Self-steeping

Figure 12-46D, Part 1. View toward inlet of 4 Vj-in. diameter brazed aluminum impeller. Note Regardless of the metal of manufacture, enclosed impellers with back-leaning blades are extremely useful in applications requiring a steep head-volume characteristic and the highest attainable efficiency. Applications include parallel operation with other compressors or boosting of another compressor s output. The power-volume curve will show a self-limiting feature at higher volumes. This feature is very beneficial when the driver has limited power available but operation throughout the full capacity range is required. (Used by permission A C Compressor Corporation.)...

More recently, there have been attempts to study band patterns as they are affected by shock layers in nonlinear chromatography.42 Shock layers are steep boundaries that develop when the boundary front of an elution band becomes very steep and self-sharpening at high concentrations. While comparison of predicted and experimental data was promising, this study, like the others mentioned above, was done with single-component samples and awaits further analysis with the kinds of multi-component feeds more frequently encountered in process purifications. 

Two classical models have been described for runaway calculations in which the important difference between the two is in the degree of mixing. The first model, proposed by Semenov [165], applies to well stirred mixtures where the temperature is the same throughout the mixture. Heat removal occurs with a steep temperature gradient at the surface of the walls or coils, and is governed by the usual factors of area, temperature of coolant, and heat transfer coefficients. Case A in Figure 3.20 shows a temperature distribution by the Semenov model for self-heating. 

The more recent Thomas model [209] comprises elements of both the Semenov and Frank-Kamenetskii models in that there is a nonuniform temperature distribution in the liquid and a steep temperature gradient at the wall. Case C in Figure 3.20 shows a temperature distribution curve from self-heating for the Thomas model. The appropriate model (Semenov, Frank-Kamenetskii, or Thomas) is determined by the ratio of the heat removal from the vessel and the thermal conductivity in the vessel. This ratio is determined by the Biot number (Nm) which has been described previously as hx/X, in which h is the film heat transfer coefficient to the surroundings (air, cooling mantle, etc.), x is the distance such as the radius of the vessel, and X is the effective thermal conductivity. 

To eliminate the errors caused by lead wire resistance changes, it is recommended to use transmitters that accept 4-wire RTD inputs as a standard feature. In order to eliminate errors by self-heating, the measuring current should be minimized. For platinum elements, it should not exceed 250 pA. The best installation practice is to place all electronics directly on top of the thermowell and thereby eliminate lead wire and noise effects. If this cannot be done, the lead wires should be twisted and shielded the wires should also not be stressed, strained, or made to go through steep gradients. The... 

Steeping at temperatures >55°C can result in a favorable environment for the propagation of Clostridium spp., bacteria which produce acetic acid. Some strains of Clostridium are highly exothermic and can result in a self-regulated steep temperature of 59°C, even with all heat exchangers turned off. Total acidity does not seem to be much different than in a Lactobacillus spp. fermentation, except that the primary acid produced is acetic rather than lactic acid. There does not seem to be any discernible effect on starch yield or quality. 

Recently,21,28 two kinds of self-consistent mean field models were developed to calculate the interaction potential between layers of flexible polymer chains grafted to spherical surfaces whose radii are comparable to the separation between the two surfaces. The calculations showed that for small particles the repulsion is less steep than that provided by the Derjaguin approximation, while with increasing radii, the interaction potential becomes close to that given by the... 

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

Self-sharpening A self-sharpening boundary is a shock layer, a boimdary which sharpens when the injection is not a sharp front, and retains a constant steepness during its migration. The band fronts of compoimds with Langmuirian isotherms are self-sharpening. 

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