Water diffusion flux

The water diffusive flux through the membrane is considered following the ideas in [4]. Water content (molecule per sulphonate group) Cwiy) is considered through the MEA. It is assumed to obey a simple diffusive mechanism and that the diffusive flux is not influenced by the electro-osmotic drag. The following equation is assumed ... 

By replacing the mole fraction of water with the ratio of water vapor pressure (Pw) divided by the total gas pressure (PT), one can solve for the diffusive flux of water vapor. Also, by multiplying Nw by the molecular weight of water, the mass flux of water vapor is arrived at ... 

In coastal sediments where organic carbon concentrations are high, the redox boundary is at or near the sediment-water interfece. Under these conditions, denitrification acts as a sink for nitrate. In some settings, the rate of sedimentary denitrification is fast enough to drive a diffusive flux of nitrate from the bottom waters into the sediments. Remineralization of organic matter imder suboxic and anoxic conditions releases... 

If water movement in the membrane is also to be considered, then one way to do this is to again use the Nernst—Planck equation. Because water has a zero valence, eq 29 reduces to Pick s law, eq 17. However, it is also well documented that, as the protons move across the membrane, they induce a flow of water in the same direction. Technically, this electroosmotic flow is a result of the proton—water interaction and is not a dilute solution effect, since the membrane is taken to be the solvent. As shown in the next section, the electroosmotic flux is proportional to the current density and can be added to the diffusive flux to get the overall flux of water... 

In the above, D rn is the water diffusion coefficient through the membrane phase only. Note also that the water fluxes through the membrane phase, via electro-osmotic drag and molecular diffusion, represent a source/sink term for the gas mixture mass in the anode and cathode, respectively. 

In bulk water (free solution), the diffusive flux, given in units of mass per area per time, is related to the concentration by Pick s first law. 

Summary of Landmine Flux Results Since no one has devised a method of directly measuring the flux of explosive molecules from a mine, whether in situ or in the laboratory, several laboratory measurements have been reported in which the mine was placed in a sealed container, surrounded by soil, water, or air. The concentrations of explosive molecules in the surrounding media were then measured at intervals of several days and the flux inferred from the total concentration divided by the elapsed time. This likely provides the best estimate that can be expected. The various measurements have substantial variation, depending on the techniques and media used. Phelan and Webb describe several experiments [1, pp. 23, 24], It appears that a reasonable expectation of flux of explosive compounds from a buried landmine that move into the surrounding soil will be in the range of 1 to 200 pg/day. There are some complications, of course, since the surrounding soil produces a level of resistance, or back pressure, to the flux of the molecules. While the mechanisms are complex, the net effect is that wet soil permits a lower diffusive flux than dry... 

Finally, the diffusion of a chemical may be influenced by another diffusing compound or by the solvent. The latter effect is known as solute-solvent interaction it may become important when solute and solvent form an association that diffuses intact (e.g., by hydration). This may be less relevant for neutral organic compounds, but it plays a central role for diffusing ions. But even for noncharged particles the diffusivities of different chemicals may be coupled. The above example of the glycerol diffusing in water makes this evident in order to keep the volume constant, the diffusive fluxes of water and glycerol must be coupled. 

First note that benzene is primarily moving through the gas-filled pores. Diffusion through the water-filled pores is too slow to account for much of the total flux. To calculate the steady-state diffusive flux through the 3-meter-thick gas-filled pores, use Eq. 18-56 and replace Dipm by diffusivity in the unsaturated zone, Djuz, and ( > by 0g. The latter is the gas-filled void which amounts to 75% of the 40% total porosity. That is, 0 = 0.30. 

Is it possible that the molecular diffusive flux in water along the x-axis is different from zero for a chemical that has constant concentration along x Explain ... 

The diffusive flux of the aqueous species of a chemical between the open water (op) and the pore water of the sediment column (sc) can be described by the linear expression ... 

The corresponding dynamic equations of the open water column are constructed from Eq. 22-6. They are completed by the sediment-water boundary flux derived in Eq. 23-38. We assume that the net vertical advection of water is zero. Thus, the vertical water movement is incorporated in the turbulent diffusivity, Ez. The assumption implies that if chemicals are directly introduced at depth z (term 1), they would not be accompanied by significant quantities of water. Typically, such inputs are due to sewage outlets (treated or untreated) into the lake. We get ... 

The amount of P supplied by resuspension was relatively small compared with water-column standing pools and major flux vectors. Thus, resuspension of bottom sediments may not be a major mode of phosphorus resupply. The pool of resuspendable P is finite. The deposition-resuspension cycle will not increase the amount of P in this pool unless P is added from another source (e.g., by diffusion of P from lower sediment levels). However, the diffusive flux would be relatively small. The resuspendable particulate P can be recycled during spring mixing by repeated deposition and resuspension, but this cycle does not increase the amount of P in the resuspendable pool. Eadie et al. (24) reported a resuspended P flux (sediment-trap-based) of3200 mg of P/m2, 66 times our estimate here. However, this large P flux would require the resuspension of over 2.0 cm of surface sediment and much higher suspended Al levels than were measured in the water column. 

Measurements of S cycling in Little Rock Lake, Wisconsin, and Lake Sempach, Switzerland, are used together with literature data to show the major factors regulating S retention and speciation in sediments. Retention of S in sediments is controlled by rates of seston (planktonic S) deposition, sulfate diffusion, and S recycling. Data from 80 lakes suggest that seston deposition is the major source of sedimentary S for approximately 50% of the lakes sulfate diffusion and subsequent reduction dominate in the remainder. Concentrations of sulfate in lake water and carbon deposition rates are important controls on diffusive fluxes. Diffusive fluxes are much lower than rates of sulfate reduction, however. Rates of sulfate reduction in many lakes appear to be limited by rates of sulfide oxidation. Much sulfide oxidation occurs anaerobically, but the pathways and electron acceptors remain unknown. The intrasediment cycle of sulfate reduction and sulfide oxidation is rapid relative to rates of S accumulation in sediments. Concentrations and speciation of sulfur in sediments are shown to be sensitive indicators of paleolimnological conditions of salinity, aeration, and eutrophication. 

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