Layer flow free surface

A thorough description of the internal flow stmcture inside a swid atomizer requires information on velocity and pressure distributions. Unfortunately, this information is still not completely available as of this writing (1996). Useful iasights on the boundary layer flow through the swid chamber are available (9—11). Because of the existence of an air core, the flow stmcture iaside a swid atomizer is difficult to analyze because it iavolves the solution of a free-surface problem. If the location and surface pressure of the Hquid boundary are known, however, the equations of motion of the Hquid phase can be appHed to reveal the detailed distributions of the pressure and velocity. 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

On the other hand, potential measurements at the free surface of purified water have shown50 that the value for a flowing surface differs by about 0.3 V from that for a quiescent surface, as a result of adsorption of surface-active residual impurities in the solution (probably also coming from the gas phase). Since emersed electrodes drag off the surface layer of the solution as they come out of the liquid phase, the liquid layer attached to emersed solid surfaces might also be contaminated. 

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

Residual Current A small current that flows in the solution free of electroactive species (see curve 1 in Fig. 5.10). The residual current in DC polarography is mainly the charging current, which is for charging the double layer on the surface of the DME (Fig. 5.13).6)... 

Keulegan (K13) applied the semiempirical boundary-layer concepts of Prandtl and von K arm an to the case of turbulent flow in open channels, taking into account the effects of channel cross-sectional shape, roughness of the wetted walls, and the free surface. Most of the results are applicable mainly to deep rough channels and bear little relation to the flow of thin films. 

It seems possible, therefore, that in this initial region the upper part of the film, outside the growing boundary layer, is in potential-like flow, and that once the boundary layer reaches the free surface, its vorticity is sufficient to trigger the wave disturbances, which can then propagate or not, depending on whether the flow is unstable or stable (jVFr > 1 or N < 1). 

The solution of the hydrodynamic problem of boundary layer flow, excluding the effects of surface tension, requires simplification of the formulation this is achieved by introducing the flow function t /. Then the transition to a system of differential equations written for a new coordinate system (turn angle and flow function) can be made, and we can find the form of the free surface... 

The boundary layer equations for free convective flow will be deduced using essentially the same approach as was adopted in forced convective flow. Attention will, as discussed above, be restricted to the case of two-dimensional laminar boundary layer flow. Attention will initially be focused on a plane surface that is at an angle, 4>, the vertical as shown in Fig. 8.4. The x-axis is chosen to be parallel to this surface as shown in Fig. 8.4. 

The effect of these atomic layers of foreign atoms adhering to the surface is undoubtedly due to an alteration in the strength of the double layer at the surface of the metal. If positive ions of a metal identical with the underlying metal are deposited on its surface, and the deficiency in electrons made up by supply through a wire, which is essentially what occurs in electrodeposition of a metal on the same metal, the free electrons flow out to the new surface layers, and the strength of the double layer at the surface is not altered by the new surface layer. But if the metal deposited on the surface has a smaller affinity for electrons than the... 

There is a fundamental difference between external and internal flows. In external flow, considered in Chapter 7, the fluid has a free surface, and thus the boundary layer over the surface is free to grow indefinitely. In internal flow, however, the fluid is completely confined by the inner surfaces of the tube, and thus there is a limit on how much Ihe boundary layer can grow. 

Consider the flow of air over the free surface of a water body such as a lake under isothermal conditions. If the air is not saturated, the concentration of water vapor will vtsry from a maximum at the water surface where the air is always saturated to the free steam value far from the surface. In heat convection, we defined the region in which temperature gradients exist as the thermal boundary layer. Similarly, in mass convection, we define the region of the fluid in which concentration gradients exist as the conceniration boundary layer, as shown in Figure 14 -38. In external flow, the thickness of the concentration boundary layer S,. for a. species A at a. specified location on the surface is defined as the normal distance y from the surface at which... 

Fig. 5 Cascading flow occurs in large tumblers or during tumbling of fine, but freely flowing, grains. This snapshot shows a 1 m diameter transparent disk tumbler partially filled with colored 500 im irregular grains. The free surface is manifestly not flat, and the cascading layer is thin and nearly uniform with distance along the flowing surface.

The bubble wake released at the free surface, joined with the upflow, constitutes the downflow so that there is no downward return flow through the bubble layer. Under these circumstances, the mean bubble velocity b relative to the column wall is... 

Figure 16 Stripping voltammetry (first cycle) (0.5 M H2SO4, 100mVs ) of saturated CO layers on clean and ruthenium-modified Pt(l 11) and Pt(533) surfaces. The ruthenium has been deposited by dipping, and following rinsing CO was adsorbed and stripped in CO-free electrolyte (Pt(l 11) and Pt(533) ). The same surfaces were subsequently reduced in a flow of 10% H2 in Ar, CO adsorbed and stripping voltammetry carried out (Pt(lll) and Pt(533) °). The second cycle in each case corresponds to the CO-free surface. (From Ref. 98.) The working electrode area was about 20mm. ...

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