Schmidt numbers

The values of d and n are given in Table 3 typical values for can be found in Table 4. The exponent of 0.5 on the Schmidt number (l-L /PiLj) supports the penetration theory. Further examples of empirical correlations provide partial experimental confirmation of equation 78 (3,64—68). The correlation reflecting what is probably the most comprehensive experimental basis, the Monsanto Model, also falls in this category (68,69). It is based on 545 observations from 13 different sources and may be summarized as... 

The packing parameter ( ) (m) reflects the influence of the Hquid flow rate as shown in Figure 20. reflects the influence of the gas flow rate, staying at unity below 50% of the flooding rate but beginning to decrease above this point. At 75% of the flooding velocity, = 0.6. Sc is the Schmidt number of the Hquid. 

X 10 m /s. Diffusion coefficients may be corrected for other conditions by assuming them proportional to Schmidt numbers depend only weaMy on temperature (113). 

Schmidt number = p D flow-line separation number = D j inertial separation number = U /U /... 

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. ... 

In chemical engineering, the primary application of the diffusivity is to calculate the Schmidt number ( l/pD) used to correlate mass transfer properties. This number is also used in reaction rate calculations involving transport to and away from catalyst surfaces. 

The film thickness 6g depends primarily on the hydrodynamics of the system and hence on the Reynolds number and the Schmidt number. Thus, various correlations have been developed for different geometries in terms of the following dimensionless variables ... 

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

Radius of cylindrical vessel Reynolds number Schmidt number... 

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. 

Since the Schmidt number, Prandtl number, latent heat of vaporization, and humid heat are all essentially independent of pressure, the adiabatic-saturation-temperature and wet-bulb-temperature hues will be substantially equal at pressures different from atmospheric. 

The flnid properties are represented by the Schmidt numbers of the gas and liqnid phases. For gases, the Schmidt unmbers normally are close to nuity and are independent of temperatnre and pressnre. Thns, the gas-phase mass-transfer coefficients are relatively independent of the system. 

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. 

Re = R nolds number, dpS UolV Sc = Schmidt number, V/D D = axial dispersion coefficient dp = Diameter of particle or empty tube = Fraction voids in packed bed Uq = Superficial velocity in the vessel. 

The dimensionless numbers in tlris equation are the Reynolds, Schmidt and the Sherwood number, A/ sh. which is defined by this equation. Dy/g is the diffusion coefficient of the metal-transporting vapour species in the flowing gas. The Reynolds and Schmidt numbers are defined by tire equations... 

Another property of gases which appears in the Reynolds and the Schmidt numbers is the viscosity, which results from momentum transfer across the volume of the gas when drere is relative bulk motion between successive layers of gas, and the coefficient, y], is given according to the kinetic theoty by the equation... 

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. 

When bodr phases are producing eddies a more complicated equation due to Mayers (1962) gives the value of the mass transfer coefficient in terms of the Reynolds and Schmidt numbers which shows that die coefficient is proportional to... 

For conditions in industrial production reactors and in corresponding recycle reactors, the mass transfer coefficients of Gamson et al (1943) will be used. These are approximately correct and simple to use. There may be better correlations for specific cases and especially for larger molecules, where diffiisivity is low and Schmidt number is high. In such cases literature referring to given conditions should be consulted. 

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