Collision hydrodynamic regime

The reader may be surprised not to And a Reynolds number defined speciflcally for the disperse phase. This is because the disperse-phase viscosity is well defined only for Knp 1 (i.e. the collision-dominated or hydrodynamic regime). In this limit, Vp oc oc Knp/Map so that the disperse-phase Reynolds number would be proportional to Map/Krip when Map < 1. However, in many gas-particle flows the disperse-phase Knudsen number will not be small, even for ap 0.1, because the granular temperature (and hence the collision frequency) will be strongly reduced by drag and inelastic collisions. In comparison, molecular gases at standard temperature and pressure have KUp 1 even though the volume fraction occupied by the molecules is on the order of 0.001. This fact can be... 

The characteristics of mutual approach of drops, and consequently, of their collisions, depend on the hydrodynamic regime of emulsion motion. Consider first the coalescence of drops settling under gravity in a quiescent liquid. Such kind of coalescence is called the gravitational coalescence. 

Where u < 1 (u = 1 for the Einstein diffusion regime). At very short times (i < 1 ps), the MSD may be quadratic iv n time ( = 2) which is characteristic of free flight as may occur in a pore or solvent cage prior to collision with the pore or cage wall. The result of anomalous diffusion, which may or m not occur in intermediate time scales, is to create a smaller slope at short times, resulting in a larger value for the diffusion coefficient. At sufficiently long times (the hydrodynamic limit), a transition from anomalous to Einstein diffusion ( = 1) may be observed [71]. 

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