Spherical transport

In 1962 the report, TID-14844 was published presenting analysis and assumptions coneeming the behavior of containment (essentially Hazard State 2). The TID report postulated the release of all of the noble gas, 50% of the iodine, and 1% of the radioactive solids to the containment. In addition, TBD-14844 provided assumptions for containment leakage (the TMI-2 containment is intact) and for atmo.spheric transport of the fission products. These results form the basis for Regulatory... 

Only three simple transport geometries are normally encountered planar, cylindrical, and spherical. These are shown in Fig. 13. In planar transport, the flux lines are parallel to each other and normal to the electrode. Cylindrical transport occurs with electrodes that are cylindrical, such as wires, or hemicyclindrical the flux lines converge in the plane which is normal to the cylinder axis but are parallel in planes which include the cylinder axis. Spherical transport is encountered with spherical or hemispherical electrodes, the flux lines being continuations of the radii... 

Figure 17 Concentration of NiCl2 at a corroding Ni surface as a function of the product Ht for linear and spherical transport (including nonstationaiy conditions) calculated with Eqs. (17) and (20). (From Ref 30.)...

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. 

Of course, in order to vary the mass transport of the reactant to the electrode surface, the radius of the electrode must be varied, and this unplies the need for microelectrodes of different sizes. Spherical electrodes are difficult to constnict, and therefore other geometries are ohen employed. Microdiscs are conunonly used in the laboratory, as diey are easily constnicted by sealing very fine wires into glass epoxy resins, cutting... 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

The flux-corrected-transport technique was also used by Phillips (1980), who successfully simulated the process of propagation of a detonation wave by a very simple mechanism. The reactive mixture was modeled to release its complete heat of combustion instantaneously after some prescribed temperature was attained by compression. A spherical detonation wave, simulated in this way, showed a correct propagation velocity and Taylor wave shape. 

Although the early studies on HdC were done using packed columns, the basic principles of HdC are easily explained by considering the transport of spherical... 

Recent developments of the chemical model of electrolyte solutions permit the extension of the validity range of transport equations up to high concentrations (c 1 mol L"1) and permit the representation of the conductivity maximum Knm in the framework of the mean spherical approximation (MSA) theory with the help of association constant KA and ionic distance parameter a, see Ref. [87] and the literature quoted there in. 

The main transport form of lipids in the cir culation. They are spherical macromolecules of 10-1200 nm diameter-composed of a core of neutral lipids (mostly cholesterol ester and triglycerides) surrounded by an amphipathic shell of polar phospholipids and cholesterol. Embedded in the shell of lipoproteins are apolipoproteins that are essential for assembly of theparticles in tissues that secrete lipoproteins, and for their recognition by target cells. 

Parker G. A., Pack R. T. Rotationally and vibrationally inelastic scattering in the rotational IOS approximation. Ultrasimple calculation of total (differential, integral, and transport) cross sections for non-spherical molecules, J. Chem. Phys. 68, 1585-601 (1978). 

In Og (Figure 8.1.5b), xmlike in the Ig case, the fuel jet momentum dispersed and the centerline velocity decayed rapidly owing to the lack of buoyancy. As a result, the fuel molecules diffused in every direction and formed a quasi-spherical flame. The slow diffusion processes (1) limited the transport rates of the fuel and oxygen into the flame zone and (2) decreased... 

TABLE 4 Theoretical Equations for the Transport of a Single Spherical Particle in a Constant Electric Eield... 

Neale, GH Nader, WK, Prediction of Transport Processes Within Porous Media Diffusive Flow Processes Within a Homogeneous Swarm of Spherical Particles, AIChE Journal 19, 112, 1973. 

Phillips, RJ Deen, WM Brady, JF, Hindered Transport of Spherical Macromolecules in Fibrous Membranes and Gels, AIChF Journal 35, 1761, 1989. 

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