes and the development of specific monitoring activities.

Flow and residence time in a two-dimensional aquifer recharged by rainfall

Abstract

Investigation of Post-Darcy Flow in Thin Porous Media

We present numerical simulations of post-Darcy flow in thin porous medium: one consisting of staggered arrangements of circular cylinders and one random distribution of cylinders bounded between walls. The simulations span a range of Reynolds numbers, 40 to 4000, where the pressure drop varies nonlinearly with the average velocity, covering nonlinear laminar flow to the fully turbulent regime. The results are compared to those obtained by replacing the bounding walls with symmetric boundaries with the aim to reveal the effect of bounding walls on microscopic characteristics and macroscopic measures, i.e., pressure drop, hydrodynamic dispersion and Reynolds stresses. We use large eddy simulation to directly calculate the Reynolds stresses and turbulent intensity. The simulations show that vortical structures emerge at the boundary between the cylinders and the bounding walls causing a difference between the microscopic flow in the confined and non-confined porous media. This affects the averaged values of pressure drop, the hydrodynamic dispersion and the Reynolds stresses. Finally, the distance between the bounding walls is altered with the particle Reynolds number kept constant. It is observed that the difference between results calculated in confined and non-confined cases increases when the bounding walls are narrower.

Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media.

We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intrapore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion in terms of the characteristic pore length, Eulerian velocity distribution, and Péclet number.

Unsaturated flow effects on solute transport in porous media

A major contaminant transport process in soils is hydrodynamic dispersion by affecting the spreading and arrival of surface-applied pollutants at underlying groundwater reservoirs. When a soil is unsaturated, hydrodynamic dispersion is very much affected by soil water saturation. Centimeter- and decimeter-scale column experiments were carried out to explore the effects of fluid saturation and particle size on the unsaturated solute dispersivity. Measured in-situ breakthrough curves were analyzed in terms of both classical advection–dispersion and dual-porosity (mobile-immobile) type transport equations. A clear non-monotonic relationship was found between the dispersivity and soil water saturation. The extent of non-monotonicity was more pronounced for a relatively coarse-textured sand compared to a finer sand. This finding has been reported rarely before; it explains some of the inconsistencies of saturation-dispersivity relationships in the literature.

Dynamics of CO2 Density‐Driven Flow in Carbonate Aquifers: Effects of Dispersion and Geochemistry

AbstractThe dissolution of carbon‐dioxide (CO2) in deep saline aquifers is an important trapping mechanism in carbon storage. This process is triggered by unstable high‐density CO2 front, which later promotes density‐driven mixing, hydrodynamic dispersion of CO2, and favors the long‐term sequestration. In many former studies, effects of hydrodynamic dispersion and multispecies geochemical reactions have been ignored. This work elaborates the impacts of these simplifications on the dynamics of convective mixing by numerical simulations. Geochemical effects were studied by the implementation of rock‐fluid and fluid‐fluid interactions for a typical carbonate aquifer. Results show that accounting for the hydrodynamic dispersion decreases the convection onset time and increases the CO2 dissolution flux, which is more significant in larger dispersivities and Rayleigh numbers. Results indicate that carbonate geochemical reactions intense the long‐term overall efficiency of the process, while decrease the total amount of sequestered carbon in the diffusion‐dominated period. Results also reinforce the importance of realistic geochemical representation and importance of spatial and temporal dependence of the reactions pathway, subsequent to the finger development for more detailed simulation of the CO2 storage process.

A numerical study of the influence of sediment compaction caused by groundwater pumping on contaminant transport

Studies of clay liners have shown that deformation caused by loading can have an important influence on the transport of contaminants. However, very little comparable work has been carried out on aquifers, even though pumping of groundwater from alluvial aquifer systems often causes sediment compaction and could create a similar effect. In this study, a coupled, multi-field, numerical simulation model was used to investigate the extent to which groundwater pumping affects the porosity and hydraulic conductivity of the aquifer and how such changes may, in turn, modify contaminant transport by altering parameters such as hydrodynamic dispersion. The model was based on aquifer conditions encountered at a representative site in east-central China with pumping introduced at a single well located in the centre of the model domain. Model results for an observation well located 5 m from the pumping well showed that sediment compaction caused by a steady-state drawdown of just 10 m produces a 0.41% reduction in porosity. While a reduction in porosity would normally enhance contaminant movement due to higher seepage velocities and, consequently, higher values of hydrodynamic dispersion, this effect is more than compensated by a reduction in seepage velocity associated with a 1.9% decline in hydraulic conductivity that is also caused by sediment compaction. At the well, where steady-state drawdown approaches 20 m, porosity reduces by 0.77% and hydraulic conductivity declines by over 3%. For the system investigated, the overall effect of sediment compaction is to inhibit the transport of contaminants and significantly reduce the magnitude and areal extent of the contaminant impact.

