Binary Fluid Systems

A quite different set of dynamic high-pressure techniques are based on the use of chemical or nuclear explosions to produce transient shock waves of high peak pressure but short duration. With such methods, one can often penetrate the high-T, P regions where kinetic barriers become unimportant and a catalyst is unnecessary. However, the same kinetics that allows facile conversion of graphite to diamonds as the shock front arrives also allows the facile back-conversion as the shock wave passes. As a pioneer of shock-wave diamond synthesis remarked ruefully, We were millionaires for one microsecond [B. J. Alder and C. S. Christian. Phys. Rev. Lett. 7, 367 (1961) B. J. Alder, in W. Paul and D. M. Warschauer (eds). Solids under Pressure (McGraw-Hill, New York, 1963), p. 385]. 

Let us return to the simple case of a two-component (c = 2) A/B chemical solution (A = solvent, B = solute ), as considered in Chapter 6. We focus primarily on the fluid (liquid-vapor) region of the phase diagram, neglecting for the moment the melting/ freezing phenomena that lie at lower T and higher P. 

From the Gibbs phase rule (7.6), we deduce for this case that 

Compared with corresponding/values for c = 1 (Section 7.2), we can see that each phase multiplicity p enters a new dimension, and in addition four-phase coexistence becomes possible for binary solutions. Thus, each degree of phase coexistence presents new challenges to geometric visualization for c = 2. 

For the base p= 1 case with/ = 3, the three independent variables of the phase diagram might be chosen as intensives T, P, and puA (or pbB). However, it is instead convenient to choose a composition variable, such as mole fraction 

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Second, the number of binary fluid systems which are (or may soon become) of interest in technical processes is already large, and if one thinks of... 

When KT is positive, component A moves to the colder region otherwise, it moves to the warmer region. Some typical values of thermal diffusion ratios for binary fluid systems are given in Table 7.1. 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Swift, M., S. Orlandini, W. Osborn, and J. Yeomans. Lattice Boltzmann Simulations of Liquid-Gas Binary-fluid Systems. Phys. Rev. E 54 5041-5042 (1996). 

The phenomenological equations for an isotropic binary fluid system become... 

Schneider, GAl (1968) Phase equilibria in binary fluid systems of hydrocarbons with carbon dioxide, water and methane, Chem. Eng. Progr., Symp. Ser., 64,9-15. 

These observations point to the complex nature of the phase behavior of these systems and possible solubility maximum for the polymer in the binary fluid system consisting of monomer plus carbon dioxide. 

Recently, a new type of phase separation called viscoelastic phase separation was observed in polymer solutions or dynamically asymmetric fluid mixtures [1-3]. It is an interesting feature of this phenomenon that network-like domains of more viscous phase emerge in a transient regime. It has little been understood what ingredient of physics is crucial to this phenomenon. Various numerical approaches have been made for the phase separation phenomena in binary fluid systems in the last decade [4-6]. Most of these studies have been concerned with classical fluids and have not involved viscoelasticity. A new numerical model was recently proposed by the author [7] based upon the two-fluid model [8,9] using the method of smoothed-particle hydrodynamics (SPH) [10,11]. In this model the Lagrangian picture for fluid is adopted and the viscoelastic effect can easily be incorporated. In this paper we carry out a computer simulation for the viscoelastic phase separation in polymer solutions with this model. 

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