Fluid flow solute transport

Increasingly since the mid-1970s, with the advent of high-speed digital computers, process-based mathematical models of coupled subsurface fluid flow, solute transport, and geochemistry have been used to assess subsurface water contamination impacts. 

A second, even more speculative point is that the mathematical framework of nonlinear dynamics may provide a basis to begin to bridge the gap between local microstructural features of a fluid flow or transport system and its overall meso- or macroscale behavior. On the one hand, a major failure of researchers and educators alike has been the inability to translate increasingly sophisticated fundamental studies to the larger-scale transport systems of traditional interest to chemical engineers. On the other hand, a basic result from theoretical studies of nonlinear dynamical systems is that there is often an intimate relationship between local solution structure and global behavior. Unfortunately, I am presently unable to improve upon the necessarily vague notion of a connection between these two apparently disparate statements. 

The MOTIF code is a three-dimensional finite-element code capable of simulating steady state or transient coupled/uncoupled variable-density, variable- saturation fluid flow, heat transport, and conservative or nonspecies radionuclide) transport in deformable fractured/ porous media. In the code, the porous medium component is represented by hexahedral elements, triangular prism elements, tetrahedral elements, quadrilateral planar elements, and lineal elements. Discrete fractures are represented by biplanar quadrilateral elements (for the equilibrium equation), and monoplanar quadrilateral elements (for flow and transport equations). 

Fig. 6. Solute transport in hemodialysis. Clearance vs solute mol wt for dialy2ers prepared from the two different membranes illustrated in Figure 5. Numbers next to points represent in min /cm calculated from equations 10 and 5. Data is in vitro at 37°C with saline as the perfusion fluid. Lumen flow, dialysate flow, and transmembrane pressure were 200 ml,/min, 500 mL/min, and 13.3 kPa (100 mm Hg) area = 1.6. Inulin clearance of the SPAN...

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

In addition to impurities, other factors such as fluid flow and heat transfer often exert an important influence in practice. Fluid flow accentuates the effects of impurities by increasing their rate of transport to the corroding surface and may in some cases hinder the formation of (or even remove) protective films, e.g. nickel in HF. In conditions of heat transfer the rate of corrosion is more likely to be governed by the effective temperature of the metal surface than by that of the solution. When the metal is hotter than the acidic solution corrosion is likely to be greater than that experienced by a similar combination under isothermal conditions. The increase in corrosion that may arise through the heat transfer effect can be particularly serious with any metal or alloy that owes its corrosion resistance to passivity, since it appears that passivity breaks down rather suddenly above a critical temperature, which, however, in turn depends on the composition and concentration of the acid. If the breakdown of passivity is only partial, pitting may develop or corrosion may become localised at hot spots if, however, passivity fails completely, more or less uniform corrosion is likely to occur. 

The attractive feature of LADM Is that once the fluid structure Is known (e.g., by solution of the YBG equations given In the previous section or by a computer simulation) then theoretical or empirical formulas for the transport coefficients of homogeneous fluids can be used to predict flow and transport In Inhomogeneous fluid. For diffusion and Couette flow In planar pores LADM turns out to be a surprisingly good approximation, as will be shown In a later section. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

These derivations yield general expressions for the transport coefficients that may be evaluated by simulating MPC dynamics or approximated to obtain analytical expressions for their values. The shear viscosity is one of the most important transport properties for studies of fluid flow and solute molecule... 

The deposition mechanism of CBD CdZnS thin films under the current stirring conditions are dominated by convection mode (stirring or hydrodynamic transport). In a solution, fluid flow occurs by a natural convection mode... 

The principal determinants of lOP are the rate of aqueous fluid production by the ciliary epithelium and the rate of fluid drainage (outflow) in the canal of Schlemm. Aqueous fluid production involves passive, near-isosmolar fluid secretion driven by active salt transport across the ciliary epithelium. Ion and solute transporters have been identified on pigmented and non-pigmented layers of the ciliary epithelium that probably facilitate active solute secretion. Aqueous fluid drainage is believed to involve pressure-driven bulk fluid flow in the canal of Schlemm, as well as fluid movement through the sclera by seepage across the ciliary muscle and supraciliary space. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

A number of authors [46 to 48] employ the single sphere model in which the packed bed is considered as a set of equal spheres that are under the same state of extraction, and the fluid flowing around them is solute-free. That is, equation (3.4-90) would be valid, but without the generation term [46], The transport at the solid-fluid interface obeys the boundary condition (Eqn. 3.4-94) with C = 0 (fluid-flows at a large velocity). Under these assumptions, there is an analytical solution to the above problem (without axial dispersion) in terms of the Biot number (Bi = k, R/De), included in the following equation ... 

Clearly, the solution of this equation at forced-convection electrodes will depend on whether the fluid flow is laminar, in the transition regime, or turbulent. Since virtually all kinetic investigations have been performed in the laminar flow region, no further mention will be made of turbulent flow. The reader interested in mass transport under turbulent flow is recommended to consult refs. 14 and 15. 

Most of the models assume that neutral-species transport can be represented with either a well-mixed model or a plug flow model. The major drawback to these assumptions is that important inelastic rate processes such as molecular dissociation are usually localized in space in the reactor and are often fast compared with rates of diffusion or convection. As a result, the spatial variation of fluid flow in the reactor must be accounted for. This variation introduces a major complication in the model, because the solution of the nonisothermal Navier-Stokes equations in multidimensional geometries is expensive and difficult. 

One method of transporting solutions and compounds in low permeability soils is the application of an electric current to the soil using a process called Electroosmosis (EO). EO fluid flow is a result of ions movement in the double layer of clay surfaces. For this reason, EO is ideally suited to fine-grained, clay-rich soils. The magnitude of electroosmotic... 

Urban, J.P., Holm, S., Maroudas, A. and Nachemson, A. (1982) Nutrition of the intervertebral disc Effect of fluid flow on solute transport. Clin Orthop 170, 296-302... 

The proposed model consists of a biphasic mechanical description of the tissue engineered construct. The resulting fluid velocity and displacement fields are used for evaluating solute transport. Solute concentrations determine biosynthetic behavior. A finite deformation biphasic displacement-velocity-pressure (u-v-p) formulation is implemented [12, 7], Compared to the more standard u-p element the mixed treatment of the Darcy problem enables an increased accuracy for the fluid velocity field which is of primary interest here. The system to be solved increases however considerably and for multidimensional flow the use of either stabilized methods or Raviart-Thomas type elements is required [15, 10]. To model solute transport the input features of a standard convection-diffusion element for compressible flows are employed [20], For flexibility (non-linear) solute uptake is included using Strang operator splitting, decoupling the transport equations [9],... 

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