Radial geometry

Attention will be paid to the systematic relationship of the geometries of B- XY to those of hydrogen-bonded complexes in the corresponding series B- HX, especially for angular geometries, which are dealt with in detail in Sects. 3.1, 3.2 and 3.3. Radial geometries are treated only in summary (Sect. 3.4) here, but a detailed analysis is available in [19]. 

Radial geometries of B- XY and B- HX are also systematically related. Only a summary will be given here the reader is referred to earlier publications for detailed discussion [19,174-178]. 

The simplest case for modeling particle dissolution is to assume that the particles are monodisperse. Under these conditions, only one initial radius is required in the derivation of the model. Further simplification is possible if the assumption is made that mass transport from a sphere can be approximated by a flat surface or a slab, as was the case for the derivation for the Hixson-Crowell cube root law [70], Using the Nernstian expression for uniaxial flux from a slab (ignoring radial geometry or mass balance), one can derive the expression... 

Similarly, in 3D-radial geometries of interest for petroleum engineers, an equivalent wellbore radius re is defined. The near-wellbore region, including radially distributed wormholes from rw up to re, is infinitely permeable and therefore becomes a mere radial extension of the wellbore itself. Equation 2 can be used to calculate the pseudodecrease of the skin when an undamaged primary porosity formation of permeability k0 includes wormholes as described hereabove ... 

The, for example in C 16, is required to fix the row reference for the radial-geometry functions. Otherwise, subsequent relative dragging of the difference formula would not preserve these functions correctly. 

The geometry shown here corresponds to a semi-infinite planar diffusion. Other geometries (e.g., radial geometries) typical for microsensors can be used. The enzyme-containing layer is usually a hydrogel, whose optimum thickness depends on the enzymatic reaction, on the operating pH, and on the activity of the enzyme (i.e., on the Km). Enzymes can be used with nearly any transduction principle, that is, thermal, electrochemical, or optical sensors. They are not, however, generally suitable for mass sensors, for several reasons. The most fundamental one is the fact... 

Several different membrane materials have been used, namely Teflon, polyethylene, and silicon rubber among others. It is possible to obtain some degree of selectivity by choosing the material of this membrane according to the conditions of the application. The diffusion through such a structure is more complicated. For radial geometry, the steady-state current is given as... 

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.

Hydraulic jump in a radial geometry is easily demonstrated in any sink, as shown in Fig. 7.28. DeFive an equation analogous to Eq. C.5 for this radial hydraulic... 

Figure 7.28 shows a hydraulic jump, in radial geometry, easily demonstrated in a sink. If the sink drain is open, then the flow is steady and the depths and velocities in the sink are not changing with time. If we now close the drain, without changing the flow from the faucet, what will happen Describe the situation in terms of the mathematical description of hydraulic jumps. 

In this chapter, we present an ab initio study of the potential energy surface and stability of the Lia+CX Sg" ") alkali dimer interacting with the xenon atom in different radial geometries and for six angles from 0° to 90°. In Sect. 16.2, the ab initio calculation method is presented. Section 16.3 reports the results of calculation and analysis of the interesting and unusual feature of the strong interaction and anisotropy of the potential. Finally, we present our conclusions in Sect. 16.4. 

The PSR blocks provide lateral restraint for the hexagonal core elements and maintain the core radial geometry. The PSR transmits lateral seismic loads from the core barrel to the reactor core and it limits neutron fluences to... 

The results from simulations using all three models are presented in Table 9.3. No significant differences in the simulated overall detection efficiencies were observed, suggesting that the insertion of holes in the ring electrode does not affect adversely detection efficiency. It is perhaps not surprising that the axial ejection of ions is relatively insensitive to changes in the radial geometry of the trap. 

Supported liquid membranes offer excellent selectivity for use in gas separation. The transport of CO2 through an aqueous diethanolamine solution held within a hollow fibre membrane is modelled in this paper. When compared with flat-sheet models, the results demonstrated that radial geometry has to be taken into account in a hollow fibre model. The model was used to simulate the CO2 separation in membrane contactors and the results were compared with experimental data. The discrepancy between the results and the experimental data is thought to be due to the conditions within the membrane contactors, which are far from ideal. 

The main objectives of this paper are 1) To extend a model for facilitated transport through SLMs, previously presented in the literature for flat-sheet membranes, to allow for transport through hollow fibre membranes, 2) to compare the flat sheet and hollow fibre models and show that the radial geometry must be taken into account when considering hollow fibre units, 3) to demonstrate, by comparison with experimental data, that even with radial variations, the model is still too simple to accurately describe the transport through a hollow fibre unit and 4) to suggest how the model can be improved. 

In this paper, we argue that an accurate simulation of a hollow fibre SLM should incorporate radial geometry in the mass balance equations as the fibre radius can have a significant effect upon the permeation rates as will indeed be demonstrated. Because Teramoto s approach is not suitable for radial systems, the full mass balance equations must be solved. 

Next, the CO2 flux through membrane fibres with different sized inner radii was predicted (Eqs. 9-12). The use of a radial geometry model accounts for the difference in membrane surface area between the outside and inside of the fibre and the effect upon the membrane concentration profiles. 

This effect is less significant if the membrane thickness is small in relation to the fibre diameter as shown in Fig. 2. However, as the fibre diameter decreases, the effects of radial geometry become more pronounced. The fluxes were all predicted for the same conditions - feed and sweep CO2 pressures of 20.73 and 1.08 cmHg. respectively through an SLM of aqueous DBA at 1.94 mol.dm . The tortuosity was set at 5. 

The broken lines show the fluxes obtained using the flat sheet models under the same conditions. This shows that the radius of the fibre must be approximately 1000 times greater than the wall thickness before the effects of radial geometry become negligible. In commercial hollow fibre units, the ratio of fibre radius to wall thickness is typically between 2 and 5. This illustrates that radial geometry must be taken into account when simulating hollow fibres as the use of an equivalent flat sheet model could over-estimate the CO2 flux by as much as 25%. 

A simple model for predicting the flux of CO2 through hollow fibre supported liquid membranes has been presented. It has been shown that radial geometry must be considered in order to accurately simulate the flux of the gas through the walls of a hollow fibre and that a flat sheet model is not able to capture this. However, because of... 

The RA-8 critical facility has been designed and constmcted to measure neutronic parameters typical of the CAREM core. It provides a reactor shielding block and a reactor tank that can be adapted to contain custom designed reactor cores. Experiments were performed using fuel rods of the same radial geometry and pitch as in the CAREM-25 fuel element. Components of the neutronic calculation lines were validated with the use of data for VVER type reactors obtained in the experiments at ZR-6 Research Reactor (Central Research Institute for Physics, Academy of Sciences, Hungary) and data for PWR critical experiments. 

In this work a 2 fractional factorial design was run on the factors shown in Table 1, requiring 32 model simulations. The ranges of the variables were chosen to cover conditions likely in industrial practice. The factors y and tt/Z were included to assess the magnitude of their effects e, dp and 0 would all be expected to influence bed resistance. The bed width was kept constant, so, for a given y specifying R fixed radial geometry. The variables e and dp were... 

If elastic-plastic and gravity terms are ignored, similar transformations of Equation (G.3) to radial geometry give for conservation of energy... 

If elastic-plastic, heat conduction, and gravity terms are ignored, transformation of Equation (G.2) to radial geometry gives for conservation of momentum. 

The radial geometry provides better stability and precision while the axial geometry can achieve lower detection limits. Many ICP emission systems allow both geometries. 

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