Overlap wall region

Intuitively one could imagine that the boundary layer as a whole can be characterized in terms of the boundary layer thickness and related dimensionless groups. However, experimental data reveals that the laminar shear is dominant near the wall (i.e., in the inner wall layer), and turbulent shear dominates in the outer wall layer. There is also an intermediate region, called the overlap wall region, where both laminar and turbulent shear are important. 

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

As we have reviewed here, the linear region is not fully repulsive, and transitions of the ground-state, linear conformer access vibrationally excited intermolecular levels that are delocalized in the angular coordinate. As depicted in Fig. 1, however, the internuclear distance is significantly longer in the excited state at the linear geometry. Consequently, there is favorable Franck-Condon overlap of the linear conformer with the inner-repulsive wall of the excited-state potential. It is therefore possible for the linear Rg XY conformers to be promoted to the continuum of states just above each Rg - - XY B,v ) dissociation limit. 

Because of finite radius a, the centers of the spheres can get no closer than distance a from the cylinder wall. Thus the sphere centers are excluded from an annular volume extending from radial position dc - a to dJ2 in the cylinder. If the component species were point objects rather than bulky spheres, they could freely occupy the entire pore volume and (in the absence of attractive or repulsive forces near the wall) K would equal unity. Spheres, by contrast, are excluded from the annular region that point objects readily occupy. Excluded sphere positions are shown as open dashed circles in Figure 2.2. Since these excluded positions are forbidden due to overlap with the wall, the number of allowed spheres is reduced in number to the few spheres (shaded circles) falling in the accessible volume closer to the cylinder axis. 

With a simplifying assumption that local adsorption equilibrium is instantaneously attained between gas and particles, the mass-transfer process is expressed by Fig. 58 for the cloud-overlap region. Here the influence of bubble wall curvature is neglected, since the region is very thin. When no catalyst is suspended in the bubble void, the equations of continuity for the reactant gas are as follows (M30) ... 

In practical applications, this technique is applied by performing a meta-d3mamics reconstruction for each local minimum in the free energy surface. The walkers are forced to remain in their minimum by reflecting walls located just behind the saddle point region. In this manner the transition regions are explored in two independent metad3mamics, and the overlap is sufficient to make the solution to (36) reliable. 

The constant A cannot be determined from the boundary condition at the wall but must be obtained from the matching requirement that (4-27) reduce to the form of the core solution (4-17) in the region of overlap between the boundary layer and the interior region. Now, any arbitrarily large, but finite, value of Y will fall within the boundary-layer domain on the other hand, the corresponding value of y can be made arbitrarily small in the asymptotic limit R0J - oo. Thus the condition of matching is often expressed in the form... 

The difference in scaling between the central core of the thin cavity (6-122) and the vicinity of the end walls (6-123) means that the asymptotic solution for s <dimensionless equations and a different form for the asymptotic expansion for e <[Pg.387]

Spectroscopically determined potential energy curves for bound electronic states may be extrapolated into the repulsive region by an expression V2 (R) — aR n+b where n = 12 is typically chosen. (A repulsive wall with n > 12 would cause the overlap factor to be even smaller than for n = 12 because the amplitude... 

The comer region, where boundary layers from adjacent walls overlap, must be acceptably small. This requirement establishes an upper bound on... 

Immediately outside the comer region where mass transfer boundary layers from adjacent walls do not overlap or influence each other, the molar density of reactant A at the catalytic surface must be acceptably close to Ca. inlet- This requirement establishes an upper bound on Zsiart-... 

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