Molecular mixing models desirable properties

The reasoning behind each of these properties will be illustrated in the next section. We will then look at three simple molecular mixing models (namely, the CD, the IEM, and the FP models) and discuss why each is not completely satisfactory. For convenience, the list of constraints and desirable properties is summarized in Table 6.1. 

Although much effort has gone into searching for molecular mixing models that improve upon the existing models,54 no model completely satisfies all of the desirable properties... 

Table 6.1. Constraints and desirable properties of molecular mixing models. 

Like the IEM model, the FP model weakly satisfies property (iv). Likewise, property (v) can be built into the model for the joint scalar dissipation rates (Fox 1999), and the Sc dependence in property (vi) is included explicitly in the FP model. Thus, of the three molecular mixing models discussed so far, the FP model exhibits the greatest number of desirable properties provided suitable functional forms can be found for (e 0). 

Owing to the sensitivity of the chemical source term to the shape of the composition PDF, the application of the second approach to model molecular mixing models in Section 6.6, a successful model for desirable properties. In addition, the Lagrangian correlation functions for each pair of scalars (( (fO fe) ) should agree with available DNS data.130 Some of these requirements (e.g., desirable property (ii)) require models that control the shape of /, and for these reasons the development of stochastic differential equations for micromixing is particularly difficult. 

As PILs can be mixed with molecular solvents, this provides new opportunities to study the conductivity of electrolyte solutions in salt-rich regions up to 15 mol. L Numerous studies concern the specific conductivity and viscosities of pure PILs [70-73], since it is desirable and of great importance to understand and predict the transport properties of PIL-i-molecular solvent solutions using classical and theoretical models. 

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