Homogeneity of confined phases

An important issue in the thermodynamics of confined fluids concerns their symmetry which is lower than that of a corresponding homogeneous bulk phase because of the presence of the substrate and its inherent atomic structure [52]. The substrate may also be nonplanar (see Sec. IV C) or may consist of more than one chemical species so that it is heterogeneous on a nanoscopic length scale (see Sec. VB 3). The reduced symmetry of the confined phase led us to replace the usual compressional-work term —Pbuik F in the bulk analogue of Eq. (2) by individual stresses and strains. The appearance of shear contributions also reflects the reduced symmetry of confined phases. 

The results are compared with solutions determined using fixed-length management periods. The hypothetical homogeneous, isotropic, confined aquifer is comprised of 60 finite elements and 77 nodes, with dimensions 1500 m by 900 m (Culver and Shenk, 1998). The initial contaminant plume, which has a maximum toluene concentration of 40 mg/L, is shown in Figure 1. An easterly steady flow was maintained with a constant hydraulic head of 12.0 m and contaminant concentration of 0.0 mg/L on the left side, a constant hydraulic head of 0.0 m and contaminant concentration of 0.0 mg/L on the right side, and no flow at the top and bottom boundaries. In this example, the sorbed phase is assumed to remain in equilibrium with the... 

Toxvaerd319 has studied nucleation in homogeneous systems, in systems with a carrier gas, and in confined systems. It is shown how confinement catalyses nucleation due to the formation of dense phases near the wall. 

The assumption of homogeneity can be abandoned if the continuous me m-field treatment is replaced by a discrete treatment where the positions of fluid molecules are restricted to nodes on a lattice. The discussion in Section 5.4.2 and 5.6.5 showed that the mean-field lattice density functional theory developed in Section 4.3 w as crucial in unraveling the c.om-plex phase behavior of fluids confined by chemically decorated substrate surfaces. A similar deep understanding of the phase behavior would not have been possible on the basis of simulation results alone. Nevertheless, the relation between these MC data and the lattice density functional results remained only qualitative on accoimt of the continuous models employed in the computer simulations. Thus, we aim at a more quantitative comparison between MC simulations and mean-field lattice density fimctioiial theory in the closing. section of this diaptcr. 

Figure 7.2 Replica HNC results for the temperatures corresponding to the stability limits of the homogeneous isotropic phase of confined Stodonayer fluids (and for the bulk) as a function of the renormalized fluid density (tf = npa /6). Curves are labeled according to values of the reduced matrix density pm-...

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