Nonuniform fluids

Lebowitz J L and Percus J 1961 Long range correlations in a closed system with applications to nonuniform fluids Phys. Rev. 122 1675... 

II. Nonuniform Fluids with Spherically Symmetric Associative... 

II. NONUNIFORM FLUIDS WITH SPHERICALLY SYMMETRIC ASSOCIATIVE POTENTIALS... 

We need, however, some means to calculate the direct correlation functions F2) of a nonuniform fluid. In order to make further progress, the... 

A set of equations (15)-(17) represents the background of the so-called second-order or pair theory. If these equations are supplemented by an approximate relation between direct and pair correlation functions the problem becomes complete. Its numerical solution provides not only the density profile but also the pair correlation functions for a nonuniform fluid [55-58]. In the majority of previous studies of inhomogeneous simple fluids, the inhomogeneous Percus-Yevick approximation (PY2) has been used. It reads... 

In order to accurately describe such oscillations, which have been the center of attention of modern liquid state theory, two major requirements need be fulfilled. The first has already been discussed above, i.e., the need to accurately resolve the nonlocal interactions, in particular the repulsive interactions. The second is the need to accurately resolve the mechanisms of the equation of state of the bulk fluid. Thus we need a mechanistically accurate bulk equation of state in order to create a free energy functional which can accurately resolve nonuniform fluid phenomena related to the nonlocality of interactions. So far we have only discussed the original van der Waals form of equation of state and its slight modification by choosing a high-density estimate for the excluded volume, vq = for a fluid with effective hard sphere diameter a, instead of the low-density estimate vq = suggested by van der Waals. These two estimates really suggest... 

The quantity of primary interest in the study of nonuniform fluids is the density profile of the fluid at a surface. Dickman and Hall [28] reported the density profiles of freely jointed hard-sphere chains at hard walls. Their focus was on the equation of state of melts of hard-chain polymers, and they performed simulations of polymers at hard walls because the bulk pressure, P, can be calculated from the value of the density profile at the surface using the wall sum rule ... 

Integral equations can also be used to treat nonuniform fluids, such as fluids at surfaces. One starts with a binary mixture of spheres and polymers and takes the limit as the spheres become infinitely dilute and infinitely large [92-94]. The sphere polymer pair correlation function is then simply related to the density profile of the fluid. 

The simplest choice for Fex is to approximate the nonuniform fluid direct correlation function in Eq. (47) with the uniform fluid direct correlation at some bulk density, that is, to set... 

Here, we report some basic results that are necessary for further developments in this presentation. The merging process of a test particle is based on the concept of cavity function (first adopted to interpret the pair correlation function of a hard-sphere system [75]), and on the potential distribution theorem (PDT) used to determine the excess chemical potential of uniform and nonuniform fluids [73, 74]. The obtaining of the PDT is done with the test-particle method for nonuniform systems assuming that the presence of a test particle is equivalent to placing the fluid in an external field [36]. 

Benvegnu DJ and McConnel HM (1992) Line tension between liquid domains in lipid monolayers. J Phys Chem 96 6820-6824 Chou T and Nelson DR (1994) Surface wave scattering at nonuniform fluid interfaces. J. Chem. Phys 101 9022-9032... 

Nonuniform fluid velocity This condition can induce local anodic and cathodic regions, causing variations at the surface in the concentration of cathodic species supporting corrosion and by removing corrosion products. This condition is frequently found in piping systems and pumps. 

As we noted in Rems. 12 in Chap. 1, 6, 11 in this chapter, the stability conditions of equilibria must be added which in model B means that for equilibrium pressure (2.33) and (2.26) we have dP° jdV < 0, dij jdT > 0. This follows from the fact that equilibrium in model B is, similarly as in model A (see Rem. 7 in this chapter), a specitil case of equilibrium in a model of nonuniform fluid from Sect. 3.8, cf. (3.256), (3.257). Stability forms a part of regular conditions (see end of Sect. 1.1, Rem. 6 in this chapter). To exclude rather pathological cases in applications we add to regular conditions that Pjv = Oonlyif V = 0 (entropy production E(V, V, T) has a sharp minimum at V = 0, i.e., equalities in (2.30), (2.37) are excluded). In linearized model B from Rem. 8 such regularity means that volume viscosity coefficient is only positive C > 0, cf. (3.232). 

Abraham, F.F. (1979) On the thermodynamics, structure, and phase stability of the nonuniform fluid state, Phys. Rep. 53, 95. 

Evans R Density functionals in the theory of nonuniform fluids. In Henderson D, editor Fundamentals of inhomogeneous fluids. New York, 1992, Marcel Dekker, pp 85—175. 

Lebowitz, J.L. and Percus, J.K., 1963, Statistical thermodynamics of nonuniform fluids Asymptotic behavior of the radial distribution function, J. Math. Phys., 4 116, 248. 

Understanding the mechanism of adsorption is timely and important from a fimdamental scientiflc perspective. Adsorption is defined as a change in concentration of a given substance at the interface with respect to its concentration in the bulk part of the system. Such a perturbation in the local concentration is the most characteristic feature of nommiform fluids. Adsorption is one of the fascinating phenomena connected with the behavior of fluids in a force field extorted by the solid surface. This process has a great influence on the structure of thin films and it affects phase transitions and critical phenomena near the surface. Briefly, adsorption dictates the thermodynamical properties of nonuniform fluids. 

The other model of the adsorption system, the so-caUed three-dimensional model, seems to be more realistic and promising. In this model, we do not assume the existence of a distinct surface phase but consider the problem of a fluid in an external force field. From a theoretical point of view a solution of this task requires only knowledge of the adsorbate-adsorbate and adsorbate-adsorbent interactions. However, in practice, we encounter difficulties connected with the mathematical complexity of the derived equations. The majority of the statistical-mechanical theories of nonuniform fluids have been formulated for adsorption on homogeneous siufaces. Nevertheless, the recent results obtained for heterogeneous sohds are really interesting and valuable [16]. 

As was mentioned in Section II.A, phase transitions in adsorbed films have been (and continue to be) one of the most intensively studied problems in surface science [9,12,15,62,99]. The experimental findings described in Section II.A have led to different theoretical approaches based mainly on partial localization models [161,164], on theoretical models for completely mobile films [227], on various lattice gas models [144,181,183], and, finally, on models of nonuniform fluids such as density functional theories [98,186-189]. 

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