Schmidt relation

With 7ti = 7t2 = 1/2 we observe that relation (4.123) has the same form as the relation used for the numerical solving of the unsteady state diffusion of one species or the famous Schmidt relation. The model described by Eq. (4.123) is known as the random walk with unitary time evolution. 

The constant depends on the hydraulic diameter of the static mixer. The mass-transfer coefficient expressed as a Sherwood number Sh = df /D is related to the pipe Reynolds number Re = D vp/p and Schmidt number Sc = p/pD by Sh = 0.0062Re Sc R. ... 

C.-M. Brauner and C. Schmidt-Laine, Mathematical Modeling in Combustion and Related Topics, Martinus Hijhoff Pubhshers, Dordrecht, The Netherlands, 1988. 

The Einstein relation can be rearranged to the following equation for relating Schmidt numbers at two temperatures ... 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

By contrast, the hqnid-phase Schmidt unmbers range from about 10" to lO and depeua strongly on the temperature. The effect of temperature on the liquid-phase mass-transfer coefficient is related primarily to changes in the hquid viscosity with temperature, and this derives primarily from the strong dependency of the hqnid-phase Schmidt number upon viscosity. 

The comparison of the magnitude of the two resistances clearly indicates whether tire metal or the slag mass transfer is rate-determining. A value for the ratio of the boundary layer thicknesses can be obtained from the Sherwood number, which is related to the Reynolds number and the Schmidt number, defined by... 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

For mass transfer, which is considered in more detail in Chapter 10, an analogous relation (equation 10.233) applies, with the Sherwood number replacing the Nusselt number and the Schmidt number replacing the Prandtl number. 

For mass transfer to a surface, a similar relation to equation 12.117 can be derived for equimolecular counterdiffusion except that the Prandtl number is replaced by the Schmidt number. It follows that ... 

In Chapter 12 it is shown that when the Schmidt and Prandtl numbers for a mixture of gas and vapour are approximately equal to unity, the Lewis relation applies, or ... 

Schmidt M, P Roger, F Lingens (1991) Microbial metabolism of quinoline and related compounds XL Degradation of quinoline-4-carboxylic acid by Microbacterium sp. Hj, Agrobacterium sp. IB and Pintelo-bacter simplex 4B anf 5B. Biol Chem Hoppe-Seyler 370 1015-1020. 

Sakaki S (2005) Theoretical Studies of C-H s-Bond Activation and Related by Transition-Metal Complexes. 12 31-78 Satoh T, see Miura M (2005) 14 1-20 Satoh T, see Miura M (2005) 14 55-84 Savoia D (2005) Progress in the Asymmetric Synthesis of 1,2-Diamines from Azomethine Compounds. 15 1-58 Schmalz HG, Gotov B, Bbttcher A (2004) Natural Product Synthesis. 7 157-180 Schmidt B, Hermanns J (2004) Olefin Metathesis Directed to Organic Synthesis Principles and Applications. 13 223-267... 

Carboxylic acids and esters can also be converted to amines with loss of the carbonyl group by reaction with hydrazoic acid, HN3, which is known as the Schmidt reaction,278 The mechanism is related to that of the Curtius reaction. An azido intermediate is generated by addition of hydrazoic acid to the carbonyl group. The migrating group retains its stereochemical configuration. 

Schmidt, H.j von Stetten, 0. Kellermann, G.j Patzelt, H.j Naegele, W. In Radioimmunoassay and Related Procedures in Medi— cine 1982, International Atomic Energy Agency, Ed.j Vienna, 1982,... 

For turbulent flow, we shall use the Chilton-Colburn analogy [12] to derive an expression for mass transfer to the spherical surface. This analogy is based on an investigation of heat and mass transfer to a flat plate situated in a uniform flow stream. At high Schmidt numbers, the local mass transfer rate is related to the local wall shear stress by... 

Tornhamre S, Schmidt TJ, Nasman-Glaser B, Ericsson I, Ake L. Inhibitory effects of helenalin and related compounds on 5-lipoxygenase and leukotriene C4 synthase in human blood cells. Biochem Pharmacol 2001 62 903-911. 

Schmidt, M Valatx, J.-L., Sakai, K., Fort, P., Jouvet, M. (2000). Role of the lateral preoptic area in sleep-related erectal mechanisms and sleep generation in the rat. J. Neurosci. 20, 6640-7. 

The temperature difference is thus directly proportional to the heat of reaction per mole of diffusing species and to the difference in concentration between the bulk fluid and the exterior surface of the solid. If we recognize that jD jH from the Chilton-Colburn relation, and that the ratio of Prandtl and Schmidt numbers is close to unity for many simple gas mixtures, the previous relation may be approximated as... 

Bott, G. Schmidt, M. Rommel, T. O., and Lingens, F., Microbial Metabolism of Quinoline and Related Compounds. V. Degradation of lh-4-Oxoquinoline by Pseudomonas Putida 33/1. Biol. Chem. Hoppe-Seyler, 1990. 371 pp. 999-1003. 

The mobility of eh was determined by measuring the equivalent conductance following pulse irradiation (Schmidt and Buck, 1966 Schmidt and Anbar, 1969). After correcting for the contribution of H30 and OH ions, they found the equivalent conductance of eh = 190 10 mho cm2. From this, these authors obtained the mobility p(eh) = 1.98 x 10"3 cm2/v.s. and the diffusion coefficient D(eh) = 4.9 x 10-5 cm2/s using the Nernst-Einstein relation, with about 5% uncertainty. The equivalent conductance of eh is the same as that for the OH - ion within experimental uncertainty. It is greater than that of the halide ion and smaller than that of eam... 

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