Beyond Model Mixtures

In general, the rate of permeation of the permeating species is difficult to calculate. It is a complex matter which intimately involves a knowledge of the structure and dynamics of the membrane and the structure and dynamics of the complex fluid mixture in contact with it on one side and the solvent on the other side. Realistic membranes with realistic fluids are beyond the possibihties of theoretical treatment at this time. The only way of dealing with anything at all reahstic is by computer simulation. Even then one is restricted to rather simplified models for the membrane. 

A slightly more realistic concept is the Zel dovich-Von Neumann-Dohring (ZND) model. In this model, the fuel-air mixture does not react on shock compression beyond autoignition conditions before a certain induction period has elapsed (Figure 3.4). 

Figure 5.20. The flamelet model requires the existence of unmixed regions in the flow. This will occur only when the mixture-fraction PDF is non-zero at = 0 and = 1. Normally, this condition is only satisfied near inlet zones where micromixing is poor. Beyond these zones, the flamelets begin to interact through the boundary conditions, and the assumptions on which the flamelet model is based no longer apply.

Scamehorn et. al. (19) reported the adsorption isotherms for a binary mixture of anionic surfactants. A formal adsorption model developed for single surfactant systems ( ) was extended to this binary system and shown to accurately describe the mixed adsorption isotherms (19). That theoretically based model was very complex and is probably not feasible to extend beyond two surfactant components. 

Academic kinetic investigations are generally performed in stationary solutions, typically in a cuvette. Continuous reactors are much more common in industrial situations. Using fiber-optic probes, absorption spectroscopy is routinely performed in flow reactors. The flow of reagents into a reactor or of a reaction mixture out of a reactor is also quantitatively modeled by appropriately modifying the set of differential equations. Refer to the engineering literature for details that are beyond the scope of this chapter [40],... 

To move beyond the primitive model, we must include a molecular model of the solvent. A simple model of the solvent is the dipolar hard sphere model, Eq. (16). A mixture of dipolar and charged hard spheres has been called the civilized model of an electrolyte. This is, perhaps, an overstatement as dipolar hard spheres are only partially satisfactory as a model of most solvents, especially water still it is an improvement. 

Tier 4 includes all methods that go beyond CA or RA and attempt to provide some kind of mechanistic explanation for the mixture effects, including potential interactions between the mixture components. It requires detailed information on the toxicokinetic and toxicodynamic processes involved. The diversity of models that belong to this category is huge. Examples from human mixture assessment include the application of PBPK and BRN models. In ecological risk assessment, it may involve the consideration of multiple modes of action per mixture component as well as the assumed characteristics of sets of receptor species. Therefore, tier 4 methods only apply to problems that are defined in a very specific way (regarding site, species, compounds), and where an accurate result is preferred over a conservative one. 

Toxicity testing of mixtures should move beyond the standard tests for deviations from the default models of CA and RA, toward a more mechanistic understanding of the process involved in mixture toxicity. These studies should focus not only on the processes and effects involved in concurrent exposure to multiple substances (i.e., cocktails), but also on those involved in sequential exposure to multiple substances. 

The calculations reported in this paper and a related series of publications indicate that it is now quite feasible to obtain reasonably accurate results for phase equilibria in simple fluid mixtures directly from molecular simulation. What is the possible value of such results Clearly, because of the lack of accurate intermolecular potentials optimized for phase equilibrium calculations for most systems of practical interest, the immediate application of molecular simulation techniques as a replacement of the established modelling methods is not possible (or even desirable). For obtaining accurate results, the intermolecular potential parameters must be fitted to experimental results, in much the same way as parameters for equation-of-state or activity coefficient models. This conclusion is supported by other molecular-simulation based predictions of phase equilibria in similar systems (6). However, there is an important difference between the potential parameters in molecular simulation methods and fitted parameters of thermodynamic models. Molecular simulation calculations, such as the ones reported here, involve no approximations beyond those inherent in the potential models. The calculated behavior of a system with assumed intermolecular potentials is exact for any conditions of pressure, temperature or composition. Thus, if a good potential model for a component can be developed, it can be reliably used for predictions in the absence of experimental information. 

---