Surface roughness element height

For particles with rough surfaces, e.g., with roughness elements of height less than 20% of d, the mass transfer coefficient is usually larger than predicted here (A5, J4, S3, S4), but at most by about 50%. Roughness is treated in more detail in Chapter 10. For a particle made up of a small number of particles in a cluster, the use of d in Eq. (6-35) gives good results (S4). 

For the case of a surface with roughness elements of height e, one can repeat the analysis used in the previous section for a smooth surface. In this case there is no laminar sublayer so we do not need to use the kinematic viscosity in our analysis. On the other hand, we do need to add the height of the roughness elements. Thus the five parameters for the dimensional analysis are now dux/dz, e, p,z, and ut. One can then show that... 

Analyze small chips of various rocks, or samples of sand or soil from different geographic locations. Identify the elements present in each sample. Can you distinguish between sands or soils from different locations by their XRF spectra Look for any trace or minor elements that may differentiate the samples. (Remember that peak intensities will vary due to surface roughness, so particle size differences between samples may account for peak height differences in the spectra.)... 

Note Re c = M A/v where A = 10 cm, the height of the bottom roughness elements. The range of correction factors is 1.6-2.3 with 1.8 the average. All values of ro indicate bed surface roughness enhances the MTCs. 

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 ... 

As an application, the flow in rough microchannels was applied theoretically in the nucleic acid extraction process [8], which is the first critical step for many nucleic acid probe assays. Using a microchannel with 3D prismatic elements on the channel wall can dramatically increase the surface area-to-volume ratio and hence enhance the nuclei acid adsorption on the wall. The opportunity for molecule adsorption is also increased due to the induced pressure resisting the central bulk electroosmotic flow. It is found that decreasing the electroosmotic flow velocity or the channel height enhances nuclei adsorption. 

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