Inverted temperature gradients

Closely related to the superheating effect under atmospheric pressure are wall effects, more specifically the elimination of wall effects caused by inverted temperature gradients (Fig. 2.6). With microwave heating, the surface of the wall is generally not heated since the energy is dissipated inside the bulk liquid. Therefore, the temperature at the inner surface of the reactor wall is lower than that of the bulk liquid. It can be assumed that while in a conventional oil-bath experiment (hot vessel surface, Fig. 2.6) temperature-sensitive species, for example catalysts, may decompose at the hot reactor surface (wall effects), the elimination of such a hot surface will increase the lifetime of the catalyst and therefore will lead to better conversions in a microwave-heated as compared to a conventionally heated process. 

Figure 5.3 Inverted temperature gradients in microwave versus oil-bath heating difference in the temperature profiles (finite element modeling) after 1 min of micro-wave irradiation (a) and treatment in an oil bath (b). Copyright Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission...

These first three examples of specific microwave effects (observed heating differences based on microwave absorptivity, inverted temperature gradients, and macroscopic superheating) are very real, observable phenomena. While they can occasionally be exploited and have an impact on observed reaction rates, it is... 

The definition of thermodynamic variables adopted here has also been used by Green and Mori, and seems to be the most natural generalization of the equilibrium definitions. It should be noted, however, that there is a problem connected with the measurement of, say, the temperature for a non-equilibrium state. One is assured by the general principles of thermodjmamics that a properly calibrated thermometer will always yield correct results in an equilibrium measurement. This is no longer true in a non-equilibrium situation. The result of a temperature measurement could depend on, say, the orientation of the thermometer with respect to the temperature gradient. However, we will simply dismiss this difficulty by taking the point of view that it concerns a matter of experimental practice. Note that there is really no difficulty in principle, since one could measure the mechanical quantities and invert Eqs. (67) and (68) to obtain the thermodynamic variables. 

Figure 3.25 Schematics and SEM micrographs of cross-sections of PLA vessel tubular elements realized under different temperature gradients. The warmer and the colder walls are inverted in the two sets of panels (left and right panels, respectively). The size of the radially oriented voids decreases by moving from the hot to the cold interface with the external template material. In both the investigated cases, PLA benzene solutions at different concentrations are used (A) 2.5%, (B) 5.0%, (C) 7.5%, (D) 10.0% (weight/volume). Adapted with permission from Ref. 308, Adv. Funct. Mater., 2010, 20, 2833-2841. Doi 10.1002/ adfm.201000922. Copyright 2010, Wiley-VCH Verlag GmbH Co. KGaA.

Fig. 11. Temperature-composition isobaric phase diagram for the monolinolein/water system constructed using the lyotrope gradient method. See ligand to Fig. 3 for notation. Hn, inverted hexagonal phase CP4, cubic, primitive (aspect 8) BCC12, cubic, body-centered (aspect 12) Isotropic,...

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