EPR in the form of a multispeed droplet layer

Engineers would still unlikely be satisfied with many assumptions of the above models of a droplet layer as it is much more complex in reality. However, no results can be obtained without appropriate assumptions. 

A shortcoming of the models for droplet layers developed so far is the assumption that the droplets move vertically in only one direction, from the fountain top z = h 

Let the droplets be of the same size. The difficulty of the Eulerian simulation is that one needs associate two droplet speeds to the same space point, one for the droplets rising up and another for the droplets falling down. This ambiguity could be overcome if, again, one introduces two continuous media for both kinds of droplets. Two methodological multispeed droplet EPR models have been suggested here. 

Droplets of each kind have the same concentration n(z) on each level and contribute to the smeared force acting onto the air flow. These three continuous media in the area 0 z h are governed by the equations 

Consider a methodological Id-problem of the flow in a duct to ensure that this problem is well-posed. Assume that such a two-speed droplet EPR has been symmetrically placed near both walls of the infinite duct. The steady-state pressure-driven flow in such a duct is governed by the following boundary-value problem for the internal flow  

---