Hydrodynamic regimes

When two metallic surfaces are lubricated in a hydrodynamic regime, the oil film is stable and problems of wear are not very important. In severe service, the film can be destroyed from then on the metallic parts rubbing on each other can cause first metal loss and then even the seizing of the parts by welding. 

In this work, we determine constraints on the dimensionless parameters of the system (dimensionless electrode widths, gap size and Peclet number), first qualitatively and then quantitatively, which ensure that the proposed flow reconstmction approach is sufficiently sensitive to the shape of the flow profile. The results can be readily applied for identification of hydrodynamic regimes or electrode geometries that provide best performance of our flow reconstmction method. 

Table 1.3 Comparison of miscellaneous dimensionless groups characterizing different hydrodynamic regimes in macroscopic vessels and micro reactors.

Figure 19. Double-phase-separated morphology reported from the 2D simulations of the phase separation in the hydrodynamic regime [158]. This figure has been kindly provided by Dr. T. Araki. 

If instead of semi-infinite diffusion, some distance (5m acts as an effective diffusion layer thickness (Nernst layer approximation), then a modified expression of equation (63) applies where ro is substituted by 1 / (1 /Vo + 1 /<5m ) (see equation (38) above). For some hydrodynamic regimes, which for simplicity, are not dealt with here, the diffusion coefficient might need to be powered to some exponent [57,58],... 

In the preceding section, it was demonstrated that the walls of the system can be neglected when the system is in the hydrodynamic regime, i.e., when D is sufficiently large. In this situation, it is often desirable to treat the system as a bulk fluid and apply shear directly without any boundary effects. In this section, we describe two different methods with which to shear bulk systems. 

Rotational fluid velocities are calculated since horizontal (rotational) flow prevails in the hydrodynamic regime within the dissolution vessels. Thus, the overall hydrodynamics and hence dissolution is dominated by the substantially higher rotational (tangential) fluid velocities. 

Strong influence of hydrodynamic regimes on reactor performance, making the reactor type very sensitive to flow-rates. 

Flow rate Catalyst activity Reaction kinetics Its importance depends on the hydrodynamic regime Dependent Dependent Depend strongly on the gas velocity below 0.1 m/s... 

Heat removal is accomplished by internal cooling coils or wall jacket exchangers. Hydrodynamic regimes are complex, because of complicated flow patterns, prone to quick and dramatic changes. Usually a few overall parameters are considered, such as gas residence time and holdup, solid suspension, energy input, volumetric mass transfer coefficient (sec 3.2. 

When 02 since the first term is proportional to oJ2 and the second one to 02, the diffusion is primarily given by the second term. Thus the hydrodynamic regime can be recovered. 

Zipfel et al. [55] observed a vesicle radius of 3 pm, which is clearly compatible with our calculation. We note that this estimate assumes that the experiments are done in the hydrodynamic regime. 

Lesser instability problems, despite the fact the hydrodynamic regime is greatly affected by the contactor dimen-... 

Figure 1.142 A kind of flow-pattern map for zig-zag micro mixers of various dimensions correlating their Reynolds numbers with their hydrodynamic regimes as a function of their ratio of bend length to hydraulic diameter [151]...

Now we consider the hydrodynamic regime to Fermi-surface. In this case the imaginary part of M is important, and we obtain from (42) and (44)... 

Note that both a small disc in the large volume of a liquid and a large disc in the small volume of a liquid will hardly produce reliable data on the dissolution kinetics of the solid in the liquid. In the former case, the small disc will not ensure suffucient convective agitation of the liquid phase. In the latter, the treshould of turbulency may happen to be exceeded. Turbulence is known to occur at Reynolds numbers in excess of 105. The Reynolds number, Re = wr2/v, r being the disc radius, is a dimensionless parameter characterising the hydrodynamic regime of flow of liquids.299 300 Reproducible results are readily obtained if the flow is laminar. 

Vibration of an electrode is an experimentally simple way of producing hydrodynamic modulation. Whilst the advantage is experimental simplicity, the disadvantage is that the hydrodynamic regime is difficult to describe accurately (see Section 10.3.6.3). 

Fig. 10. Qualitative diagram of stirrer zone hydrodynamic regimes for a Rushton turbine. (Adapted from Bruijn et al., 1974.)...

Literature Characterization of Three Fundamental Hydrodynamic Regimes ... 

Fio. li. Vessel hydrodynamic regimes and the evolution of dispersion as stirrer speed increases at a constant gas feed rate. 

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