Complex fluids chemical potential

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

The above classification tends to explain the properties of a more complex fluid in terms of an excess over a less complex (simpler) fluid pointing to a perturbation treatment as a suitable tool for both theory and applications. The properties of fluids belonging to different classes seem thus to be determined by the different types of predominant interactions. Consequently, to be able to understand and thus to predict the macroscopic properties of fluids, it is natural (and important) to determine the effect of the individual terms contributing to u on the macroscopic behavior. However, this need not be the case when the origins of the potential functions are considered. With the advance of computer technology, quantum chemical computation methods have also made considerable progress in the development of reasonably accurate effective pair potentials, but in a form which differs from that of Eqs. (2)-(4). Consequently, the simple physical picture of intermolecular interactions is lost and decompositions (3)-(4) become of little use. 

Dialysis is a diffusion-based separation process that uses a semipermeable membrane to separate species by vittue of their different mobilities in the membrane. A feed solution, containing the solutes to he separated, flows ou one side of the membrane while a solvent stream, die dialysate, flows on die other side (Fig. 21. -1). Solute transport across the membrane occurs by diffusion driven by the difference in solme chemical potential between the two membrane-solution interfaces. In practical dialysis devices, no obligatory transmembrane hydraulic pressure may add an additional component of convective transport. Convective transport also may occur if one stream, usually the feed, is highly concentrated, thus giving rise to a transmembrane osmotic gradient down which solvent will flow. In such circumstances, the description of solute transport becomes more complex since it must incorporate some function of die trans-membrane fluid velocity. 

The approach outlined previously is also applicable to the aqueous phase in an invert emulsion oil-based drilling fluid. The chemical potential of the water in the aqueous (dispersed) phase is usually controlled by the concentration of calcium chloride. The transport of water between the shale and the aqueous phase of the invert emulsion is less complex than with water-based drilling fluids, because with the emulsions there is no cation exchange between the ions in the fluid and in the shale. The thin emulsified layer surrounding the water droplets is postulated to act as a semipermeable membrane that allows only the passage of water (61). 

Considering the rather large amount of data required to implement virial methods even at 25°C (e.g., Tables 7.4-7.7), it is tempting to dismiss the methods as no more than statistical fits to experimental data. In fact, however, virial methods take chemical potentials measured from simple solutions containing just one or two salts to provide an activity model capable of accurately predicting species activities in complex fluids. Eugster et al. (1980), for example, used the virial method of Harvie and Weare (1980) to accurately trace the evaporation of seawater almost to the point of desiccation. Using any other activity model, such a calculation could not even be contemplated. Other... 

For an ordinary fluid two-phase system, minimization of the free energy at constant temperature flrst of all results in the well-known chemical potential condition for diffusive equilibrium with respect to the soluble components present. Furthermore, the mathematical extremum condition for the free energy contains the pressure difference AP across the interface as a parameter. Solving for AP, this condition takes the form of a generalized Laplace equation. Whether or not this equation signifies a stable equilibrium is, however, often a rather complex issue where the detailed system properties may enter in a crucial manner. 

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