Pressure inhomogeneity

The thermodynamic force (affinity) X is a pivotal concept in thermo dynamics of nonequilibrium processes because of its relationship to the concept of driving force of a particular irreversible process. Evidently, thermodynamic forces arise in spatially inhomogeneous systems with, for example, temperature, concentration, or pressure inhomogeneity. In spatially uniform homogeneous systems, such forces arise either in the presence of chemically reactive components that have not reached thermodynamic equiHbrium via respective chemical transformations or at the thermodynamic possibility of some phase transformations. 

Figure 15.13 Luminescence spectra of ruby chips irradiated with the blue 488 nm line of an argon ion laser. The double line structure shifts with pressure in the direction of increasing wavelength by 2.74 GPa nm (ref 30). The broadening visible in the measurement performed at 11 GPa is attri buted to pressure inhomogeneity and strain in the employed pressure medium paraffin.

Another feature of an extruder is the presence of a gauze filter after the screw and before the die. This effectively filters out any inhomogeneous material which might otherwise clog the die. These screen packs as they are called, will normally filter the melt to 120-150 fim. However, there is conclusive evidence to show that even smaller particles than this can initiate cracks in plastics extrudates e.g. polyethylene pressure pipes. In such cases it has been found that fine melt filtration ( 45 p.m) can significantly improve the performance of the extrudate. 

Sinee our system in the slit is anisotropie and inhomogeneous, it makes sense to eonsider the loeal pressure tensor, Eq. (42), whieh depends on the distanee z from the adsorbing wall. If one defines Px = Pxx Py = Pyy ... 

Focusing on the example of a sohd/gas interface, in the following, we will describe how to evaluate the stabihty of non-electrochemical interfaces, which are not influenced by a potential apphed externally or caused by an inhomogeneous ion distribution within the system. In the case that both the solid and the gaseous phase are present in macroscopic quantities, we have already seen in the previous section that each of these reservoirs is characterized by its chemical potential fifT, pi), which for the non-electrochemical interface is a function of temperature and partial pressure. 

In the past two decades, 129Xe NMR has been employed as a useful technique for the characterization of the internal void space of nanoporous materials. In particular, the xenon chemical shift has been demonstrated to be very sensitive to the local environment of the nuclei and to depend strongly on the pore size and also on the pressure [4—6], Assuming a macroscopic inhomogeneity resulting from a distribution of adsorption site concentrations, 129Xe NMR spectra of xenon in zeolites have been calculated, and properties such as line widths, shapes as well as their dependence on xenon pressure can be reproduced qualitatively. A fully quantitative analysis, however, remains difficult due to the different contributions to the xenon line shift. (See Chapter 5.3 for a more detailed description of Xe spectroscopy for the characterization of porous media.)... 

Dahnke S, Keil F (1998) Modeling of three dimension linear pressure field in sonochemical reactores with homogenous and inhomogenous density distribution of cavity bubbles. Ind Eng Chem Res 37 848-864... 

Dahnke S, Keil F (1999) Modeling of linear pressure fields in sonochemical reactor considering an inhomogeneous density distribution of cavitation bubble. Chem Eng Sci 54 2865-2872... 

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