Bent ramp

One of the predictions to emerge from the model is that improved Cr(VI) conversion should result from a "convex bent ramp," usually represented as just a "bent ramp." The object is to accelerate the heat-up process while the temperatures are low, because the Cr(VI) is least sensitive to water vapor in this temperature range. Then, at high temperatures when the sensitivity is greatest, the heat-up rate is slowed so that water is not released as fast. Thus, the catalyst is exposed to a lower water vapor concentration during the most critical period, and the conversion to Cr(VI) is consequently improved. The result is improved conversion to Cr(VI) with no loss in heat-up time, compared with the standard linear thermal ramp. 

Figure 254 provides an example of the benefit of the "bent ramp." A Cr/silica catalyst containing 1 wt% Cr was activated three times at 800 °C in the laboratory. Each time the temperature was ramped to 800 °C in 4 h but in a different way. First, the standard linear ramp was used at a rate of 200 C h 1. This gave a conversion to Cr(VI) of 73%. Then, in the "concave... 

Each of the three ramp profiles took the same time to reach 800 °C, but there was a major difference in the conversion to Cr(VI). The "convex bent ramp" led to the release of water vapor slowly as the highest temperature was reached, which produced higher Cr(VI) levels. The improvement in conversion resulting from the "convex bent ramp" has been confirmed in commercial operations in many manufacturing plants where it has now been adopted. 

Similar complex structmes, characterized as folded sheets or bent walls, have been observed in optical microscopy experiments of ferrofluid emulsions at high ramping rates of the magnetic field [288]. When viewed along the field direction they form a labyrinthine pattern whose complexity increases with ceU thickness, particle volume fraction and ramping rate [288]. 

Many numerical experiments with ramps lead to patterns containing a lot of bent stripes and defects probably because of the ubiquitous presence of undulated stripes that are stable for a wide range of values of 5, as was mentioned before. 

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