Stagnation layer

Figure 5.32. Catalyst particles in a plug-flow reactor surrounded by a gas flowing through the catalyst bed. Note the stagnation layer of gas around the particle that may cause...

Figure 5.37. Arrhenius plot illustrating the effect on the apparent activation energy of pore diffusion and transport limitations through the stagnation layer surrounding a catalyst...

At catalytically active centers in the center of carrier particles, external mass transfer (film diffusion) and/or internal mass transfer (pore diffusion) can alter or even dominate the observed reaction rate. External mass transfer limitations occur if the rate of diffusive transport of relevant solutes through the stagnating layer at a macroscopic surface becomes rate-limiting. Internal mass transfer limitations in porous carriers indicate that transport of solutes from the surface of the particle towards the active site in the interior is the slowest step. 

If external diffusion dominates the overall rate, the process obviously reduces the observed enzyme activity. The flux N through the stagnating film at the surface can be expressed as in Eq. (5.54), where 8 signifies the thickness of the stagnating layer and ks is the mass transfer coefficient of the respective solute ks can be estimated by the simple relationship of Eq. (5.55). 

The primary cause of efficiency losses in an axial-flow turbine is the buildup of boundary layer on the blade and end walls. The losses associated with a boundary layer are viscous losses, mixing losses, and trailing edge losses. To calculate these losses, the growth of the boundary layer on a blade must be known so that the displacement thickness and momentum thickness can be computed. A typical distribution of the displacement and momentum thickness is shown in Figure 9-26. The profile loss from this type of bound-ary-layer build-up is due to a loss of stagnation pressure, which in turn is... 

Different processes like eddy turbulence, bottom current, stagnation of flows, and storm-water events can be simulated, using either laminar or turbulent flow model for simulation. All processes are displayed in real-time graphical mode (history, contour graph, surface, etc.) you can also record them to data files. Thanks to innovative sparse matrix technology, calculation process is fast and stable a large number of layers in vertical and horizontal directions can be used, as well as a small time step. You can hunt for these on the Web. 

Velocity measurements in flow regions where other devices fail to operate suitably—boundary layers, stagnating air zones—are typical applications. 

Hydrodynamic theory shows that the thickness, 8, of the boundary layer is not constant but increases with increasing distance y from the flow s stagnation point at the surface (Fig. 4.4) it also depends on the flow velocity ... 

Let CO be the angular velocity of rotation this is equal to Inf where/is the disk frequency or number of revolutions per second. The distance r of any point from the center of the disk is identical with the distance from the flow stagnation point. The hnear velocity of any point on the electrode is cor. We see when substituting these quantities into Eq. (4.34) that the effects of the changes in distance and hnear vefocity mutuaUy cancel, so that the resulting diffusion-layer thickness is independent of distance. 

We further consider that the boiling crisis occurs when the bubble-layer shielding effect reaches a maximum at bubble stagnation. A criterion for bubble-layer stagnation is suggested by Tong (1968b) to be... 

Weder s experiments were carried out with opposing body forces, and large current oscillations were found as long as the negative thermal densification was smaller than the diffusional densification. [Note that the Grashof numbers in Eq. (41) are based on absolute magnitudes of the density differences.] Local mass-transfer rates oscillated by 50%, and total currents by 4%. When the thermal densification dominated, the stagnation point moved to the other side of the cylinder, while the boundary layer, which separates in purely diffusional free convection, remained attached. 

With regard to the flow over an immersed body (e.g., a sphere), the boundary layer grows from the impact (stagnation) point along the front of... 

As mentioned, the type of concentration-depth profiles observed in oceans should also be observed in lakes. However, the vertical concentration differences in lakes are often not as pronounced as in the ocean. The reason for this is, that the water column in lakes is much shorter mixing and stagnation in lakes is much more dynamic than in the oceans. Due to the presence of high concentrations of different particles in lakes, the release of trace elements from biogenic particles may not be clearly observed, due to readsorption to other particles. This would mean that low concentrations are observed throughout the water column, but that concentration differences are small. Atmospheric inputs to the upper water layers may also make it more difficult to observe a depletion of certain elements in the epilimnion. 

Any consideration of mass transfer to or from drops must eventually refer to conditions in the layers (usually thin) of each phase adjacent to the interface. These boundary layers are envisioned as extending away from the interface to a location such that the velocity gradient normal to the general flow direction is substantially zero. In the model shown in Fig. 8, the continuous-phase equatorial boundary layer extends to infinity, but the drop-phase layer stops at the stagnation ring. At drop velocities well above the creeping flow region there is a thin laminar sublayer adjacent to the interface and a thicker turbulent boundary layer between this and the main body of the continuous phase. 

Two particularly useful equations can be derived by applying the thin concentration boundary layer approximation to steady-state transfer from an axisymmetric particle (L2). The particle and the appropriate boundary layer coordinates are sketched in Fig. 1.1. The x coordinate is parallel to the surface x == 0 at the front stagnation point), while the y coordinate is normal to the surface. The distance from the axis of symmetry to the surface is R. Equation (1-38), subject to the thin boundary layer approximation, then becomes... 

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