Cylinders diffusion

Concentration Diameter of a gel cylinder Diffusion coeffieient Cooperative diffusion eoeffieient Helmholtz free energy Gibbs free energy Storage modulus Loss modulus... 

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

The diffusion layer widtli is very much dependent on tire degree of agitation of tire electrolyte. Thus, via tire parameter 5, tire hydrodynamics of tire solution can be considered. Experimentally, defined hydrodynamic conditions are achieved by a rotating cylinder, disc or ring-disc electrodes, for which analytical solutions for tire diffusion equation are available [37, 4T, 42 and 43]. 

Washing equipment typically includes cylinder or dmm washers, diffusion ring washers, pressure diffusers, pressure washers, and belt washers. 

The three most common diffuser configurations are a vertical cylinder in which the semifluidized cossettes ate scrolled upward (tower), a pair of upward-moving inclined twin-screw scrolls with cascading juices (slope), and a horizontal rotating dmm equipped with offset compartments which allow the cossettes to fall forward as the dmm turns (Raffinetie Tirlemontoise (RT) horizontal). Residence time within all of these diffusers is typically 45 to 60 minutes. 

The mechanism of poisoning automobile exhaust catalysts has been identified (71). Upon combustion in the cylinder tetraethyllead (TEL) produces lead oxide which would accumulate in the combustion chamber except that ethylene dibromide [106-93-4] or other similar haUde compounds were added to the gasoline along with TEL to form volatile lead haUde compounds. Thus lead deposits in the cylinder and on the spark plugs are minimized. Volatile lead hahdes (bromides or chlorides) would then exit the combustion chamber, and such volatile compounds would diffuse to catalyst surfaces by the same mechanisms as do carbon monoxide compounds. When adsorbed on the precious metal catalyst site, lead haUde renders the catalytic site inactive. 

For shorter penetration the use of p emitting isotopes is widely made applying much the same absorption law for p radiation as for y rays, with a minor modification. An alternative procedure used by Kingety and Paladino for the study of diffusion in AI2O3 employs two right cylinders, one only containing the radioactive Al isotopic species which emits relatively low energy ( ,nax = 0.511 MeV) p particles. 

If the total amount of radioactivity transfened from one cylinder to another is measured the solution of the diffusion equation is... 

The measurement of oxygen diffusion is usually made by the use of as die labelling isotope. If a gas containing an initial concentration C, of in O , and Co is the initial conceiiuation of in a right cylinder oxide sample of thickness 21, and a is the ratio of oxygen atoms in the original gas phase compared widi that in the solid, dieii after a time t, when the concentration in the gas phase is C/... 

Analysis of neutron data in terms of models that include lipid center-of-mass diffusion in a cylinder has led to estimates of the amplitudes of the lateral and out-of-plane motion and their corresponding diffusion constants. It is important to keep in mind that these diffusion constants are not derived from a Brownian dynamics model and are therefore not comparable to diffusion constants computed from simulations via the Einstein relation. Our comparison in the previous section of the Lorentzian line widths from simulation and neutron data has provided a direct, model-independent assessment of the integrity of the time scales of the dynamic processes predicted by the simulation. We estimate the amplimdes within the cylindrical diffusion model, i.e., the length (twice the out-of-plane amplitude) L and the radius (in-plane amplitude) R of the cylinder, respectively, as follows ... 

The study found that the slot-type inlet at the bottom of the cabinet door resulted in higher pressure losses (lower CJ than the diffuser or perforated plate inlet. The exhaust configuration had little effect on Q or tracer gas clearance time. The study also concluded that an exhaust rate 0.118 m s for a two-cylinder cabinet was sufficient as little improvement was seen with an increase to 0.165 m s F" The slotted inlet took longer to clear a leak than either the perforated plate or diffuser inlet. Measured coefficients of entry for a two-cylinder gas storage cabinet are shown in Table 10.9. 

This type of damage is dealt with comprehensively in Section 8.8. It can be particularly severe in seawater giving rise to cavitation corrosion or cavitation erosion mechanisms, and hence can be a considerable problem in marine and offshore engineering. Components that may suffer in this way include the suction faces of propellers, the suction areas of pump impellers and casings, diffusers, shaft brackets, rudders and diesel-engine cylinder liners. There is also evidence that cavitation conditions can develop in seawater, drilling mud and produced oil/gas waterlines with turbulent high rates of flow. 

A little bit of physical intuition as to how the vortices form in the first place may help in explaining the behavior as TZ is increased still further. We know that u = 0 at the cylinder s surface. We also know that the velocity increases rapidly as we get further from that surface. Therefore vortices are due to this rapid local velocity variation. If the variation is small enough, there is enough time for the vorticity to diffuse out of the region just outside the cylinder s surface and create a large von Karman vortex street of vorticity down stream [feyn64]. 

All of us are familiar with the process of gaseous diffusion, in which gas molecules move through space from a region of high concentration to one of low concentration. If your instructor momentarily opens a cylinder of chlorine gas at the lecture table, you will soon recognize the sharp odor of chlorine, particularly if you have a front-row seat in the classroom. On a more pleasant note, the odor associated with a freshly baked apple pie also reaches you via gaseous diffusion. 

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