Schmidt number, definition

In Fig. 2, the normalized model scalar energy spectrum is plotted for a fixed Reynolds number (ReL = 104) and a range of Schmidt numbers. In Fig. 3, it is shown for Sc = 1000 and a range of Reynolds numbers. The reader interested in the meaning of the different slopes observed in the scalar spectrum can consult Fox (2003). By definition, the ratio of the time scales is equal to the area under the normalized scalar energy spectrum as follows ... 

The Schmidt-number dependence of Pm is a result of the definition of kd, and has been verified using DNS (Fox and Yeung 1999). 

From the definition of cqd, it can be seen that the minimum Schmidt number that can be used corresponds to K2 = K D-... 

These groups have a definite, important, physical meaning. The Reynolds number is the ratio of inertial forces to viscous forces, the Sherwood number the ratio of mass transfer resistance in fluid film to mass transfer in bulk fluid, and Schmidt number the ratio of momentum diffusivity to mass diffusivity. 

A commonly used expression for this number is Sh = 2.0 - - 0.55Re/ Scp where Rcp = d u —u /i/ is the particle Reynolds number and Scp is the fuel vapor Schmidt number. In this definition v is the carrier phase kinematic viscosity. In Eq. (8.2), one important parameter is the Spalding number Bm = Ypx f)/(1 — Yfx) where Ypx is the fuel mass fraction at the droplet surface, calculated from the fuel vapor partial pressure at the interface ppx which is evaluated from the Clausius-Clapeyron relation ... 

The difference between the exponent on the Schmidt number and the usual value of I may not be significant, but the exponent for the Reynolds number is definitely greater than 0.80. Other studies of heat transfer with large Prandtl numbers have also shown an exponent of about 0.9 for the Reynolds number. Various empirical equations that cover the entire range of Nsc or Vp, with good accuracy are available. "... 

The Nernst boundary layer thickness is a simple characteristic of the mass transfer but its definition is formal since no boundary layer is in fact stagnant and least of all boundary layers on gas-evolving electrodes furthermore, the Schmidt number, known to influence mass transfer, is not incorporated in the usual dimensionless form. For this reason, lines representing data from gas evolution in two different solutions can be displaced from one another because of viscosity differences. Nevertheless, the exponent in the equation = aib (32)... 

In order to calculate the conversion of a reaction the axial mixing coefficient has to be known. There are ample experimental data available. In principle, the axial mixing coefficient of a component A is determined by flow conditions and by the diffusivity of A, Generally speaking, the Bodenstein number for axial mixing is a function of the Reynolds and Schmidt numbers (for definitions see eq. 4.23) ... 

Heat and mass transfer coefficients are usually reported as correlations in terms of dimensionless numbers. The exact definition of these dimensionless numbers implies a specific physical system. These numbers are expressed in terms of the characteristic scales. Correlations for mass transfer are conveniently divided into those for fluid-fluid interfaces and those for fluid-solid interfaces. Many of the correlations have the same general form. That is, the Sherwood or Stanton numbers containing the mass transfer coefficient are often expressed as a power function of the Schmidt number, the Reynolds number, and the Grashof number. The formulation of the correlations can be based on dimensional analysis and/or theoretical reasoning. In most cases, however, pure curve fitting of experimental data is used. The correlations are therefore usually problem dependent and can not be used for other systems than the one for which the curve fitting has been performed without validation. A large list of mass transfer correlations with references is presented by Perry [95]. 

The values of some of the parameters in these equations, such as the diffusion coefficient D and the characteristic length parameter d, will depend on specific models and definitions (see below). Using the definitions of the Sherwood number, Sh = kd/D, the ratio of total and molecular mass transfer (with k the mass transfer coefficient), and the Schmidt number. Sc = r]/pD the ratio of momentum and molecular mass transfer, the equation can be written as ... 

As shown in Table III, several authors (Fidaleo and Moresi, 2005a Kraaijeveld et al., 1995 Kuroda et al., 1983 Sonin and Isaacson, 1974) established power function relationships between the Sherwood number (Sh) and the Reynolds (Re) and Schmidt (Sc) numbers in ED cells equipped with different eddy promoters, even if different definitions of the equivalent diameter were used to calculate the Reynolds number. 

If T terface and Tbuik replace Ca, equilibrium and Ca, bulks respectively, in the definition of the dimensionless profile P, and the thermal diffusiv-ity replaces a. mix. then the preceding equation represents the thermal energy balance from which temperature profiles can be obtained. The tangential velocity component within the mass transfer boundary layer is calculated from the potential flow solution for vg if the interface is characterized by zero shear and the Reynolds number is in the laminar flow regime. Since the concentration and thermal boundary layers are thin for large values of the Schmidt and Prandtl... 

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