Oscillatory temperature profiles

When a cyclic temperatiore profile is applied to a sample the heat flow signal will oscillate as a result of the temperature program, and the size of the oscillation will be a function of the heat capacity of the sample. Therefore, the amplitude of the heat flow signal allows a heat capacity value to be obtained. This is similar to DMA (see Chapter 4) where the amplitude of the oscillation allows a modulus value to be obtained. Whilst other methods already exist to provide heat capacity, the value of this method is that the heat capacity measurement is separated from other potentially overlapping events, such as reactions or stress relaxations and can also be obtained with increased sensitivity compared to the slow linear scan rates of traditional DSC. 

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It is straightforward to show that the desired steady-state (i.e., the origin) is unstable. A robust tracking control law can be constructed to stabilize the CSTR under forced oscillatory operation. That is, we can derive a controller to track an oscillatory temperature profile (say, yr t) = a- - sin(47rt)), which can be generated by the exosystem (3) where... 

The results of applying these strategies under the influence of initial error conditions are shown in Figure 6. As can be observed, both linear regulators ensure the asymptotic tracking of the desired oscillatory temperature profile. Both regulators performance is different because the error feedback regulator behavior depends on the initial states of zi and Z2. 

Figure 7.21 Temperature profiles from T2 parameter images of SBR cylinders with different carbon-black filler contents undergoing oscillatory shear deformation (a) Temperature calibration curves, (b) Temperature profiles across the cylinders...

A detailed experimental study of operating conditions in a nonadiabatic fixed bed reactor revealed that for certain inlet conditions oscillatory or erratic behavior of temperature profiles can be observed [23]. To follow this phenomenon local thermocouple temperature reading and axial temperature profiles were monitored. The results of measurements are reported in Fig. 3. 

If attention is restricted to the vicinity of the bifurcation point, then a nonlinear perturbation analysis can be developed for describing analytically the nature of the pulsating mode [111]. In effect, the difference between A and its bifurcation value is treated as a small parameter, say , and oscillatory solutions for temperature profiles are calculated as perturbations about the... 

If attention is restricted to the vicinity of the bifurcation point, then a nonlinear perturbation analysis can be developed for describing analytically the nature of the pulsating mode [111]. In effect, the difference between A and its bifurcation value is treated as a small parameter, say e, and oscillatory solutions for temperature profiles are calculated as perturbations about the steady solution in the form of a power series in /e. The departure of the oscillation frequency from its value at bifurcation is expressed in the same type of series. The methods of analysis possess a qualitative similarity to those of the shock-instability analysis discussed at the end of the previous section. The results exhibit the same general behavior that was found from the numerical integrations [109] for conditions near bifurcation. 

With oscillatory reactors being very promising candidates for intensifying slow processes with gradual heat requirement, a possible temperature distribution of heating medium and process medium could be very close to the temperature profiles of a counter-current tubular heat exchanger (see Figure 10.16). 

Fig. 37. Temperature profiles from T2 parameter images of SBR cylinders with different carbon-black filler contents undergoing oscillatory shear deformations, (a) Temperature calibration curves and (b) temperature profiles across the cylinders. ( ) 10 phr ( ) 30 phr, (a) 50 phr, and (T) 70 phr. The pixel resolution was 0.4 x 0.4 nun. Reproduced from Ref. 180, with permission from Rapra Technology.

VHiereas the previous case revealed temperature and conversion profiles propagating with almost constant velocity ("constant-pattern profiles"), the next case shows oscillatory behavior of the filtration combustion process for parameters a = 1.0, p = 0.08, y = 0.05, 6 = 1.0, (A) = 100.0, L =50.0 and 8 = -10.0. Figure 3a... 

Note that the usage of 10-fs laser pulse leads to rich oscillatory components as well as these rapid kinetics in their pump-probe time-resolved profiles. Obviously in this timescale, the temperature T will have no meaning except for the initial condition before the pumping process. In addition, such oscillatory components may be due not only to vibrational coherence but also to electronic coherence. A challenging theoretical question may arise, for such a case, as to how one can describe these ultrafast processes theoretically. 

In this section we develop a scheme implemented in a continuous polymerization reactor to regulate polydispersity by tracking periodic conversion profiles and maintaining stable temperature conditions. Oscillatory conversion is tracked by manipulating the initiator feedrate while the heat exchange rate is used to regulate reactor temperature. 

The oscillatory behavior of pore-water profiles near the interface can be accounted for by the different temperature dependence of microbial and macrofaunal activity that control production (consumption) and biogenic transport processes respectively. A non-steady-state model is used to show this is the case. 

Surface-directed spinodal decomposition was first observed in an isotopic polymer blend (Jones et al. 1991) thin films of a mixture of poly(ethylene-propylene) and its deuterated analogue were annealed below the upper critical solution temperature and the depth profiles measured using forward recoil spectrometry, to reveal oscillatory profiles similar to those sketched in figure 5.30. Similar results have now been obtained for a number of other polymer blends, including polystyrene with partially brominated polyst)u-ene (Bruder and Brenn 1992), polystyrene with poly(a-methyl styrene) (Geoghegan et al. 1995) and polystyrene with tetramethylbisphenol-A polycarbonate (Kim et al. 1994), suggesting that the phenomenon is rather general. 

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