Coexistent-continua model

In order to show that the model of independent, coexistent continua represents correctly a real mixture of gases composed of different chemical species, we must compare the results obtained from this model with those of the kinetic theory of nonuniform gas mixtures (see Appendix D). Quantities such as the density p, the mass-weighted average velocity v j, and the body force fj have obviously analogous meanings in both the kinetic theory and the coexistent-continua model. On the other hand, the precise kinetic-theory meaning of terms such as the stress tensor, the absolute internal energy per unit mass and the heat-flux vector qf is not immediately apparent. In view of the known success of continuum theory for one-com-... 

As far as qualitative aspects of the ion-size dependence of the friction coefficients are concerned, which has a minimum with increasing ionic radius, both models (the solventberg and dielectric friction models) explain the experimental observations to a certain extent. Then one might ask which model of the two is more faithful to the real physics of the ionic friction and/or how do the two effects interplay if both are coexisting For instance, use of the same parameter for the effective ionic radius will not be justified since increase in the effective radius should give rise to increase in the Stokes friction but decrease in the dielectric friction. The question should be answered by microscopic theory, not by treatment based on the continuum model. 

The objective is to derive the conservation laws for multicomponent, reacting gas mixtures. To this end we invent a physical model consistent with continuum theory. The model involves the idea of a multicomponent continuum composed of coexistent continua, each obeying the laws of dynamics and thermodynamics, a notion which was first introduced by Stefan in 1871, For an N-component gas mixture we presume the existence of N distinct continua within any arbitrary volume, continuum K corresponding to the chemical species K. The terms continuum K, species K and component... 

We arrive at the model of simultaneous coexistent continua as the logical transcription to continuum theory of the fact that the entire volume is accessible to all of the dilferent molecules in a gas mixture. 

The simplest way to conduct the simulations of mesoscopic phenomena, consists in down-scaling of the continuum approach or upscaling (or coarse graining) the particle model. The limitation of the first approach is determined by the granular properties of matter, which are revealed for very small system. The behavior of granular fluid is different from that in the bulk. For example, very small systems may exhibit solid-liquid coexistence over a range of temperature different than that for large systems [31]. However, new approaches such as ... 

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