Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.     

Transport of Reacting Solutes Through the Unsaturated Zone

Unsaturated flows within subsurface regions control many large-scale hydrological and environmental processes. This contribution presents and discusses the results of numerical calculations dealing with the flow of water, the chemical reaction at the water-mineral interface and the transport of chemical species caused by such flows. The source of the water flow through the soil is solely the rainfall. The water motion is calculated for two different soil classes and for a typical annual precipitation. The codes which were used are based on the following model: The transport of chemical species is described by a set of partial differential equations, and the homogeneous chemical processes, under the assumption of equilibrium, are described by a set of nonlinear algebraic equations. The source terms of these partial differential equations are given by rate laws of the chemical weathering. Rainfall and chemical weathering are, therefore, the sources of the transport of reactive multispecies in this model.     

Computer Simulation of Non-Newtonian Flow and Mass Transport Through Coronary Arterial Stenosis

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Laboratory Investigation of Variable-Density Flow and Solute Transport in Unsaturated–Saturated Porous Media

In many groundwater systems, fluid density and viscosity may vary in space and time as a function of changes in concentration and temperature of the fluid. When dense groundwater plumes interact with less dense ambient groundwater, these density variations can significantly affect flow and transport processes. Under certain conditions, gravitational instabilities in the form of lobe-shaped fingers can occur. This process is significant because it can lead to more rapid and spatially extensive solute transport. This paper presents new experiments carried out in a sand filled glass flow container under both fully saturated and variably-saturated conditions and focuses upon the processes that occur at the capillary fringe and below the water table, as affected by a dense contaminant plumes migration through the unsaturated zone. Source fluids stained with Rhodamine-WT were introduced at the upper boundary of the tank at a range of low and high densities. In addition to the fluid density gradients and porous medium permeability that determine the onset conditions for instabilities in fully saturated experiments, volumetric water content appears critical in the variably-saturated laboratory runs. Plume behaviour at the water table appears dependent upon the density of the fluid that accumulates there. For neutral and low density fluids, plumes accumulate at the water table and then spread laterally above it and the water table forms a barrier to further vertical flow as pore water velocities reduce with increasing water content. For medium and high density fluids, vertical movement continues as instabilities form at the capillary fringe and fingers begin to grow at the water table boundary and move downwards into the saturated zone. In these cases, lateral spreading of the plume is small. Despite these more qualitative observations, the exact nature of the relevant stability criteria for the onset and growth of instabilities in variably-saturated porous media presently remain unclear. All experimental results suggest, however, that the unsaturated zone and position of the water table must be considered in contaminant studies in order to predict the migration pathways, rates and ultimate fate of dense contaminant plumes. It is possible that the results of experiments presented in this paper could form a useful basis for the testing of variable-density (and variably-saturated) groundwater flow and solute transport numerical codes because they offer controlled physical laboratory analogs for comparison. They also provide a strong basis for the development of more rigorous mathematical formulations that are likely to be either developed or tested using numerical flow and solute transport simulators.     

Measurement of the Coefficient of Transverse Dispersion in Flow Through Packed Beds for a Wide Range of Values of the Schmidt Number

Experimental values of the coefficient of transverse dispersion (D _T) were measured with the system 2-naphthol/water, over a range of temperatures between 293K and 373K, which corresponds to a range of values of viscosity () between 2.83×10^–4 Ns/m² and 1.01×10^–3 Ns/m² and of molecular diffusion coefficient (D _m) between 1.03×10^–9 m²/s and 5.49×10^–9 m²/s. Since the density () of water is close to 10³ kg/m³, the corresponding variation of the Schmidt number (Sc=/D _m) was in the range 1000 – 50. More than 200 experimental values of the transverse dispersion coefficient were obtained using beds of silica sand with average particle sizes (d) of 0.297 and 0.496mm, operated over a range of interstitial liquid velocities (u) between 0.1mm/s and 14mm/s and this gave a variation of the Reynolds number (Re=du/) between 0.01 and 3.5.Plots of the dimensionless coefficient of transverse dispersion (D _T/D _m) vs. the Peclet number (Pe_m=ud/D _m) based on molecular diffusion bring into evidence the influence of Sc on transverse dispersion. As the temperature is increased, the value of Sc decreases and the values of D _T/D _m gradually approach the line corresponding to gas behaviour (i.e. Sc 1), which is known to be well approximated by the equation D _T/D _m=1/+ud/12D _m, where is the tortuosity with regard to diffusion.     

