Potential flow regime

This solution simply implies that the velocity everywhere in the outer region is just the undisturbed free-stream velocity. The flat plate is idealized mathematically as having zero thickness, and, because the no-slip condition does not apply to the potential-flow regime, the fluid moves past the plate with no disturbance whatsoever. 

When St > 1, the inertia deposition is obviously possible, yet calculations have shown that it can also take place at St < 1 as long as St is not too small. This conclusion becomes apparent if it is considered that in a layer of thickness a the particle moves toward the surface not only due to inertia but also together with the liquid. The motion component of the particle normal to the bubble surface becomes zero at the surface of the bubble. Inertia deposition proves to be impossible if St is smaller than some critical value St . In the case of a potential flow regime and negligible particle size. Levin obtained (1961)... 

The fluid pressure distribution at the gas-liquid interface in the potential flow regime is... 

This motion of the bubble induces axisymmetric two-dimensional flow in the liquid phase. In the potential flow regime, one calculates the scalar velocity potential tb(r, 0) via Laplace s equation. The general solution in spherical coordinates is... 

In the potential flow regime, where i> = sin 6> and Re is much larger, but the flow remains laminar, the dimensionless mass transfer boundary layer thickness is... 

Corrections for cnrvatnre are most important at i/maxmmm- In the potential flow regime,... 

The latter approach is adopted because dynamic pressure gradients are calculated in the potential flow regime, outside the momentum boundary layer and far from the solid-liquid interface, where fi 0 and viscous forces are negligible. Then, 3P /3x is imposed across the boundary layer. This is standard practice for momentum boundary layer problems. Hence, if v represents the dimensionless velocity vector in the potential flow regime, then the steady-state dimensionless equation of motion is... 

Recently, hydrodynamic aspects of multiphase applications have been studied in detail for the cocurrent and countercurrent flow regimes. Useful correlations were determined and it was found that foams combine high rates and low pressure drop, proving their high potential in multiphase applications [9, 107, 108]. 

Confined flows typically exhibit laminar-flow regimes, i.e. rely on a diffusion mixing mechanism, and consequently are only slowly mixed when the diffusion distance is set too large. For this reason, in view of the potential of microfabrication, many authors pointed to the enhancement of mass transfer that can be achieved on further decreasing the diffusional length scales. By simple correlations based on Fick s law, it is evident that short liquid mixing times in the order of milliseconds should result on decreasing the diffusion distance to a few micrometers. 

Systems that are exposed to excessive turbulence of anaerobic wastewater and a potential increased release of hydrogen sulfide. Systems with a risk for increased turbulence are inlet structures, drops, cascades, sharp bends and inverted siphons. As an example, changes in the flow regime from a pressure pipe into a gravity sewer may give rise to the release of hydrogen sulfide. Corrosion of the sewer pipe wall is often pronounced near the daily water... 

---