A procedure to estimate cutoff wall transport properties from monitoring wells

AbstractOwing to their capability in limiting the transport of pollutants in the subsoil, cutoff walls are popular solutions for the confinement of contaminants. These barriers are often made of soil‐bentonite or cement‐bentonite mixtures, which are characterized by low hydraulic conductivity, low hydrodynamic dispersion, and long‐term durability. However, the aggressive chemical environment to which these walls are subjected might negatively impact on their performance. Assessment of their performance with time is thus a crucial issue in wall design. The use of dedicated monitoring wells, cast in place inside the wall during construction when the bentonitic mixture is still fluid, can be particularly suitable for both intercepting and detecting the fluids flowing through the barrier. In this research, the results of a numerical study aimed at providing a methodology to estimate the transport properties of the backfill material at the site scale are presented. The methodology relies on abaci and only requires (i) flow and concentration of contaminant data within a monitoring well inside the barrier and (ii) hydraulic head at inlet and outlet of the barrier to be known.

Effect of X-ray $$\mu$$CT Resolution on the Computation of Permeability and Dispersion Coefficient for Granular Soils

X-ray micro-computed tomography ( $$\mu$$ CT) can produce realistic 3D-images of the pore structure of a material. Extracting its geometry enables the computation of effective properties of the material—such as the permeability (k) and the hydrodynamic dispersion coefficient ( $$D_h$$ )—, through the solutions of the Stokes equation (SE) and Advection-Diffusion equation (ADE), respectively. In this study, the effect of the image resolution on these properties is discussed. For such purpose, four different resolutions are evaluated for both a real sample of Fontainebleau sand and a numerically generated sample created by degrading the Fontainebleau image with highest resolution. The SE was computed using the commercial software GeoDict. To solve the ADE, a Finite Volume software was developed which includes a high order total variation diminishing scheme for advection. The analysis of dispersion was based on numerical breakthrough curves. Our model was tested in a large range of Peclet numbers (Pe) and travel distances, accurately describing the transition between diffusion and advection dominated regimes of dispersion. The $$D_h$$ exhibits a linear increase with travel distance for Pe $$> 10$$ . This classical effect increases with increasing Pe. The percentage change on k and $$D_h$$ increases with decreasing resolution in agreement with the corresponding behavior of porosity, specific surface and pore size distributions. The images directly scaled with the $$\mu$$ CT showed more discrepancy than the numerically scaled images. The criteria to estimate the quality of permeability from the pore size distribution proposed on our previous study remains valid. The $$D_h$$ is less sensitive to resolution than k.

Transport and retention of porous silicon-coated zero-valent iron in saturated porous media.

Porous silicon-coated zero-valent iron (Fe0@p-SiO2) is a promising material for in-situ contaminated groundwater remediation. However, investigations of factors that affect the transport of Fe0@p-SiO2 remain incomplete. In the present study, Fe0@p-SiO2 composites were prepared by a SiO2-coated technology, and a series of column experiments were conducted to examine the effects of media size, ionic strength, and injection velocity and concentration on retention and transport in saturated porous media. Results showed that the obtained Fe0@p-SiO2 is a core-shell composite with zero-valent iron as the core and porous silicon as the shell. Media size, injection velocity, Fe0 concentration, and ionic strength had a significant impact on the transport of Fe0@p-SiO2. Fe0@p-SiO2 effluent concentrations decreased with a smaller media size. Increasing initial particle concentration and ionic strength led to a decrease in particle transport. High particle retention was observed near the middle of the column, especially with high injection concentration. That was also observable in the condition of lower injection velocity or finer media. The results indicated that two transport behaviors during particles transport, which were "agglomeration-straining" and "detachment-re-migration". Moreover, the dominated mechanisms for Fe0@p-SiO2 transport and retention in saturated porous media are hydrodynamic dispersion and interception. Given the results, in practical engineering applications, proper injection velocity and concentration should be selected depending on the pollution status of groundwater and the geochemical environment to ensure an effective in-situ reaction zone.