Heat Transport in Unsaturated Zone Thermal Energy Storage – Analysis with Two-Phase and Single-Phase Models

We analyze a field experiment where ambient air is injected into the soil during the summer and extracted again during the winter. A multiphase model accounting for the conductive transport as well as the convective transport with the moving liquid and gas phases is used along with a more simplified single-phase model where the convective transport is due to the gas alone. The latter model also accounts for subzero wintertime temperatures. The multiphase model captures well both the seasonal variations and the actual test sequence, the main calibration being in the adjustment of medium permeabilities based on the observed pressure responses. The effect of the injection pump on the temperature and humidity of the injection air needs to be known accurately. Taking into account the humidity of the injection air explicitly instead of using humidity-corrected enthalpy values also has an effect. The effect of various humidity and specific enthalpy assumptions is of the order of 1–1.5°C, while ignoring the wintertime subzero temperatures has an effect of 1–2°C. These differences are of the same order of magnitude as the heterogeneity-introduced differences in field data. Using the simplified single-phase model typically appears to cause a difference of 1–2°C, but can yield an even higher deviation of the order of 3–4°C.     

Heat,Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, _m ; solution osmotic pressure head _o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (),T, and C. The thermal vapor diffusivity D _Tv first increased as increased to0.22 m³/m³ then decreased with furtherincreases in . D _Tv was 3 orders of magnitudegreater than either isothermal vapor D _mv orosmotic vapor D _ov , diffusivities at of0.20~m³/m³, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D _Tv decreased with increasing C to a greater extent thanD _mv and D _ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D _d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at of0.20~m³/m³, T of 50°C, and C of 0.001 mol/kg.     

Upscaling of Nonwetting Phase Residual Transport in Porous Media: A Network Approach

Based on the volume averaging method, a macroscopic model is developed for the upscaling of NAPL transport in a porous medium idealised by a network model. Under the assumption of local mass non-equilibrium, a macroscopic equation involving a dispersion tensor, additional convective terms and a linear form for the interfacial mass flux is obtained. The resolution of the two local closure problems obtained allow the determination of the local properties without adjustable parmeters. These problems are solved in a semi-analytical, semi-numerical manner on the network. The originality of this work is the association of the upscaling by volume averaging method with the network approach. The local properties, including the dispersion tensor and the mass exchange coefficient, can therefore be calculated over a large number of pore-bodies and pore-throats in a computationaly tractable manner, thus leading to more significant results. Results are presented for 3D, spatially periodic models of porous media.     

Implementation of Richardson extrapolation in an efficient adaptive time stepping method: applications to reactive transport and unsaturated flow in porous media

Environmental studies are commonly carried out through numerical simulations, which have to be accurate, reliable and efficient. When transient problems are considered, the validity of the solutions requires the calculation and management of the temporal discretization errors. This article describes an adaptive time stepping strategy based on the estimation of the local truncation error via the Richardson extrapolation technique. The time-marching scheme is mathematically based on this a posteriori error estimation that has to be gauged. General optimizations are also suggested making the control of both the temporal error and the evolution of the time step size very efficient. Furthermore, the algorithm connecting these methods is all the more interesting as it could be implemented in many computational codes using different numerical schemes. In the hydrogeochemical domain, this algorithm represents an interesting alternative to a fixed time step as shown by the various numerical tests involving reactive transport and unsaturated flow.     

Theoretical Analysis of Anion Exclusion and Diffusive Transport Through Platy-Clay Soils

Diffusive transport through geosynthetic clay liners and engineered compacted clay landfill liners is the primary mechanism for mass transport from well-engineered modern landfills. For this reason, accurate estimates of diffusion coefficients for clay soils are essential for the design of engineered liner systems. A long-standing theoretical problem is the role of anion exclusion on the estimation of diffusion coefficients for ionic solutes migrating through charged porous media. This paper describes the steady-state solution of a fully coupled set of transport equations modeling ion movement through a permanently charged platy-clay soil. The microscale analysis takes into account the actual diffusion coefficient for each ion species, ion-pairing (as required by electroneutrality of the solution), as well as anion exclusion and cation inclusion ,arising from the permanent charge on clay particles. To render the problem tractable, the theoretical analysis focuses on an extremely small two-dimensional unit cell in an ideal, saturated, two-phase porous medium. The analysis presented here is limited to a particular geometrical example, but this example is sufficiently general for characteristic behaviours of systems of this kind to be identified. Most importantly, new insight is gained into the mechanism of ion migration through a charged platy-clay soil. The numerical results obtained from this study show that the identification of macroscopic transport quantities such as effective diffusion coefficients and membrane potentials from diffusion cell tests using standard diffusion theory only hold for a specific system. While ion exclusion behaviours are often referred to in the literature, as far as the authors are aware there has been no previous detailed microscale analysis of their role in steady-state diffusion through a charged platy-clay soil.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

