Length parameters

In addition, it is convenient to define the Bjerrum length parameter Lb = e z ) / f.eikTi (where is the universal dielectic constant) and the so-called quenching parameter, defined as g = EqTq/eiTi. 

It is also informative to express these results in dimensionless form, i.e., in terms of appropriate dimensionless groups. Because this is a noncircular conduit, the appropriate flow length parameter is the hydraulic diameter defined by Eq. (5.48) ... 

The results for spherical and cylindrical shapes are approximately in accordance with those shown in Figure 8.11, and in the limit of large, become the same, if the Thiele modulus is normalized in terms of a common effective diflusion-path-length parameter, Le, defined by... 

Two-way radios, as discussed here, are limited to a direct unit-to-unit radio communication, either via single unit-to-unit transmission and reception, or via multiple handheld units to a base station radio contact and distribution system. Radio frequency spectrum limitations apply to all handheld units, and are directed by the FCC. This also distinguishes a handheld unit from a base station or base station unit (such as those used by an amateur [ham] radio operator), which operates under different wave-length parameters. 

Equation 9 shows that the chemical capacitance in this case is similar to that derived previously in eq 6 for a thin film (Ci) however, in the co-limited situation the important length parameter is not L but rather a characteristic utilization length given by... 

The significance of this length parameter A can be understood by examining the predicted steady-state vacancy concentration profile in the porous electrode as shown in Figure 26a. At steady state, the model predicts that the mixed conductor will be reduced by an amount that decays exponentially with distance... 

The length parameter used in this correlation to represent the different types of packing may also contribute to the scatter. The use of the effective diameter may not be the best way to bring the data together, and several of the investigators found that they could correlate their own data quite well by using certain arbitrary functions of the void fraction, c. However, it was found by Bishchoff (B13) that the effective diameter was the most satisfactory size parameter when all of the data were considered. 

In the course of developing herbicides possessing N-phenyl tetrahydrophthalimide structure (20), Ohta et al. investigated structural requirements for the activity against sawa millet, Echinochloa utilis, of m- and p-substituted derivatives42 . As shown by Eq. 43, the steric dimensions expressed by the STERIMOL length parameter Lp and maximum width B of p-substituents play a decisive role in determining activity. 

Catalyst particle size also influences the deposition pattern as a consequence of the characteristic diffusion length parameter in the Thiele... 

Conditions for stable/unstable crack growth in a layered structure (a) a range of crack length parameters for stable crack growth in a laminate with a residual compressive stress in a top layer (b) stable/unstable crack growth in a laminate with a residual tensile stress in a top layer. 

The effects of miniaturization on the performance of an analytical separation system are often discussed in terms of a reduction of a characteristic length parameter (e.g., column diameter dc or particle diameter dp) and the associated consequences for lateral zone dispersion processes and their interplay with longitudinal (axial) zone dispersion. A rigid discussion of the physical-chemical basis is beyond the scope of this chapter. For a general account in terms of scaling laws and proportionality considerations, the reader is referred to the references [12,14]. A comprehensive and detailed description with emphasis on the underlying physical-chemical processes can be found in the book by Giddings [20]. 

Because the movement of the various zones is slow relative to the rates at which mass and heat are transported through the bed, a steady-state will eventually be established. The length parameter, n, is measured from the combustion interface and moves with velocity vc. 

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