Inhomogeneous fluid system

There have been other promising lines along which the theory of quenched-annealed systems has progressed recently. One of them, worth discussing in more detail, is the adsorption of fluids in inhomogeneous, i.e. geometrically restricted, quenched media [31,32]. In this area one encounters severe methodological and technical difficulties. At the moment, a set of results has been obtained at the level of a hard sphere type model adsorbed in sht-like pores with quenched distribution of hard sphere obstacles [33]. However, the problem of phase transitions has remained out of the question so far. 

As for simple fluids that have only translational degrees of freedom the structure of the confined DSS fluid is inhomogeneous on account of stratification (see Section 5.3.4). Because of the additional rotational degrees of freedom, however, the structure of the DSS fluid may be more complex as snapshots from the MC simulations in Fig. 6.7 illustrate. In the left part of that figure, a snapshot is presented for a globally isotropic system, whereas the right part shows a snapshot for an orientationally ordered phase. For the sake of clarity only molecules in one contact layer (i.e., the layers of molecules closest to one of the walls) are plotted. 

Most chemical engineering processes involve complex multiphase fluid systems, and their evolution depends on the mechanism by which the inhomogeneous subsystems exchange information at different length scales. Whereas numerous theoretical methods with specific description accuracies have been developed for investigating physicochemical properties of various fluid systems, a unified theory that enables the investigation of mesoscale problems is still needed. Here, we introduce a unified... 

Figure 2 Illustrations for homogeneous fluid system (left) and inhomogeneous fluid system (right). The spheres in different color denote different components.

While for inhomogeneous fluid systems as illustrated in Fig. 2, the thermodynamic quantities can no longer direcdy predicted by using EOS, and instead, they can be determined by the one-body density distribution Pi R). Here R is the abbreviation of the set of complete variables which describes the spatial state of the concerned molecule. This generic notation stands for different variables in different circumstances. In specific, R refers to position r for a quantum particle or spherical classical particle, to (r, 0, (p) for a dipolar molecule with 9, (p) being the Euler angle, to (r, 0, (p, yr) for a rigid nonlinear molecule, and to (rj, t2, foT a flexible polymeric molecule with r,-... 

The classical DFTs have proven to be an excellent alternative approach to the simulation method. The gas confined in MOF materials physicaUy represents nothing but a highly inhomogeneous fluid system, in which the MOF materials exert external potential to the fluid system. As demonstrated above, statistical DFTs present the same level of accuracy with but superior efficiency than computer simulations for the predictions of the physicochemical properties of inhomogeneous fluid systems. Similar to classical simulation, the practical implementation of DFT calculations relies on a semiempirical force field that describes the gas-material interaction. 

Recently, the HAB approach plus the MV closure has been applied both to hard spheres near a single hard wall [24,25] and in a slit formed by two hard walls. Some results [99] for the latter system are compared with simulation results in Fig. 7. The results obtained from the HAB equation with the HNC and PY closures are not very satisfactory. However, if the MV closure is used, the results are quite good. There have been a few apphcations of the HAB equation to inhomogeneous fluids with attractive interactions. The results have not been very good. The fault hes with the closure used and not Eq. (78). A better closure is needed. Perhaps the DHH closure [27,28] would yield good results, but it has never been tried. 

Eq. (5) is useful when analyzing different approximations in the theory of inhomogeneous fluids. In particular, if all the terms involving third- and higher-order correlations in the right-hand side of Eq. (5) are neglected, and if Pi(ro))P2( o)i )Pv( o) are chosen as the densities of species for a uniform system at temperature T and the chemical potentials p,, the singlet hypemetted chain equation (HNCl) [50] results... 

The multidensity Ornstein-Zernike equation (70) and the self-consistency relation (71) actually describe a nonuniform system. To solve these equations numerically for inhomogeneous fluids one needs only an appropriate generalization of the Lowett-Mou-Buff-Wertheim equation (14). Such a generalization, employing the concept of the partial correlation function has been considered in Refs. 34,35. 

Sec. 4 is concerned with the development of the theory of inhomogeneous partly quenched systems. The theory involves the inhomogeneous, or second-order, replica OZ equations and the Born-Green-Yvon equation for the density profile of adsorbed fluid in disordered media. Some computer simulation results are also given. 

Iv) Shear stress and viscosity. As explained In Section 1 three Independent estimates of the shear stress can be made for this particular type of flow. For both systems they all agree within the limits of statistical uncertainty as shown In Table II. The shear stress In the micro pore fluid Is significantly lower than the bulk fluid, which shows that strong density inhomogeneities can induce large changes of the shear stress. 

A final comment has to do with the concept of effective viscosity In strongly Inhomogeneous fluids. For these systems the definition of the effective viscosity depends on the type flow, hence different effective viscosities will be measured for different flow situations In the same system with the same density profile. Therefore, the effective viscosity Is a concept of limited value and measurements of this quantity do not provide much information about the effects of density structure on the flow behavior. 

Besseling, N. A. M. and Scheutjens, J. M. H. M. (1994). Statistical thermodynamics of fluids with orientation-dependent interactions in homogeneous and inhomogeneous systems, J. Phys. Chem., 98, 11 597-11 609. 

Once the free energy of an inhomogeneous system is given, one can calculate by standard methods the properties of the interface—for example, the interfacial tension or the density profile perpendicular the interface [285]. Weiss and Schroer compared the various approximations within square-gradient theory discussed earlier in Section IV.F for studying the interfacial properties for pure DH and FL theory [241, 242], In theories based on local density approximations the interfacial thickness and the interfacial tension were found to differ by up to a factor of four in the various approximations. This contrasts with nonionic fluids, where the density profiles and interfacial... 

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