Interfacial Momentum Transfer Closures

Many authors of scientiflc literature have addressed the mathematical problem of averaging microscopic balance equations in order to derive macroscopic model formulations. However, the result is always a set of equations in which extra terms involving integrals over the microscopic domains remain. While various hypotheses 

This equation is referred to as the Basset [10]-Boussinesq [18]-Osceen [94] (BBO) equation. 

The linear split of the net drag force acting on the particle is not always valid as there can be non-linear interactions between the various forces. Such interactions are not well understood, but are typically small enough to be neglected for many conditions [79]. 

For a particle moving in a fluid in motion the momentum equation might be extended including the so-called pressure gradient force term  

For gas-rigid particle and gas-droplet flows, where the ratio of the continuous phase density to the dispersed particle material density is small ( 10 ), the RHS 

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The resulting decomposition of the interfacial momentum transfer term is equivalent to the conventional closure outlined in sect 3.4.3, and adopted by several investigations on gas solids flow [64, 65, 39, 108]. Nevertheless, as for the conventional formulation, several simplifying assumptions are invoked in... 

In practice, however, it is difficult to parameterize the interfacial area averaged velocity so in the momentum equation it s often set equal to the bulk velocity and in the momentum jump condition the mass transfer terms are simply neglected enabling a closure relation for the interfacial drag terms which are in agreement with Newton s 3. law. Hence,... 

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