Schmidt number high values

The experimental results for udp /Dr) in Figure 9.1 show a wide range of values at low Reynolds numbers. The physical properties of the fluid, and specifically its Schmidt number. Sc = /x/(pS) ), are important when the Reynolds number is low. Liquids will lie near the top of the range for u dp /Dr)oo gases near the bottom. At high Reynolds numbers, hydrodynamics dominate, and the fluid properties become unimportant aside from their effect on Reynolds number. This is a fairly general phenomenon and is discussed further... 

This correlation has been shown to agree with Bank s (3) numerical results for Sc = 0.7 and 1.0. At high Schmidt numbers, the second and third terms are negligible, and Eq. (46) asymptotically approaches to the values predicted by Eq. (42). 

For flow parallel to an electrode, a maximum in the value of the mass-transfer rate occurs at the leading edge of the electrode. This is not only the case in flow over a flat plate, but also in pipes, annuli, and channels. In all these cases, the parallel velocity component in the mass-transfer boundary layer is practically a linear function of the distance to the electrode. Even though the parallel velocity profile over the hydrodynamic boundary layer (of thickness h) or over the duct diameter (with equivalent diameter de) is parabolic or more complicated, a linear profile within the diffusion layer (of thickness 8d) may be assumed. This is justified by the extreme thinness of the diffusion layer in liquids of high Schmidt number ... 

The sub-grid-scale turbulent Schmidt number has a value of Scsgs 0.4 (Pitsch and Steiner 2000), and controls the magnitude of the SGS turbulent diffusion. Note that due to the filtering process, the filtered scalar field will be considerably smoother than the original field. For high-Schmidt-number scalars, the molecular diffusion coefficient (T) will be much smaller than the SGS diffusivity, and can thus usually be neglected. 

Reynolds numbers, its value is significantly smaller than the high-Reynolds-number limit. Despite its inability to capture low-Reynolds-number effects on the steady-state scalar dissipation rate, the SR model does account for Reynolds-number and Schmidt-number effects on the dynamic behavior of R(t). 

This case was treated by Potter [ 18] by means of the integral method. Since for high values of the Schmidt number only the region in the vicinity of the planar fluid boundary contributes appreciably to the value of the mass... 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = yu/(p a), but the dependence on Sc is weak for Re > 5000. As indicated in Figure 9.6, data for gases will lie near the top of the range and data for liquids will lie near the bottom. For high Re, udt/D = 5 is a reasonable choice. 

Local heat transfer rates from the surface of a cylinder in cross flow in air were measured by Schmidt and Wenner [68] and are shown in Fig. 6.28. The local Nusselt number is based on the local heat transfer coefficient and the cylinder diameter. Note that for subcritical Reynolds numbers (Red < 170,000), the local Nusselt number decreases initially along the surface from the forward stagnation point to a minimum at the separation point and subsequently reaches high values again in the separated portion of the flow on the back surface. For... 

Dissolution rate data obtained under forced convection conditions can be correlated by means of equation 6.64 or 6.65. As described in section 6.2.2, equation 6.64 is the preferred relationship on theoretical grounds, since Sh = 2 for mass transfer by convection in stagnant solution (Re = 0), whereas equation 6.65 incorrectly predicts a zero mass transfer rate (Sh = 0) for this condition. However, at reasonably high values of Sh (>100) the use of the simpler equation 6.65 is quite justified. The exponent of the Schmidt number b is usually taken to be and for mass transfer from spheres the exponent of the Reynolds number a =... 

The diffusion coefficient as defined by Fick s law, Eqn. (3.4-3), is a molecular parameter and is usually reported as an infinite-dilution, binary-diffusion coefficient. In mass-transfer work, it appears in the Schmidt- and in the Sherwood numbers. These two quantities, Sc and Sh, are strongly affected by pressure and whether the conditions are near the critical state of the solvent or not. As we saw before, the Schmidt and Prandtl numbers theoretically take large values as the critical point of the solvent is approached. Mass-transfer in high-pressure operations is done by extraction or leaching with a dense gas, neat or modified with an entrainer. In dense-gas extraction, the fluid of choice is carbon dioxide, hence many diffusional data relate to carbon dioxide at conditions above its critical point (73.8 bar, 31°C) In general, the order of magnitude of the diffusivity depends on the type of solvent in which diffusion occurs. Middleman [18] reports some of the following data for diffusion. 

Figure 1 compares the experimental data of various investigators with Eqs. (11) and (12). Equation (11) compares more favorably with the experimental results at lower values of Schmidt to Prandtl number ratios, whereas Eq. (12) compares more favorably at higher values. It is evident that further work is needed to derive a theoretical relationship which encompasses the entire range of the experimental results. Furthermore, practically no data exist for the psychrometric ratio at high temperatures and high humidities. 

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