Enskogs Macroscopic Equations of Change

Analogous to the equation of change of mean molecular properties for dilute gas that was examined in Sect. 2.6, similar macroscopic conservation equations may be derived for dense gas from the Enskog equation. Multiplying the Enskog s equation (2.663) with the summation invariant property, //, and integrating over c, the result 

The last part of J2iff) gives a zero contribution to the integral h due to the same reason that lo vanishes. The remainder two parts can after several manipulations be approximated as [39]  

A comparison of the resulting fluxes Ii,i = 0,1,2 with (2.674) reveals that  

This equation is a generalization of the macroscopic moment equation for dilute gas to dense gas of identical, rigid spherical molecules. 

If we choose as the summational invariants m, mC and mC, we obtain the Cauchy set of conservation equations named the continuity (2.217), the equation of motion (2.223), and the equation of energy (2.230). The only difference in the final result is that the pressure tensor, p, and the heat flux vector, q, are made up of two parts (i.e., a kinetic and a collisional contribution)  

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