Stokes number flow regimes

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

In the first two cases the Navier-Stokes equation can be applied, in the second case with modified boundary conditions. The computationally most difficult case is the transition flow regime, which, however, might be encountered in micro-reactor systems. Clearly, the defined ranges of Knudsen numbers are not rigid rather they vary from case to case. However, the numbers given above are guidelines applicable to many situations encoimtered in practice. 

Similar to the Qian and Ban s mixer in Ref. [20], this mixer also utilizes electroosmotic flow, which operates in the Stokes flow regime. As a result, the streamlines are rather insensitive to the variations in Re molds number. 

Separate from particle/droplet size and the Knudsen number, there is another reason that aerosol sedimentation does not always follow Stokes law. As the flow regime goes from laminar flow (viscous dominated Reynolds number, Af u < 1) to turbulent flow (inertia dominated Reynolds number, Nr > 1000), things change (see Section 6.1 and Equation 6.6 for more on the Reynolds number). 

It can be seen from Fig. 1 that gas flows in micron size channels are typically relevant to the slip flow regime, at any rate for usual pressure and temperature conditions. For lower sizes, i.e., for Knudsen numbers higher than 10 , the slip flow regime could remain valid, provided that classical velocity slip and temperature jump boundary conditions are modified (taking into account higher-order terms as explained below) and/or that Navier—Stokes equations are extended to more general sets of conservation equatiOTis, such as the quasi-gasodynamic (QGD), the quasi-hydrodynamic (QHD), or the Burnett equatiOTis [3]. 

Another way of identifying the flow regime is to substitute the V fiom Stokes Law into the Reynolds number and see that... 

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