Granular Transport Coefficient, Source and Flux Closures

5 Granular Transport Coefficient, Source and Flux Closures 

The kinetic pressure tensor represents the momentum transfer due to the free translational motions of the solid particles between particle collisions. The pressure tensor closure is derived by use of the same modeling concepts and approximate solution method as employed in the kinetic theory of dilute gases. The kinetic pressure tensor 

By use of the Chapman-Enskog approximate solution method [25], the granular fluid kinetic pressure tensor can thus be approximated as [49]  

This pressure tensor closure (4.106) was derived by Gidaspow [49] in analogy with the Enskog dense gas theory presented by Chapman and Cowling [25], Chap. 16. That is, with the restitution coefficient, e, equal to one, (4.108) corresponds to the Chapman and CowUng s [25] Eq. (16.34-2), where the x factor used for dense gases is substituted by 2 to(a /)(l + c) for solid particles, and bp = Aad. 

The limiting viscosity for the dilute regime can be approximated from the dilute mono atomic gas relation (2.620) by converting the molecular temperature (2.200) to the granular temperature (4.70). The result is [49]  

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