An Enthalpy Control Volume Method for Transient Mass and Heat Transport with Solidification

A single domain enthalpy control volume method is developed for solving the coupled fluid flow and heat transfer with solidification problem arising from the continuous casting process. The governing equations consist of the continuity equation, the Navier–Stokes equations and the convection–diffusion equation. The formulation of the method is cast into the framework of the Petrov–Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The use of the step test function and the constant flux approximation leads to the derivation of the exponential interpolating functions for the velocity and temperature fields within each control volume. The exponential fitting makes it possible to capture the sharp boundary layers around the solidification front. The method is then applied to investigate the effect of various casting parameters on the solidification profile and flow pattern of fluids in the casting process.     

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed (CFB) designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process.Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-off between computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient.A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementation is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed (solid flux) is implemented through additional mass source/sink terms in the continuity equations of the two phases.For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations. The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system.The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.     

Finite element analysis of multicomponent two-phase flows with interphase mass and momentum transport

The application of the finite element method to multiphase flow problems with interphase mass and heat transfer is described. A general forinulation is used that determines the position of the interfacial boundary and allows for multiple solvents, differential volatilities and concentration- and temperature-dependent thermophysical properties. Species phase change and the dramatic volume change that acompanies interphase mass transfer make implementation of the theory challening, since these events lead to discontinuous velocities and concentrations at phase boundaries. These discontinuities are especially large in processes involving rapid evaporation or condensation. As examples we examine the effects of rapid drying on film and fibre formation of sol--gel materials, which are often laden with volatile species.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.     

DNS and Modelling of Passive Scalar Transport in Turbulent Channel Flow with a Focus on Scalar Dissipation Rate Modelling

A direct numerical simulation of turbulent channel flow with an imposed mean scalar gradient is analyzed with a focus on passive scalar flux modelling and in particular the treatment of the passive scalar dissipation equation. The Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half width is 265. Budgets are presented for the passive scalar variance and its dissipation rate, as well as for the individual scalar flux components. These form a basis for a discussion of modelling issues related to explicit algebraic scalar flux modelling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bifurcation of flow and mass transport in a curved blood vessel

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis. The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign Researcher and Foundation for University Teachers, the Ministry of Education     

Wall Region Porosity Distributions for Packed Beds of Uniform Spheres with Modified and Unmodified Walls

A mathematical derivation of the porosity (local void fraction) distribution near the walls of packed beds of uniform spheres is presented. This investigation supports the study of methods of reducing or eliminating the so-called wall effect, or bypass flow, which accompanies the increase in porosity when spheres come in contact with a solid boundary. Limiting the amount of bypass flow is important in certain applications such as in packed bed nuclear reactors where bypass flow allows some coolant to avoid the high power density core region. Four basic porosity distributions are determined. The first investigates the case where spheres against a flat wall are packed in the tightest possible packing density. This density is then reduced by changing the sphere spacing until the minimum porosity matches that obtained experimentally. In the other cases, the effect of various ways of embedding spheres in the wall on the wall region porosity is examined. By partially embedding spheres in the wall, the porosity at the wall is reduced and the most direct cause of the bypass flow is thereby eliminated. The porosity is found by evaluating the ratio of the solid area to total area in a plane which is parallel to the wall. The local porosity is derived as a function of distance from the wall in the region within one-half a sphere diameter from the wall. The average porosity of the wall region is also calculated. This research has application to flow situations such as packed bed chemical reactors, pebble bed nuclear reactors and flow in packed beds.     

Radiative and Thermal Dispersion Effects on Non-Darcy Natural Convection with Lateral Mass Flux for Non-Newtonian Fluid from a Vertical Flat Plate in a Saturated Porous Medium

The problem of natural convective heat transfer for a non-Newtonian fluid from an impermeable vertical plate embedded in a fluid-saturated porous medium has been analyzed. Non-Darcian, radiative and thermal dispersion effects have been considered in the present analysis. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation. The resulting system of equations is solved by using a double shooting Runge–Kutta method. The effect of viscosity index n, the conduction–radiation parameter R, the non-Darcy parameter Gr*, the thermal dispersion parameter Ds and the suction/injection parameter f_w on the fluid velocities, temperatures and the local Nusselt number are discussed.