Mass transport advection

Park and Ortoleva (2003) have developed WRIS.TEQ, a comprehensive reaction-transport-mechanical simulator that includes kinetic and thermodynamic properties with mass transport (advection and diffusion). A unique property of this code is a dynamic compositional and textural model specifically designed for sediment alteration during diagenesis. 

Biofilms adhere to surfaces, hence in nearly all systems of interest, whether a medical device or geological media, transport of mass from bulk fluid to the biofilm-fluid interface is impacted by the velocity field [24, 25]. Coupling of the velocity field to mass transport is a fundamental aspect of mass conservation [2]. The concentration of a species c(r,t) satisfies the advection diffusion equation... 

Data for the bulk fluid, line A, indicate that vz varies as a function of z but maintains a value near 0.75 of maximum velocity. The periodicity of vx and vy is clearly evident in the graph of line A and a 1800 out of phase coupling of the components is seen with one positive when the other is negative. This indicates a preferred orientation to the plane of the oscillatory flow and this feature was seen in all the biofilms grown throughout this study. The secondary flow components are 0.1-0.2 of the maximum axial velocity and are spatially oscillatory. The significant non-axial velocities indicate non-axial mass transport has gone from diffusion dominated, Pe = 0, in the clean capillary, to advection dominated, Pe 2 x 103, due to the impact of the biofilm. For comparison, the axial Peclet number is Pe L 2x 10s. Line B intersects areas covered by biomass and areas of only bulk... 

Chemical mass is redistributed within a groundwater flow regime as a result of three principal transport processes advection, hydrodynamic dispersion, and molecular diffusion (e.g., Bear, 1972 Freeze and Cherry, 1979). Collectively, they are referred to as mass transport. The nature of these processes and how each can be accommodated within a transport model for a multicomponent chemical system are described in the following sections. 

Let us consider the transport of one component i in a liquid solution. Any disequilibration in the solution is assumed to be due to macroscopic motion of the liquid (i.e. flow) and to gradients in the concentration c,. Temperature gradients are assumed to be negligible. The transport of the solute i is then governed by two different modes of transport, namely, molecular diffusion through the solvent medium, and drag by the moving liquid. The combination of these two types of transport processes is usually denoted as the convective diffusion of the solute in the liquid [25] or diffusion-advection mass transport [48,49], The relative contribution of advection to total transport is characterised by the nondimensional Peclet number [32,48,49], while the relative increase in transport over pure diffusion due to advection is Sh - 1, where Sh is the nondimensional Sherwood number [28,32,33,49,50]. 

Advection The large-scale mass transport of matter. 

Typical DB values for Long Island Sound estuary (USA) and Chesapeake Bay have been estimated to range from 0.5 to 110 cm2 y-1 (Aller and Cochran, 1976 Aller et al., 1980) and 6 to >172 cm2 y 1 (Dellapenna et al., 1998), respectively. Since mixing is clearly not a one-dimensional process, estimated biodiffusivity values may seriously underestimate mass transport when mixing is affected by horizontal advection (Wheatcroft et al., 1991). 

Advection is the transport of dissolved contaminant mass due to the bulk flow of groundwater, and is by far the most dominant mass transport process [2]. Thus, if one understands the groundwater flow system, one can predict how advection will transport dissolved contaminant mass. The speed and direction of groundwater flow may be characterized by the average linear velocity vector (v). The average linear velocity of a fluid flowing in a porous medium is determined using Darcy s Law [2] ... 

When biochemical systems are studied in vitro, it is typically under well mixed conditions. Yet the contents of living cells are not necessarily well mixed and the biochemical workings within cells are inseparably coupled to the processes that transport material into, out of, and within cells. The three processes responsible for mass transport in living systems are advection, diffusion, and drift. Characterizing which, if any, of these processes is active in a given system is an important component of building differential equation-based models of living biochemical systems. 

Transport (advection and diffusion) of tracers (both passive and reactive) is performed on-line at each meteorological time-step using WAF scheme for advection and a true (second order) diffusion, with diffusion coefficient carefully estimated from experiments (Tampieri and Maurizi 2007). Vertical diffusion is performed using ID diffusion equation with a diffusion coefficient estimated by means of an k-l turbulence closure scheme. Dry deposition is computed through the resistance-analogy scheme and is provided as a boundary condition to the vertical diffusion equation. Furthermore, vertical redistribution of tracers due to moist convection is parameterized consistently with the Kain-Frisch scheme used in the meteorological part for moist convection. Transport of chemical species is performed in mass units while gas chemistry is computed in ppm. 

Other models directly couple chemical reaction with mass transport and fluid flow. The UNSATCHEM model (Suarez and Simunek, 1996) describes the chemical evolution of solutes in soils and includes kinetic expressions for a limited number of silicate phases. The model mathematically combines one- and two-dimensional chemical transport with saturated and unsaturated pore-water flow based on optimization of water retention, pressure head, and saturated conductivity. Heat transport is also considered in the model. The IDREAT and GIMRT codes (Steefel and Lasaga, 1994) and Geochemist s Workbench (Bethke, 2001) also contain coupled chemical reaction and fluid transport with input parameters including diffusion, advection, and dispersivity. These models also consider the coupled effects of chemical reaction and changes in porosity and permeability due to mass transport. 

Effective rates of sorption, especially in subsurface systems, are frequently controlled by rates of solute transport rather than by intrinsic sorption reactions perse. In general, mass transport and transfer processes operative in subsurface environments may be categorized as either macroscopic or microscopic. Macroscopic transport refers to movement of solute controlled by movement of bulk solvent, either by advection or hydrodynamic (mechanical) dispersion. For distinction, microscopic mass transfer refers to movement of solute under the influence of its own molecular or mass distribution (Weber et al., 1991). 

In fixed-bed operation, in addition to the two-step mass transport mechanism, advection and dispersion play key roles in ion exchange. These factors must be considered. As influent concentration is assumed low, solution velocity can be considered constant. If pore diffusion is an important factor in the ion uptake, the following equations can be used. Similar expressions for surface diffusion can be obtained ... 

The three principal variables considered in this analysis are temperature, which influences all biological and chemical reactions, dispersion and advective flow, which are the primary mass transport mechanisms in a natural body of water, and solar radiation, the energy source for the photosynthetic growth of the phytoplankton. 

An additional time-dependent advection-diffusion equation is used to represent the mass transport of the cupric ions. This equation can be expressed as,... 

Passive micromixers rely on the mass transport phenomena provided by molecular diffusion and chaotic advection. These devices are designed with a channel geometry that increases the surface area between the different fluids and decreases the diffusion path. By contrast, the enhancement of chaotic advection can be realized by modifying the design to allow the manipulation of the laminar flow inside the channels. The modified flow pattern is characterized by a shorter diffusion path that improves the mixing velocity. In this section, an overview of the different types of passive micromixers is provided. Mixed phase passive micromixers can be categorized as ... 

Cook SJ, Bowman JR (1994) Contact metamorphism snrronnding the Alta stock Thermal constraints and evidence of advective heat transport from calcite + dolomite geothermometry. Am Mineral 79 513-525 Cook SJ, Bowman JR, Forster CB (1997) Contact metamorphism surrounding the Alta stock finite element model simulation of heat- and mass-transport dnring prograde metamorphism. Am J Sci 297 ... 

Apparent reaction rate constants indicating mass transport factors, and mass transport coefficients indicating diffusion processes from mineral surface to bulk solution, are introduced into an advection - diffusion - reaction model. 

---