Schmidt number temperature dependence

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). 

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 average Nusselt number is not very sensitive to changes in gas velocity and Reynolds number, certainly no more than (Re)I/3. The Sherwood number can be calculated with the same formula as the Nusselt number, with the substitution of the Schmidt number for the Prandtl number. While the Prandtl number of nearly all gases at all temperatures is 0.7 the Schmidt number for various molecules in air does depend on temperature and molecular type, having the value of 0.23 for H2, 0.81 for CO, and 1.60 for benzene. 

The physics of the problem under study is assumed to be governed by the compressible form of the Favre-filtered Navier-Stokes energy and species equations for an ideal gas mixture with constant specific heats, temperature-dependent transport properties, and equal diffusion coefficients. The molecular Schmidt, Prandtl, and Lewis numbers are set equal to 1.0, 0.7, and 1.43, respectively [17]. 

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. 

By contrast, the liquid-phase Schmidt numbers range from about 102 to 104 and depend strongly on temperature. The temperature dependence of the liquid-phase Schmidt number derives primarily from the strong dependence of the liquid viscosity on temperature. 

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 Temperature on kG and k, The Stanton-number relationship for gas-phase mass transfer in packed beds, Eq. (5-301), indicates that for a given system geometry the rate coefficient kG depends only on the Reynolds number and the Schmidt number. Since the Schmidt number for a gas is approximately independent of temperature, the principal effect of temperature upon kG arises from changes in the gas viscosity with changes in temperature. For normally encountered temperature ranges, these effects will be small owing to the fractional powers involved in Reynolds-number terms (see Tables 5-17 to 5-24). It thus can be concluded that for all... 

Table 10.1. Molecular diffusion coefficients, D, and Schmidt numbers, Sc, for gases The molecular diffusion coefficients, D (in units of 10 cm s see note"), were determined from the equations presented in Chapter 9, Table 9.1. The Idnematic viscosity of water is from Pilson (1998). The Idnematic viscosity is 3%-5% greater in seawater than in freshwater, and we assume here that this is the only factor causing a salinity dependence on sc. Opposite trends with T for diffusion coefficients and Idnematic viscosity create greater temperature dependence for Schmidt numbers than for the molecular diffusion coefficients. ...

A better analytically based equation which is valid over a wide range of Prandtl or Schmidt numbers is obtained if we presume a turbulent parallel flow, i.e. a steady-state turbulent flow with vanishing pressure gradient, and velocity, temperature and concentration profiles which are only dependent on the coordinate y normal to the wall. Then, as follows from (3.134) to (3.139),... 

Measurements of piston velocities for different gases and at different temperatures and salinities are often compared for a Schmidt number of 600, i.e. the Schmidt number for CO2 at 20 °C. However, the influence of bubbles, spray and adsorbed surfactants may substantially alter the dependence of gas exchange on the Sc [18], and thus scaling of different gas exchange measurements based on assumptions about the value of the exponent may be sometimes in error. 

For a given system the temperature difference between bulk and surface depends on the reactant concentration via AT j, the ratio between Prandtl and Schmidt number, and the Carberry number. The temperature difference is maximum for reactions limited by mass transfer (Ca = >l). As for gases the Schmidt and Prandtl numbers are approximately unity Pr os Scoi 1), the temperature difference can reach the adiabatic temperature T - — T ). 

Figure 5-7. Dependence of the length L of the observed long period on the number n of chain links in alkanes (PE) with the constitutional formula H(CH2) H (54°C, c direction), and in polyurethanes (PU) with the constitutional formula HO-f-CH2)2—O—(CH2)2—[—O— CO—NH—(CH2)6—NH—C0-0-(CH2)2—0-CH2)2T,-0H (room temperature). The long periods of the low-molecular-weight polyurethanes are considerably lower than those calculated for an dA -trans conformation (—), the molecular axes must therefore be diagonal to the base plane. [Measurements on alkanes and poly(ethylenes) from various authors, and on urethanes from W. Kern, J. Davidovits, K. J. Rauterkus, and G. F. Schmidt.]...

The eoncentration of solvent in a saturated vapor layer depends on temperature and vapor pressure. The coefficient of mass transfer on the air-side depends on the air velocity in the layer on the surface and Schmidt s number (includes dynamic vapor viscosity, vapor density, and diffusion coefficient). Emissions are measured in mass unit per unit of time and the amount depends on surface area and the rate of evaporation, whieh, in turn, depends on temperature, air velocity over the surface of solvent and the mass of solvent earried out on the wetted parts which have been degreased. 

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