Taylor ratio

Catalytic experience tells us that frequently only a small fraction of the sites at the surface of the metal participate in the reaction. Recently, Krai measured the metal surface area of palladium catalysts supported on carbon, their specific activity for various hydrogenation reactions, and their poisoning by thiophene (44). By combining the classic technique of poisoning with the measurement of metal surface area. Krai was able to show that the Taylor ratio, i.e., the fraction of active sites in each particular reaction, changed from unity to about 10 . With a Taylor ratio of unity, the reaction would be called facile. Otherwise, we deal with a structure-sensitive or demanding reaction. 

The number of active centres is therefore generally less than the total number of surface atoms,the ratio of the two being termed the Taylor fraction Fj (or Taylor ratio). A.A. Balandin attempted to make Taylor s ideas more precise by proposing a Multiplet Hypothesis by which each type of reaction required a multiplet of several atoms to be an active centre. So for example to chemisorb a benzene molecule either for its hydrogenation or in its formation by dehydrogenation, a hexagonal multiplet with one central atom as found in the fcc(l 11) plane would be needed. If the number of atoms composing the multiplet (or ensemble as it was called by Kobozev ) is the Balandin number Nb, then... 

Taylor (1987) reports some experiments performed in a horizontal duct (2 m long, 0.05 X 0.05 m cross section). Obstacles were placed in the channel. The top of the duct could be covered by perforated plates with a minimum of 6% open area. Terminal flame speeds of 80 m/s were reported for propane in a channel with a blockage ratio of 50% and a 12% open roof. 

Concerning a liquid droplet deformation and drop breakup in a two-phase model flow, in particular the Newtonian drop development in Newtonian median, results of most investigations [16,21,22] may be generalized in a plot of the Weber number W,. against the vi.scos-ity ratio 8 (Fig. 9). For a simple shear flow (rotational shear flow), a U-shaped curve with a minimum corresponding to 6 = 1 is found, and for an uniaxial exten-tional flow (irrotational shear flow), a slightly decreased curve below the U-shaped curve appears. In the following text, the U-shaped curve will be called the Taylor-limit [16]. 

According to the criteria, the dispersed phase embedded in the matrix of sample 1 must have been deformed to a maximum aspect ratio and just began or have begun to break up. By observing the relative position of the experimental data to the critical curve, the deformational behavior of the other samples can be easily evaluated. Concerning the fibrillation behavior of the PC-TLCP composite studied, the Taylor-Cox criteria seems to be valid. 

To a good approximation this structure can be regarded as f.c.c. based with (002) planes composed alternatively of Tl and Al the cubic crystallographic notation Is. therefore, commonly used. If we denote as c and a the lattice parameters In the [001) and 11001/1010) directions, respectively, the c/a ratio is 1.02 at the stoichiometric composition and Increases to 1.03 at Al-rich compositions (Duwez and Taylor 1952 Huang, et al. 1987). 

Figure 10-74. Ratio of heat transfer to pressure loss for 3 shell-side configurations—RODbaffles . (Used by permission Small, W. M., and Young, R. K. Heat Transfer Engineering, V. 2, 1979. Taylor and Francis, Inc., Philadelphia, PA. All rights reserved.)...

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Aleifres, P.G., Y. Hardalupas, A.M.K.P. Taylor, K. Ishii, and Y. Urata, Flame chemiluminescence studies of cyclic combustion variations and air-to-fuel ratio of the reacting mixture in a lean-bum stratified-charge spark-ignition engine. Combustion and Flame, 136 72-90, 2004. 

Furthermore, in Searle cylinder systems, secondary currents occur above certain Taylor numbers, resulting in greater power input than that resulting with Eq. (12). Comparison with experimentally determined Ne numbers shows that the laminar flow range in internally driven cylindrical stirrers in the range of radius ratios r2/ri= 1.05-2 is only valid for Taylor numbers Takrit= <400-200 [38]. Above Ta >Takritsecondary currents in the... 

In the limit as 2 —> oo, this ratio becomes p/k, which approaches zero for finite p. Thus, the series converges for all finite values of p. To test the behavior of the power series as p oo, we consider the Taylor series expansion of... 

Quetel CR, Prohaska T, Hamester M, Kerl W, Taylor PDP (2000b) Examination of the performance exhibited by a single detector double focusing magnetic sector ICP-MS instrument for uranium isotope abundance ratio measurements over almost three orders of magnitude and down to pg g-1 concentration levels. J Anal At Spectrom 15 353-358... 

The simplest method for propagation of the analytical errors into the °Th/U age equation (Eqn. 1) involves linear expansion (Albarede 1995, ch. 4.3) of the effect on the calculated age of very small perturbations of the measured ratios (in effect, a Taylor expansion using only the first term). As long as the effect of the errors of the measured ratios on the age is not a large fraction of the age itself, this method will yield acceptably accurate age-errors with minimal effort. 

To handle the time delay, we do not simply expand the exponential function as a Taylor series. We use the so-called Pade approximation, which puts the function as a ratio of two polynomials. The simplest is the first order (1/1) Pade approximation ... 

Probably the first instrument designed for reflectance studies was that described by Nutting [8], and improved by Taylor [9]. Since that time, a large number of instruments have been proposed, and numerous modifications suggested to continually improve signal-to-noise ratios [1,2]. 

In principle, the same rules hold true when zeolitic alkylation catalysts are used. A detailed study of the influence of PO and OSV on the performance of zeolite H-BEA in a backmix reactor was reported by de Jong et al. (80). The authors developed a simple model of the kinetics, which predicted catalyst lifetimes as a function of P/O and OSV. Catalyst lifetime (which is equivalent to the catalyst productivity, the reciprocal of acid consumption) increased with increasing P/O ratio and decreasing OSV. Furthermore, the authors persuasively demonstrated the superiority of a backmix reactor over a plug flow reactor. Qualitatively similar results were obtained by Taylor and Sherwood (222) employing a USY zeolite catalyst in a backmix reactor. The authors stressed the detrimental effect of unreacted alkene on the catalyst lifetime and product quality. Feller et al. (89) tested LaX zeolites in a backmix reactor and found the catalyst productivity to be nearly independent of the OSV within the examined OSV range. At higher values of OSV, the catalyst life was shorter, but in this shorter time the same total amount of product was produced. The P/O ratio had only a moderate influence on the catalyst performance. 

Likewise, the ratio of the transverse Taylor microscale and the turbulence integral scale can be expressed as... 

---