Schmidt number in water

Deacon s model has also been applied to the air-phase exchange velocity, but the physical basis for such an extension is weak since typical Schmidt Numbers in air are about 1 (Sc,a 0.57 for water vapor at 20°C). Furthermore, the temperature dependence of Scia is small since both va and D,a increase with air temperature. In fact, for most substances Sc,a varies by less than 10% for temperatures between 0°C and 25°C. 

The range of the Prandtl number is narrower than that of the Schmidt number. In gases such as air, Pr — 1, and in liquids like water, Pr 10. In extremely viscous liquids like glycerin, the Prandtl number is of the order of 103. Liquid metals (sodium, lithium, mercury, etc.) are characterized by low Prandtl numbers 5 x 10-3 < Pr < 5 x 10 2. 

The correlation of Rowe et al. is different from the others in that it involves a dependence of the yp factor on the Schmidt number. In fact, Rowe and Claxton assumed an equation of the form of Eq. (7.3.28) (i.e., assumed a dependence of the j factor on and then proceeded to determine the values of A, B, and n which would best fit their data. To test the assumed dependence ofon N c requires measurement at low Reynolds numbers and at low Schmidt numbers. Unfortunately the low Reynolds number experiments carried out by these workers were confined to water (N c — 1400). 

It is seen that we are comparing kinematic viscosity, thermal diffusivity, and diffu-sivity of the medium for both air and water. In air, these numbers are all of the same order of magnitude, meaning that air provides a similar resistance to the transport of momentum, heat, and mass. In fact, there are two dimensionless numbers that will tell us these ratios the Prandtl number (Pr = pCpv/kj = v/a) and the Schmidt number (Sc = v/D). The Prandtl number for air at 20°C is 0.7. The Schmidt number for air is between 0.2 and 2 for helium and hexane, respectively. The magnitude of both of these numbers are on the order of 1, meaning that whether it is momentum transport, heat transport, or mass transport that we are concerned with, the results will be on the same order once the boundary conditions have been made dimensionless. 

The gas film coefficient is dependent on turbulence in the boundary layer over the water body. Table 4.1 provides Schmidt and Prandtl numbers for air and water. In water, Schmidt and Prandtl numbers on the order of 1,000 and 10, respectively, results in the entire concentration boundary layer being inside of the laminar sublayer of the momentum boundary layer. In air, both the Schmidt and Prandtl numbers are on the order of 1. This means that the analogy between momentum, heat, and mass transport is more precise for air than for water, and the techniques apphed to determine momentum transport away from an interface may be more applicable to heat and mass transport in air than they are to the liquid side of the interface. 

One other measurement technique that has been used to measure Kl over a shorter time period, and is thus more responsive to changes in wind velocity, is the controlled flux technique (Haupecker et al., 1995). This technique uses radiated energy that is turned into heat within a few microns under the water surface as a proxy tracer. The rate at which this heat diffuses into the water column is related to the liquid film coefficient for heat, and, through the Prandtl-Schmidt number analogy, for mass as well. One problem is that a theory for heat/mass transfer is required, and Danckwert s surface renewal theory may not apply to the low Prandtl numbers of heat transfer (Atmane et al., 2004). The controlled flux technique is close to being viable for short-period field measurements of the liquid film coefficient. 

Deacon derived his model for volatile compounds whose air-water transfer velocities solely depend on the conditions in the water phase. In its original form, which is valid for a smooth and rigid water surface and for Schmidt Numbers larger than 100, it has the form ... 

Table 20.3 Molecular Diffusivities, Kinematic Viscosities, and Schmidt Numbers (ScJW) in Water for Selected Chemicals... 

In the film model of Whitman the water-phase exchange velocity, v,w, is a function of the molecular diffusion coefficient of the chemical, while in Deacon s boundary layer model v[W depends on the Schmidt Number Sc W. Explain the reason for this difference. 

Table B.4 Schmidt Numbers Scfw = vw / Diw of Gases Dissolved in Water...

The measured values demonstrate, in analogy to point 4 where power characteristic was discussed, that D, and consequently the Schmidt number, are not as relevant as assumed. (In the same system of materials - a mixture of water and cane syrup - at almost the same D value, the Schmidt number is varied by the kinematic viscosity, v, over many orders of magnitude.)... 

Variable material constants (p, Sc, cp) for water, fuel, oxidiser and reaction products were included. Density, Schmidt-Number and specific heat capacity are calculated at all points of the calculation grid depending on local temperature and pressure inside the reactor. The Schmidt-Number is a value for the diffusive mass transfer from methanol in water. 

Effects of System Physical Properties on kG and kL When designing packed towers for nonreacting gas-absorption systems for which no experimental data are available, it is necessary to make corrections for differences in composition between the existing test data and the system in question. The ammonia-water test data (see Table 5-24-B) can be used to estimate HG, and the oxygen desorption data (see Table 5-24-A) can be used to estimate HL. The method for doing this is illustrated in Table 5-24-E. There is some conflict on whether the value of the exponent for the Schmidt number is 0.5 or 2/3 [Yadav and Sharma, Chem. Eng. Sci. 34, 1423 (1979)]. Despite this disagreement, this method is extremely useful, especially for absorption and stripping systems. 

It must be kept in mind that these measurements were made with water, in which the molecular diffusivity is negligibly small. When the fluid is a gas, with a Schmidt number having the order of magnitude of unity, the Peclet number for molecular diffusion, being the product of Schmidt number and Reynolds number, has the order of magnitude of the Reynolds number. Even if the effect of molecular diffusion is multiplied by the fraction void and by another factor of %, to take care of... 

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