Rotary diffusivity

This model has been applied to vacuum coalers where the material being vapor deposited is evaporated from one or more point sources. Note that and Dr are empirical parameters that account for both convection and diffusion. Rotary vacuum coalers avoid any dependence in the 6 direction by rotating the substrate as it is coated. The false-transient method works here as in Section 16.2.4, but the axial and radial diffusivities are now separate and empirical. 

The flow of droplets is directed through a small orifice (Skimmer 1 Figure 12.1) and across a small region that is kept under vacuum by rotary pumps. In this region, approximately 90% of solvent and injected helium is removed from the incipient particle beam. Because the rate of diffusion of a substance is inversely proportional to its molecular mass, the lighter helium and solvent molecules diffuse away from the beam and are pumped away. The heavier solute molecules diffuse more slowly and pass through the first skimmer before they have time to leave the beam the solute is accompanied by residual solvent and helium. 

The desorptive process may be analyzed before boiling. The key assumption is that the vapor and adsorbed phases are ia equiUbrium ia the bulk of the bed. This assumption eliminates iatraparticle resistances from further consideration and is reasonable for rotary kiln appHcations. The two remaining resistances are associated with hydrocarbon diffusion out of the bed and with convection from the bed surface to the bulk gases. The flux of species Fi from the desorbiag bed becomes... 

In most cases, direct-heat rotary dryers are still sized on the basis of pilot-plant tests, because rarely is all the moisture to be removed truly Tree moisture, and residence time for diffusion is frequently needed. 

If the pump is a filter pump off a high-pressure water supply, its performance will be limited by the temperature of the water because the vapour pressure of water at 10°, 15°, 20° and 25° is 9.2, 12.8, 17.5 and 23.8 mm Hg respectively. The pressure can be measured with an ordinary manometer. For vacuums in the range lO" mm Hg to 10 mm Hg, rotary mechanical pumps (oil pumps) are used and the pressure can be measured with a Vacustat McLeod type gauge. If still higher vacuums are required, for example for high vacuum sublimations, a mercury diffusion pump is suitable. Such a pump can provide a vacuum up to 10" mm Hg. For better efficiencies, the pump can be backed up by a mechanical pump. In all cases, the mercury pump is connected to the distillation apparatus through several traps to remove mercury vapours. These traps may operate by chemical action, for example the use of sodium hydroxide pellets to react with acids, or by condensation, in which case empty tubes cooled in solid carbon dioxide-ethanol or liquid nitrogen (contained in wide-mouthed Dewar flasks) are used. 

Two vacuum systems are used to provide both the high vacuum needed for the mass spectrometer and the differential pumping required for the interface region. Rotary pumps are used for the interface region. The high vacuum is obtained using diffusion pumps, cryogenic pumps, or turbo pumps. 

With the rotary and diffusion pumps in tandem, aided by a liquid-nitrogen trap, a vacuum of 10 Torr became readily attainable between the wars by degrees, as oils and vacuum greases improved, this was inched up towards 10 Torr (a hundred-billionth of atmospheric pressure), but there it stuck. These low pressures were beyond the range of the McLeod gauge and even beyond the Pirani gauge based on heat conduction from a hot filament (limit Torr), and it was necessary to... 

For very low pressures, a diffusion pump is used with a rotary pump as the first stage. The principle of operation is that the gas diffuses into a stream of oil or mercury and is driven out of the pump by molecular bombardment. 

Figure 25 Cumulative fraction of the initial donor concentration of [1-blockers that diffused across Caco-2 cell monolayers as a function of donor pH. Transwell systems were used, and stirring was done using a rotary platform shaker. (A), pH 7.4 (B), pH 6.5.

A diffusion pump needs a forepump (usually a rotary pump). Oil can also migrate from the forepump into the vacuum chamber through the diffusion pump, when the rotary pump works in the molecular regime ( 10 2torr). 

Example 1.2. A diffusion pump with constant speed Sx = 301/s below 10-3 torr has a critical forepressure pK = 0.12 torr. It is connected to a rotary pump by a tube of length L = 150cm (see Fig. 1.15). 

Finally, we should also mention that assisted spin recoupling is by no means restricted to 1H, 13C, and 15N spin species but may also be used to facilitate H and 2H to low- spin transfers. This may be exploited in extensively deuterated samples using rf fields on JH and 2H which are matched to a rotary resonance condition to facilitate spin-diffusion between 13C spins in a longitudinal mixing process. This was recently demonstrated by van Rossum and coworkers in terms of the doublenucleus enhanced recoupling (DONER) experiment [143]. 

The vacuum chambers were pumped down by means of an oil diffusion pump backed by a rotary vane vacuum pump. The base pressure achieved was 1 x 10 5 Torr (1.33 x 10 Pa). High-purity argon gas was bled into the chamber, the high-vacuum valve throttled, and the chamber pressure maintained as close as possible to 2 x 10 2 Torr (2.66Pa). For some of the experiments, the dc self-bias on the magnetron electrode was also measured. 

As with spherical particles the Peclet number is of great importance in describing the transitions in rheological behaviour. In order for the applied flow field to overcome the diffusive motion and shear thinning to be observed a Peclet number exceeding unity is required. However, we can define both rotational and translational Peclet numbers, depending upon which of the diffusive modes we consider most important to the flow we initiate. The most rapid diffusion is the rotational component and it is this that must be overcome in order to initiate flow. We can define this in terms of a diffusive timescale relative to the applied shear rate. The characteristic Maxwell time for rotary diffusion is... 

The rod is visualised as being constrained to a tube in a similar fashion to entanglements constraining a polymer in reptation theory. So for a finite concentration our diffusion coefficient and rotary Peclet number changes ... 

In the case of operations ranging between 760 and 10 3 torr, the two-stage rotary pump is adequate. Ultimate vacuum, using the diffusion pump installation, is better than 10-6 torr. 

The principles of fluidisation, discussed in Chapter 6, are applied in this type of dryer, shown typically in Figure 16.25. Heated air, or hot gas from a burner, is passed by way of a plenum chamber and a diffuser plate, fitted with suitable nozzles to prevent any back-flow of solids, into the fluidised bed of material, from which it passes to a dust separator. Wet material is fed continuously into the bed through a rotary valve, and this mixes immediately with the dry charge. Dry material overflows through a downcomer to an integral after-cooler. An alternative design of this type of dryer is one in which a thin bed is used. 

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