Thermal diffusion ratio

Lennard-Jones gas dimensionless thermal diffusion ratio, 25 307 Lennard-Jones molecules, 25 302 Lennard-Jones potential, 7 620 23 94 Lennard-Jones potential energy function, 25 302... 

In the second expression the thermal diffusion ratio kr has been introduced it is defined for binary mixtures to be... 

In equation IV. 6, Dik represents the ordinary diffusion coefficient for binary interactions, and a, is the thermal diffusion ratio. The reactants are often present in small amounts (<1%) relative to the carrier gas thus, the multicomponent diffusion expression (equation IV. 6) may be replaced by a simple Fickian diffusion expression that includes thermodiffusion... 

Another well-known example is the coupling between mass flow and heat flow. As a result, an induced effect known as thermal diffusion (Soret effect) may occur because of the temperature gradient. This indicates that a mass flow of component A may occur without the concentration gradient of component A. Dufour effect is an induced heat flow caused by the concentration gradient. These effects represent examples of couplings between two vectorial flows. The cross-phenomenological coefficients relate the Dufour and Soret effects. In order to describe the coupling effects, the thermal diffusion ratio is introduced besides the transport coefficients of thermal conductivity and dififusivity. 

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... 

Table 7.1. Experimental values of thermal diffusion ratios for liquids and gases at low density and pressure3...

Table 7.2 shows the viscosity, mutual diffusion coefficient, and thermodynamic factor for aqueous solutions of ethylene glycol and polyethylene glycol (PEG) at 25°C the diffusivity decreases considerably with increasing molecular weight, while the viscosity increases. Table 7.2 shows the thermal diffusion ratios for liquids and gases at low density and pressure the thermal diffusion ratios are relatively larger in liquids. 

Table 7.2b. Thermal diffusion ratio, KJt thermal diffusion coefficients Dj, and heats of transport Q for aqueous ethylene glycol and polyethylene glycol (PEG) solutions at 25°Ca...

We can describe the degree of coupling q and the thermal diffusion ratio of component 1 KTl in terms of the transport coefficients and thermodynamic factor (F)... 

Figure 7.2. Change of the thermal diffusion ratio /CT1 with the alkane concentrations xx at 30°C and ambient pressure (a) straight chain alkanes, (—) /7-hexane, (—), /7-heptane, (—) n-octane (b) branched-chain alkanes, (—) 3-methylpentane, (—) 2,2-dimethylpentane, (—) 2,2,4-trimethylpentane. Reprinted with the permission from Elsevier, Y. Demirel and S.l. Sandler, Int. J. Heat Mass Transfer, 43 (2002) 75.

Concentration effects on the heats of transport and the thermal diffusion ratio of chloroform with various alkanes at 30°C and 1 atm are seen in Table 7.6. Table 7.7 shows the experimental heats of transport at various concentrations and at temperatures 298 and 308 K for binary mixtures of toluene (1), chlorobenzene (2), and bromobenzene (3) at 1 atm. The absolute values of heats of transport decrease gradually as the concentrations of the alkane increase. Table 7.7 also contains values of cross coefficients obtained from easily measurable quantities and the thermodynamic factor. 

Table 7.8 shows the thermal diffusion ratios and thermal diffusion coefficients obtained from Onsager s reciprocal rules for toluene, chlorobenzene, and bromobenzene at 1 atm and at 298 and 308 K. Thermal diffusion or heats of transport may be extremely sensitive to the molecular interactions in solutions (Rowley et al., 1988). 

Table 7.6. Heats of transports and thermal diffusion ratio Kja of chloroform in binary mixtures with selected alkanes at 30°C and 1 atmb...

Table 7.11. Thermal diffusion ratios from Onsagefs reciprocal rules for toluene (1), chlorobenzene (2), and bromobenzene (3) at 1 atm and 35oa...

Table 7.11 shows the thermal diffusion ratios obtained from Onsager s reciprocal rules for toluene (1), chlorobenzene (2), and bromobenzene (3) at 1 atm and 35°C. The heats of transport for the ternary mixtures are shown in Tables 7.12 and 7.13. For the ternary mixture of toluene (l)-chlorobenzene (2)-bromobenzene (3), the heats of transport are tabulated at 298 and 308 K. The temperature- and composition-dependent heats of transport values are fitted by the following equations by Platt et al. (1982) with a deviation below 5% ... 

The separation of polymers due to thermal diffusion may be quite large. For example, the thermal diffusion ratio for dilute solutions of polystyrene in tetrahydrofuran is around 0.6 K1. This indicates that the change of polystyrene concentration per degree is 60%. The type of solvent and polymer pair may have a considerable effect on both the thermal diffusion ratio and the thermal diffusion coefficient. 

The molality-based thermal diffusion ratio based thermal diffusion ratio... 

Since the thermal diffusion ratio is temperature dependent, the integral above can be integrated by assuming a constant thermal diffusion ratio for a reference temperature obtained from... 

Table 7.1 shows the values of the thermal diffusion ratio in the form KT(Mlv/MhM2) = 0.0548 at 7 = 264 K, which is very close to reference temperature 268 K. Therefore, we have... 

As the thermal diffusion ratio is positive, the hydrogen diffuses into the vessel at a lower temperature. We estimate the difference between the hydrogen mass fractions in two vessels by... 

Because the dimensionless parameters identified were not all independent, only several primitive variables were subsequently varied in a sensitivity study to determine the dependence of the material s thermal response to variations in the load thickness such as the refractory wall thickness, load and refractory thermal diffusivity ratio, the air/fuel mixture used in the combustion, the refractory and load emissivities, the furnace height, and the exposed area of the load. 

Under certain conditions the central line simplifies considerably. In the limit of small concentration c -> 0, the thermal diffusion ratio goes to zero... 

There is considerable evidence that the thermal diffusion ratio becomes very large in the critical region. > > > It is possible, but not certain, that the anomaly can be ascribed solely to the vanishing of Z)(r). ... 

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