Experimental and Numerical modeling on dye adsorption using pyrolyzed mesoporous biochar in Batch and fixed-bed column reactor: Isotherm, Thermodynamics, Mass transfer, Kinetic analysis

Adsorbents derived from agro-waste can be a feasible substitute for the synthesis of the activated biochar for the removal of pollutants from their aqueous solution. ZnCl2 was used to activate the pyrolyzed biochar, derived from sugarcane bagasse. Physical characterizations of synthesized activated pyrolyzed biochar were analyzed by XRD, FTIR, and SEM. From the BET analysis, the surface area of activated pyrolyzed biochar was determined as 51.733 m2/g. Investigations on the adsorption of Malachite Green (MG) dye using activated biochar was studied in batch and fixed-bed system. Isotherm study suggested that the Freundlich isotherm model (R2=0.9955) provided the best fit to the equilibrium adsorption and the biosorption capacity obtained as 90.1mg/g at 30°C. Experimental data showed well in accordance with the pseudo-second-order kinetic model. The thermodynamic study indicated the spontaneous and exothermic nature of reactions involved. Boyd's film diffusion model was used with the kinetic data of the Batch adsorption experiment to evaluate the diffusion mechanism and rate-limiting step. The derived value of the average effective diffusion coefficient (De) was 0.014 × 10−7 m2/s. The Yoon-Nelson and Thomas model ware well fitted with the experimental data obtained from column adsorption study. The dispersion coefficient and mean pore velocity for adsorbent columns were estimated using the breakthrough curves at various experimental conditions. Adsorption Kinetic parameters for MG dye were estimated using the solute transport model by combining convective flow and hydrodynamic dispersion with a two-site adsorption model and coupled with inverse modeling of breakthrough curves.

Bounds on Transport from Univalence and Pole-Skipping.

Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories. Few are exact and inviolable. I present a new set of methods and sufficient conditions for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations, including diffusivity and the speed of sound. These general techniques combine analytic properties of hydrodynamics and the theory of univalent (complex holomorphic and injective) functions. Particular attention is devoted to bounds relating transport to quantum chaos, which can be established through pole-skipping in theories with holographic duals. Examples of such bounds are shown along with holographic theories that can demonstrate the validity of the conditions involved. I also discuss potential applications of univalence methods to bounds without relation to chaos, such as for example the conformal bound on the speed of sound.

Digital Rock Physics: computation of hydrodynamic dispersion

Hydrodynamic dispersion is a crucial mechanism for modelling contaminant transport in subsurface engineering and water resources management whose determination remains challenging. We use Digital Rock Physics (DRP) to evaluate the longitudinal dispersion of a sandpack. From a three-dimensional image of a porous sample obtained with X-ray microtomography, we use the method of volume averaging to assess the longitudinal dispersion. Our numerical implementation is open-source and relies on a modern scientific platform that allows for large computational domains and High-Performance Computing. We verify the robustness of our model using cases for which reference solutions exist and we show that the longitudinal dispersion of a sandpack scales as a power law of the Péclet number. The assessment methodology is generic and applies to any kind of rock samples.

Modeling the behavior of hydrodynamic dispersion by solving boundary value problems

Modeling the behavior of hydrodynamic dispersion by solving boundary value problems

A Numerical Investigation of the Hydrodynamic Dispersion in Novel Chromatographic Stationary Phases

A Numerical Investigation of the Hydrodynamic Dispersion in Novel Chromatographic Stationary Phases

Experimental and numerical study of bimolecular reactive transport in a single rough-wall fracture

In order to test the performance of the incomplete mixing model including the advection-dispersion-reaction equation (IM-ADRE) in simulating bimolecular reactive transport in fractured media, the laboratory-controlled experiments and numerical modeling were conducted in a single rough-wall fracture. Bimolecular reaction of aniline (AN) + 1, 2-napthoquinone-4-sulfonic acid (NQS) → 1, 2-naphthoquinone-4-aminobenzen (NQAB) was employed. Three different flow rates (0.15, 0.825 and 1.5 mL/s) and three fracture apertures (2, 3 and 4 mm) were considered in the experiment. The numerical simulation was analyzed and discussed based on the Péclet (Pe) number and Damköhler (Da) number. The results showed that although the spatial distribution of product concentration varied with the Pe number, the IM-ADRE model could simulate it well. The discrepancy between the simulated and measured peak product concentrations was less than 0.7%, which was far less than the value of 5% in previous study (Qian et al., 2015) produced by the IM-ADRE model used to modeling the reactive transport in porous media. This meant that the IM-ADRE model was effective for simulating and predicting the experimental results of bimolecular reactive transport in a single rough-wall fracture. Due to the instability of the product, the simulated value of the peak product concentration was always higher than the experimental value. Through further analysis of the model parameters, it was found that the hydrodynamic dispersion coefficient (D) changed significantly with the change of Pe number. The parameters m and β0 were linearly correlated with the Pe number. In addition, the IM-ADRE model was more sensitive to the parameters m and β0 but less sensitive to D.