Vertical profiles porosity

To illustrate the behavior of the cylinder model and also to demonstrate how irrigated burrows can be expected to influence Mn " profiles, a representative vertical profile predicted by Eqs. (6.14) and (6.15) for Mn " has been plotted for the case A i = 0 (Fig. 19). The production rate for Mn ", r, rz, and L are those for core NWC-4 based on the solid-phase dissolution rate of Section 6.4.1 (Table V divided by average porosity 0.750) and the cylinder-model values of Table V in Part I. The value of D is estimated from the molecular diffusion coefficient at infinite dilution T = I9°C (Li and Gregory, 1974), multiplied by a correction factor for sediment structure of 0.56. This factor was approximated by

[Pg.392]

Where the surface is covered by tall vegetation or high densities of large roughness elements (e.g., large boulders, man-made structures), the vertical profile of wind velocity is displaced (Oke, 1978) to a new reference plane (rfo) that varies with the height, density, porosity, and flexibility of the elements (Figure 16.4c). The wind profile equation then is modified as follows ... 

A mixture of powdered poly(vinyl chloride), cyclohexanone as solvent, silica, and water is extruded and rolled in a calender into a profiled separator material. The solvent is extracted by hot water, which is evaporated in an oven, and a semiflexible, microporous sheet of very high porosity ( 70 percent) is formed [19]. Further developments up to the 75 percent porosity have been reported [85,86], but these materials suffer increasingly from brittleness. The high porosity results in excellent values for acid displacement and electrical resistance. For profiles, the usual vertical or diagonal ribs on the positive side, and as an option low ribs on the negative side, are available [86],... 

The dynamics of fire growth is strongly influenced by the kinematics of flow through porous vegetation and urban structures (the canopy). The local wind and turbulence environment at the source determines the initial spread of a fire. Wind profiles vary depending upon the density (porosity) of the surrounding objects, their distribution vertically or laterally, the presence of below canopy open regions, and the distance... 

Fig. 12.4 Effects of the depth resolution in pore water concentration profiles on calculating the rates of diffusive transport. Three samples drawn from surface sediments are shown to possess different resolutions (intervals 0.5 cm - dots, 1.0 cm diamonds, 2.0 cm - squares). All values are sufficient to plot the idealized concentration profile within the hounds of analytical error, yet very different flux rates are calculated in dependence on the depth resolution values. In the demonstrated example, the smallest sample distance indicates the highest diffusion (2.98 mmol cmA f ). As soon as the vertical distance between single values increases, or, when the sediment segments under study grows in thickness, the calculated export across the sediment-water boundary diminishes (2.34-t.64mmol cm yr ). In our example, this error which is due to the coarse depth resolution can be reduced by applying a mathematical Fit-function. A truncation of 0.05 cm yields a flux rate of 2.84 mmol cm yr. (The indicated values were calculated under the assumption of the presented porosity profile according to Pick s first law of diffusion - see Chapter 3. A diffusion coefficient of 1 cmA f was assumed. Adaptation to the resolution interval of 2.0 cm was accomplished by using a simple exponential equation).

Rocha and Paixao [38] proposed a pseudo two-dimensional mathematical model for a vertical pneumatic dryer. Their model was based on the two-fluid approach. Axial and radial profiles were considered for gas and solid velocity, water content, porosity, temperatures, and pressure. The balance equations were solved numerically using a finite difference method, and the distributions of the flow field characteristics were presented. This model was not validated with experimental results. 

Note that we have divided the Darcy velocity by fractional porosity in the last step to have true velocity. The (8p/Bx) term was previously expressed in terms of (BT/Bx) and (Bxi/3x) (see Eq. (2.122)). Equation (2.139) applies to both thermal convection, where the convection is driven by (BT/Bx) as well as natural convection where flow is driven by (BT/Bx) and (BXi/Bx). As was stated before, convection may weaken or enhance composition variation. Figure 2.33 provides a simple explanation of the change in composition due to convection. In this figure, the diagram on the right (Fig. 2.33a) shows the composition variation vs. depth with zero convection at x = 0 assuming that = 0, and that and are not functions of temperature (see Eq. (2.125)). The thin line shows zero vertical compositional grading. Now allow for small values of pv (proportional to z) as shown by thick line B. Assume that pv is identically zero. Because of convection, the composition profile A cannot stay the same, otherwise the material balance for component 1... 

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