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THERMAL DIFFUSION

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Thermal diffusion is a relative motion of the components of a gaseous mixture or solution, which is established when there is a temperature gradient in a medium. Thermal diffusion in liquids has an alternative term, the Soret effect, named after the Swiss scientist, who investigated thermal diffusion in solutions in 1879–1881. Thermal diffusion in gases was theoretically predicted by Chapman and Enskog (1911–1917) on the basis of the kinetic theory of gases, and it was later discovered experimentally by Chapman and Dutson in 1917.

Thermal diffusion disturbs the homogeneity of mixture composition: the concentration of components in the regions of increased and decreased temperatures, respectively, becomes different. Since the establishment of a concentration gradient causes, in turn, ordinary diffusion, in a stationary nonuniform temperature field a steady state inhomogeneous state is possible in which the separation effect of thermal diffusion is balanced by the counteraction of concentration diffusion.

In a binary gaseous mixture at constant pressure and with no external forces the total diffusion mass flux of each component is

where D12 is the binary diffusion coefficient, DT is the thermal diffusion coefficient, n = n1 + n2 is the total number of molecules in unit volume, ci = ni/n (i = 1, 2) is the concentration of molecules of the ith component. The thermal diffusion ratio kT = DT/D12 is proportional to the product of the component concentrations, therefore, it is often useful to introduce the thermal diffusion constant α which can be determined from the expression kT = αc1c2. The quantity α is considerably less dependent on the composition than kT, and for mixtures whose molecule properties are similar (for instance, isotopes) it does not change significantly. In gaseous mixtures α does not practically exceed 0.4; for mixture of isotopes, a typical value for α is 0.01.

In the general case, kT depends in a complex manner on the molecular masses, effective molecule size, temperature, mixture composition, and on the laws of intermolecular interaction. The closer the intermolecular forces approach the laws of interaction between the elastic solid balls, the greater is the value of kT; it also increases with increase in the molecule dimension and mass ratio. When molecules interact in accordance with the law for solid elastic bails, kT is independent of the temperature, the heavier molecules gather, in this case, in a cold region (kT > 0 for m1 > m2 > 2 where m1 and m2 are the masses of the respective components), but if m1 and m2 are equal, then larger molecules move into a cold region. For other laws of intermolecular interaction kT can depend considerably on the temperature and can even change sign. Since the thermal diffusion coefficient depends considerably on intermolecular interaction, its measurements allow us to study the intermolecular forces in gases.

The theory of thermal diffusion in liquids has been developed so far only within the limits of the thermodynamics of irreversible processes, with no external forces, chemical reactions and mechanical equilibrium, the concentration and temperature gradients cause the flow of the components which can be written for a binary solution by analogy with a gaseous mixture

where ν is the total number of moles per unit volume, ν10 = ν1/ν, ν20 = ν2/ν, the quantity a which is formally similar to α/T for gases is called the Soret coefficient. There is practically no way of calculating this quantity theoretically because of the absence of a statistical theory of fluids; therefore, the Soret coefficient is found experimentally. In the majority of cases for water and organic solutions α varies within the range 10−3 to 10−2 1/K.

When determining the thermal diffusion coefficient in gases experimentally, the concentrations of the components in communicating cells filled with the gaseous mixture, thermostatted at temperatures T' and T'', are measured. If and are the concentrations of the components in a solid cell, and and in a heated one, then α = ln q/ln (T'/T''), where q = is the coefficient of separation. When measuring the thermal diffusion coefficient in solutions, the temperature gradient is established vertically in the plane gap or horizontally between the coaxial cylinders to avoid convection. In thermal diffusion columns used for separating isotopes and other substances difficult to separate, a convective motion is, by contrast, used to intensify the separation effect of thermal diffusion. As a result of such multistage methods of thermal diffusion separation, the values of q are of the order of 100, and sometimes, of 104 −105.

REFERENCES

Chapman, S. and Cowling, T. G. (1952) The Mathematical Theory of Non-Uniform Gases, Cambridge University Press.

Wakeham, W. A., Nagashima, A. and Sengers, J. V. (1991) (Eds.) Experimental Thermodynamics, Vol. Ill, Chapter 10, Blackwell Scientific Publications, Oxford.

References

  1. Chapman, S. and Cowling, T. G. (1952) The Mathematical Theory of Non-Uniform Gases, Cambridge University Press.
  2. Wakeham, W. A., Nagashima, A. and Sengers, J. V. (1991) (Eds.) Experimental Thermodynamics, Vol. Ill, Chapter 10, Blackwell Scientific Publications, Oxford.

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