Radial viewing geometry

Figure 28-8 Viewing geometries for ICP sources, (a) Radial geometry used in ICP atomic emission spectrometers (b) axial geometry used in ICP mass spectrometers and in several ICP atomic emission spectrometers.

In Fig. 18, flow path lines are shown in a perspective view of the 3D WS. By displaying the path lines in a perspective view, the 3D structure of the field, and of the path lines, becomes more apparent. To create a better view of the flow field, some particles were removed. For Fig. 18, the particles were released in the bottom plane of the geometry, and the flow paths are calculated from the release point. From the path line plot, we see that the diverging flow around the particle-wall contact points is part of a larger undulating flow through the pores in the near-wall bed structure. Another flow feature is the wake flow behind the middle particle in the bottom near-wall layer. It can also be seen that the fluid is transported radially toward the wall in this wake flow. 

The geometry of the microelectrodes is critically important not only from the point of view of the mathematical treatment, but also their performance. Thus, the diffusion equations for spherical microelectrodes can be solved exactly because the radial coordinates for this electrode can be reduced to the point at r = 0. On the other hand, a microelectrode with any other geometry does not have a closed mathematical solution. It would be advantageous if a microdisc electrode, which is easier to fabricate, would behave identically to a microsphere electrode. This is not so, because the center of the disc is less accessible to the diffusing electroactive species than its periphery. As a result, the current density at this electrode is nonuniform. 

Figure 3. Schematic of turbulent combustor geometry and optical data acquisition system for vibrational Raman-scattering temperature measurements using SAS intensity ratios. Also shown are sketches of the expected Raman contours viewed by each of the photomultiplier detectors, the temperature calibration curve, and several expected pdf s of temperature at different flame radial positions. The actual SAS temperature calibration curve was calculated theoretically to within a constant factor. This constant, which accounted for the optical and electronic system sensitivities, was determined experimentally by means of SAS measurements made on a premixed laminar flame of known temperature. Measurements of Ne concentration were made also with this apparatus, based on the integrated Stokes vibrational Q-branch intensities. These signals were related to gas densities by calibration against ambient air signals.

In order to fulfil the requirements for the measurement of radially (f(r)) and spectrally (< (A)) resolved measurements in the ionizing part of the boundary plasma good viewing access to wall and limiter components, which define the last close flux surface, is absolutely necessary. An example of such an observation geometry can be seen in Fig. 6.1, where the capabilities of such diagnostics are demonstrated. It shows the arrangement in the sector of one... 

As well, a notch may do the same with regard to the diffusion from the points of view of the geometry and the stress effects on the transport phenomenon, if compared with the stress-unassisted diffusion in a smooth cylinder. In particular, the range of the disturbing effect of a notch on stress in assisted transport phenomena in solids can be estimated from fig. 4, where vanishing of the notch effect corresponds to fairly radial flow trajectories, or concentration contour bands parallel to the cylinder surface, the same as it occurs in smooth bars. 

Other geometries can readily be worked out. As a useful analogy, the concentration c in equation 1 can be viewed as the electrostatic potential around a conductor of potential co. The analog to the local evaporation rate is the electric field, evaluated at the surface of the conductor. By this analogy a fresh set of intuitive ideas can be brought to bear on evaporation problems. For example, it is not surprising that the vapor density around an infinite cylindrical source drops logarithmically with radial distance, and that the evaporation rate varies inversely with the radius of the cylinder. Similarly, the vapor concentration above an infinite sea drops linearly with distance, whereas the evaporation rate is constant everywhere on the surface. 

Radial lines in projection look like points and radial planes look like lines when viewed edge-on, which means that radial dimensions are lost. This correspondence dehnes the principle of duality which asserts that any dehnition or theorem in projective geometry remains valid on interchanging the words point and line, as well as the operations ... 

Simple porosity determination. In wells where mudcake controls the overall flow into the formation, and where Ar/r j. < 0.20 is satisfied, a lineal mudcake model suffices. This being so, we unwrap the cake layer adhering to our wellbore and view the buildup process as a lineal one satisfying the Vt law. But the invasion into the formation, of course, is highly radial in this farfield, the effects of borehole geometry and streamline divergence must be considered in order to conserve mass. Now consider a well with a radius r // and an axial... 

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