Temperature gradient, critical

Figure 10. Critical temperature gradient as a function of reaction-wave propagation...

This effect may also cause an oscillatory instability of the front propagation in the case of the isothermal mechanism of the auto wave process. However, in this case a jumplike onset of dispersion in the next layer of the solid matrix will be connected not with the critical temperature gradient of thermal fracture, but with the critical concentration of the final product accumulated at the boundary of this layer (fracture due to a local alteration of the density). 

The hypothesis advanced here is that the observed enhancement is due to thermocapillarity arising from the temperature dependence of the interfacial tension. Although we know of no theory for such a Marangoni effect in binary condensation per se, theory does exist for both mass transfer (M. 11) and heat transfer (16, 12) aeross an interface in the absence of bulk flow. We note that the sign of the derivative of the interfacial tension with respect to temperature is positive near a lower consolute point and that this is in the correct direction to sustain disturbances in condensation rate. Thus, in retrograde condensation, provided a critical temperature gradient normal to the interface is exceeded, a local increase in condensation flux toward the vapor liquid interface will result in its cooling. 

The situation is altered profoundly in the case of a nematic because of its anisotropic transport properties. Dubois-Violette was the first to give an approximate theoretical treatment of thermal convection in a planar (homogeneously aligned) nematic and to show by consideration of torques that such a system will be unstable against cellular flow when the film is heated from below if > 0, or when it is heated from above if < 0, where = K —K is the anisotropy of thermal conductivity (which is positive for all known nematics )- Dubois-Violette also showed that the critical temperature gradient fi (=ATJd) should be much less than that... 

P is the critical exponent and t denotes the reduced distance from the critical temperature. In the vicinity of the critical point, the free energy can be expanded in tenns of powers and gradients of the local order parameter m (r) = AW - I bW ... 

Critical meteorological variables were not always measured, especially vertical wind and temperature gradients. 

Saturated nucleate flow boiling of ordinary liquids. To maintain nucleate boiling on the surface, it is necessary that the wall temperature exceed a critical value for a specified heat flux. The stability of nucleate boiling in the presence of a temperature gradient, as discussed in Section 4.2.1.1, is also valid for the suppres-... 

Several articles in the area of microwave-assisted parallel synthesis have described irradiation of 96-well filter-bottom polypropylene plates in conventional household microwave ovens for high-throughput synthesis. While some authors have not reported any difficulties in relation to the use of such equipment (see Scheme 4.24) [77], others have experienced problems in connection with the thermal instability of the polypropylene material itself [89], and with respect to the creation of temperature gradients between individual wells upon microwave heating [89, 90]. Figure 4.5 shows the temperature gradients after irradiation of a conventional 96-well plate for 1 min in a domestic microwave oven. For the particular chemistry involved (Scheme 7.45), the 20 °C difference between the inner and outer wells was, however, not critical. 

Another example of scale-up effects relates to the storage of chemically unstable substances. Well-established procedures can be followed on a small scale. In a commercial unit, the storage of such materials must be reviewed from the standpoint of critical mass. The heat removal capacity of the equipment must be substantially larger than the spontaneous exothermic rate of heat release in the bulk material. Temperature gradients must also be considered. 

Both radial and axial temperature gradients may appear. As shown is Section 16.3.5, adsorption of polymers depends on temperature. Given the temperature and pressure dependence of the preferential sorption of the mixed eluent components within column packing [146-149], one can expect also considerable changes in the column interactivity with the temperature and pressure variations that may result in a possible gradual departure from the critical conditions. 

The original eddy motion which sets up the chain of events leading to eruptions may be caused by forced flow of the bulk phases, density differences due to concentration or temperature gradients (B12), or earlier eruptions. Strong eruptions occur when a critical concentration driving force or a critical interfacial tension depression is exceeded (03, S8, S9). At lower concentration differences ripples may result (E4), eruptions may occur only over part of the interface (S8) with the jets taking some time to form (T9), or no interfacial motion at all may occur. Attempts to correlate the minimum driving force required for spontaneous interfacial motions have met with little success. 

At particular critical points (Tq, Pc) on the phase diagram of a substance, two phases can be found in thermodynamic equilibrium. Therefore, upon application of a pressure or a temperature gradient, a transformation occurs from one phase into the other. This is a phase transition, in many aspects similar to a transformation implying the change of aggregation state. However, the extent of the changes in a solid to solid transformation is much smaller. For example, latent heat or latent volumes associated with the transformations are quite small, sometimes even difficult to detect. 

Photochemistry can be used to demonstrate solvent effects in supercritical fluids. The analysis revealed trimodal fluorescence lifetime distributions near the critical temperature, which can be explained by the presence of solvent-solute and solute-solute clustering. This local aggregation causes an increase in nonradiative relaxations and, therefore, a decrease in the observed fluorescence lifetimes. Concentration and density gradients are responsible for these three unique lifetimes (trimodal) in the supercritical fluid, as contrasted with the single lifetime observed in a typical organic solvent. The... 

We consider it essential in temperature gradient studies to recognize certain transition and critical points that could be useful in industrial practice, to select the important ones in this context, to keep them as few in number as possible, and to describe them with as little ambiguity as possible. 

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