Laminar regions dynamic model

It is easy to extend this model so as to create a physical condition closer to BQD physics. This extended dynamic model has two rather than only one laminar spatial region, divided by a border [100]. The particle in the left and right spatial laminar regions move toward the right and the left, respectively. Thus in both cases they move toward the border. When the particle reaches the border, it is injected back either to the right or to the left, with uniform probability. Let us write the corresponding density equation in the generic form... 

The effect of drag reducers on the turbulence is modelled with computational fluid dynamics (CFD) by using a two-layer turbulence model. In the laminar buffer layer, the one-equation model of Hassid and Poreh (1975) is used to describe the enhanced dissipation of turbulence caused by drag reducers. The standard k-e model is applied in the fully turbulent regions. The flow conditions necessary to elongate the polymer, the drag reduction efficiency of polymers of different apparent molar masses and their degradation kinetics have been measured. This data has been used in the model development. 

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