Thermal diffusion factor

If temperature gradients are small, Cr may be regarded as effectively constant. Furthermore, Kart is a function of composition, being approximately proportional to the product x, Xr. It is therefore useful to work in terms of the thermal diffusion factor a, where ... 

Equation 10.61 gives the mole fraction of the two components A and B as a function of the absolute temperatures and the thermal diffusion factor. 

Table 10.5. Values of thermal diffusion factor (a) for binary gas mixtures (A is the heavier component, which moves towards the cooler end)...

The quantity kr is so defined that when hr is positive the component A moves to the cold region, and when kr is negative A moves to the hot region. This definition of kr is in agreement with the accepted definitions of previous workers, and in particular with the text books of Chapman and Cowling (C3) and Grew and Ibbs (G12). In the gas phase many authors prefer to write the mass flux in terms of the thermal diffusion factor a, which is defined as... 

TABLE 8.2 Range of Values of Thermal Diffusion Factor a... 

The dependence of retention in Th-FFF on chemical composition of the polymers and solvent [84] also opens a wide field of application for Th-FFF, especially for copolymers. According to Eq. (42), retention in Th-FFF can be used to determine the thermal diffusion factor aT which was demonstrated for polystyrene in toluene [209]. Eater, this study was extended to other solvents (ethyl acetate, 2-butanone, p-dioxane, cyclohexane, dimethylformamide, chloroform, and ethylbenzene) [204]. 

Table 7.1 shows some experimental values of thermal diffusion ratios for liquids and gases at low density and pressure. If K-n is positive, component 1 diffuses to a cooler region otherwise, it diffuses to a hotter regioa The thermal diffusion factor for component 1 is mainly independent of concentration for gases, and is given by... 

Convective heat transfer is often used as an adjunct to other modes, particularly to the conductive mode. It is often more convenient to consider the agitative effect a performance-improvement influence on the thermal diffusivity factor a, modifying it to a, the effective value. 

The thermal diffusion factor a is proportional to the mass difference, (mi — mo)/(mi + m2). The thermal diffusion process depends on the transport of momentum in collisions between unlike molecules. The momentum transport vanishes for Maxwellian molecules, particles which repel one another with a force which falls off as the inverse fifth power of the distance between them. If the repulsive force between the molecules falls off more rapidly than the fifth power of the distance, then the light molecule will concentrate in the high temperature region of the space, while the heavy molecule concentrates in the cold temperature region. When the force law falls off less rapidly than the fifth power of the distance, then the thermal diffusion separation occurs in the opposite sense. The theory of the thermal diffusion factor a is as yet incomplete even for classical molecules. A summary of the theory has been given by Jones and Furry 15) and by Hirschfelder, Curtiss, and Bird 14), Since the thermal diffusion factor a for isotope mixtures is small, of the order of 10", it remained for Clusius and Dickel (8) to develop an elegant countercurrent system which could multiply the elementary effect. 

The retention is related to the size, charge, diffusion coefficient, thermal diffusion factor, and so forth of the separated species in polarization FFF. As concerns the focusing FFF, the retention is usually related with the intensive properties of the fractionated species. Consequently, the FFF can be used to characterize the properties related to the retention. Because the entry Focusing FFF of Particles and Macromolecules is fully devoted to the focusing FFF, only the polarization FFF methods will be described here. 

J.-W. Yang, A New Method of Measuring the Mass Diffusion Coefficient and Thermal Diffusion Factor in a Binary Gas System, doctoral dissertation, Univ. of Minnesota, 1966. 

Thermal diffusion factor a = D /D. It may be noted that if Onsager relation is satisfied, D" = D. ... 

AT generated is <1°C. Values of thermal diffusion factor estimated and discussed are in agreement with kinetic theory as regards order. The value of calculated Soret coefficient from the data is also found to be in agreement as regards order with the experimental values obtained by other workers. 

The retention is related to the size, charge, diffusion coefficient, thermal diffusion factor, and so forth of the separated species in polarization FFF, whereas it is exclusively... 

Thermal diffusion ratio, k-p. Thermal diffusion ratio, kp, is a measure of thermal diffusion. The sign of kp determines the direction of thermal diffusion. Another defined parameter for thermal diffusion is the thermal diffusion factor, a, which is defined as... 

Figure 2.15 Comparison of thermal diffusion factors from theory and experiments for the Cj/Cg system (adapted from Shukla and Firoozahadi, 1998).

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