Flow regime transition

A summary of the nine batch reactor emulsion polymerizations and fifteen tubular reactor emulsion polymerizations are presented in Tables III IV. Also, many tubular reactor pressure drop measurements were performed at different Reynolds numbers using distilled water to determined the laminar-turbulent transitional flow regime. 

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. 

Fain. D.E., and W.K. Brown, 1974, U.S. Atomic Energy Commission Report "Neon isotope separation by gaseous diffusion transport in the transition flow regime with regular geometries."... 

The continuum flow assumption will only be valid when Kn < 10. As Kn increases, the flow enters the slip flow regime (10 < Kn < 10 ), transition flow regime (10 < Kn < 10), and eventually the free-moleeular flow regime (Kn > 10). These four regimes are illustrated in Figure 1. 

As the flow enters the transition flow regime and eontinues into the free-molecular flow regime, the Knudsen number becomes significant enough that the molecular approach has to be utilized. Thus, the Boltzmann equation... 

Prediction of the heat-transfer coefficient in the transition flow regime is uncertain due to the strong effects of entrance conditions and instability of the flow pattern. Gnielinski [18] modified the Petukhov-Popov equation to accommodate the transition region and extend it into the turbulent flow range ... 

Figure 5. Normalized flowrate variation in the slip and early transitional flow regimes for various aspect ratio (AR) duct flows. Symbols show the linearized Boltzmann solutions. Comparisons with the proposed model are also presented by lines.

We developed a unified flow model that can accurately predict the volumetric flowrate, velocity profile, and pressure distribution in the entire Knudsen regime for rectangular ducts. The new model is based on the hypothesis that the velocity distribution remains parabolic in the transition flow regime, which is supported by the asymptotic analysis of the Burnett equations [1]. The general velocity slip boundary condition and the rarefaction correction factor are the two primary components of this unified model. 

The gas-liquid mass transfer coefficient and gas holdup tend to decrease with increasing BC diameter in the homogeneous and transition flow regime (Zahradnik et al., 1997) up to a critical value (Deckwer, 1992 Shah et al., 1982 Zahradnik et al., 1997), which is usually cited to be = 0.15m (Kantarci et al., 2005) ... 

Superficial gas velocity at which flow transitions out of the homogeneous flow regime into the transition flow regime... 

In the transition regime, the rarefaction effects dominate and the intermolecular collisions need to be taken into account. For the free-molecular flow, intermolecular collisions can be considered negligible when compared to the probability of the molecule colliding with the wall surface. As the flow enters the transition flow regime and continues into the free-molecular flow regime, the Kn becomes significant enough that the molecular approach has to be utilized. Thus, the Boltzmann equation... 

---