Constitutive Relations for the Particle Phase Closure

In this section the constitutive equations for the collisional sources and fluxes are derived. 

By the assumption of particulate chaos, the collisional pair distribution function was expanded in Taylor series following a similar approach as for mono-particle mixtures (4.25)  

In most investigations, a Maxwellian single distribution function is used [49, 87, 97]  

Inserting = Cj into (4.301), and using the coUisional dynamics relationships the collisional pressure tensor can be determined. The particular coUisional dynamics relation needed can be deduced from the relationships discussed in Sect. 2.4.2. 

The center of mass velocity, G, is constant during a colUsion as can be seen from (2.538). From these relations the velocity relationship can be derived in a simUar manner as for dilute gas (2.133) and mono-particle systems (4.52). For binary particle mixtures the velocity relation becomes (Manger [105], p. 86 Lathouwers and Bellan 

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