Lattice fluid binary mixture

A comparison of mesoscopic simulation methods with MD simulations has been performed by Denniston and Robbins.423 They study a binary mixture of simple Lennard-Jones fluids and map out the required parameters of the mesoscopic model from their MD simulation data. Their mapping scheme is more complete than those of previous workers because in addition to accounting for the interfacial order parameter and density profiles, they also consider the stress. Their mapping consists of using MD simulations to parameterise the popular mesoscale Lattice Boltzmann simulation technique and find that a... 

We now extend the previous discussion of pure confined lattice fluids to binary (A-B) mixtures on a simple cubic lattice oi J f = nz sites, whose lattice constant is again i. We deviate from our previous notation (i.e., M = nx%r ) because we concentrate on chemically homogeneous substrates where n = n riy located in a plane at some fixed distance from the substrate, which are energetically equivalent. Moreover, our subsequent development will benefit notationally by replacing henceforth n by just z. 

In the limit ab = 10, the symmetric binary mixture degenerates to a pure fluid. In this case Tcep —> 0 and the A-linc becomes formally indistinguishable from the /r-axis (and therefore physically meaningless). The remaining coexistence line /Xxb = -3 = /icb (i e-, the phase diagram) involving gas (G) and liquid phases (L) becomes parallel with the T-axis and ends at the critical point where Tcb = as expected for the bulk lattice gas [16] [see, for example, Fig. 4.12(a)]. 

However, one-dimensional confined fluids with purely repulsive interactions can be expected to be only of limited usefulness, especially if one is interested in phase transitions that cannot occur in any one-dimensional system. In treating confined fluids in such a broader context, a key theoretical tool is the one usually referred to as mean-field theory. This powerful theory, by which the key problem of statistical thermodynamics, namely the computation of a partition function, becomes tractable, is introduced in Chapter 4 where we focus primarily on lattice models of confined pure fluids and their binary mixtures. In this chapter the emphasis is on features rendering confined fluids unique among other fluidic systems. One example in this context is the solid-like response of a confined fluid to an applied shear strain despite the absence of any solid-like structure of the fluid phase. 

The basic features of the lattice theory and structure of a quasilattice EOS and its application to fluids and fluid mixtures was reviewed by Smirnova and Victorov (2000). Victorov et al. (1991) used the hole quasi-chemical group-contribution model of Victorov and Smirnova (1985) and Smirnova and Victorov (1987) to calculate the phase equilibria in water -i- n-alkane binary mixtures. This model is essentially a generalization of the Barker lattice theory in its group-contribution formulation, the main difference being the presence of vacant lattice sites (holes). The model becomes volume-dependent, and thus the derived EOS adopted the following form (Smirnova and Victorov, 1987). 

In the lattice fluid theory, as formulated by Sanchez and Lacombe(Lacombe Sanchez, 1976 Sanchez Lacombe, 1976), the energy of mixing for binary polymer containing systems is related to the Gibbs energy per mer (indicated by the double bar) of the mixture (index M) and that of the pnire components (indexlor2) by... 

To gain an understanding of the experimental findings, we adopt a lattice model of a binary fluid mixture similar to the one introduced in Section 4.6.1. As in Section 4.6.1, we consider a simple cubic lattice with lattice constant . However, unlike in Section 4.6.1, we now assume molecules to occupy the cubic cells of volume f formed by the surrounding lattice. sites rather than occupying the sites themselves. This approach allows us to account for the different sizes of water and iBA molecules (see below). 

This chapter demonstrates how to calculate phase diagrams and solubility isotherms for binary and ternary supercritical mixtures. As Johnston has pointed out (Wong, Pearlman, and Johnston, 1985 Johnston, Peck, and Kim, 1989), no single model will work for all situations. As the equations describing molecular interactions in dense fluids become more accurate, we can expect our abilities to model complex phase behavior to improve. At present, using a cubic equation of state or a lattice-gas equation appears to offer the best compromise between accuracy and ease of application. 

The two-term crossover Landau model has been successfully applied to the description of the near-critical thermodynamic properties of various systems, that are physically very different the 3-dimensional lattice gas (Ising model) [25], one-component fluids near the vapor-liquid critical point [3, 20], binary liquid mixtures near the consolute point [20, 26], aqueous and nonaqueous ionic solutions [20, 27, 28], and polymer solutions [24]. 

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