Doctoral Dissertations

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Chemical Engineering

Major Professor

John W. Prados

Committee Members

E. E. Stansbury, William H. Flecther, Herbert L. Lee, F. H. Johnson, D. H. Jerry


Investigation of the thermal diffusion phenomenon has transcended the merely academic phase. It is recognized that in some cases thermal diffusion can represent an effective means of separating components, such as isotopes in gases, close boiling components and isotopes in the liquid phase, and electrolytes in aqueous solution. If the separation in a thermal diffusion column could be predicted, it would be possible to scale up, make economic feasibility studies and other pertinent calculations. Thus thermal diffusion would join the mass transfer operations such as distillation, extraction, and the relatively new ion exchange.

Thermal diffusion in gases has been adequately explained. Theories pertaining to liquids have been varied but in general require the determination of postulated quantities, "heats of transport," which have not yet been evaluated. At present there is no unified theory applicable to gases and liquids, since extrapolation of gas concepts to liquids has not been successful.

In this report equations have been derived based on the postulation that irreversible thermal diffusion can be represented as a quasistatic transport process with the Boltzmann equation applicable. By considering gases as being composed of ideal particles, and liquids as condensed gases, a system of equations was derived which allowed, within about 30 per cent, the successful prediction of separations to be expected i helium-argon, non-polar organic liquid pairs and electrolytes in aqueous solution. It was also possible to predict the dependence of the separation upon concentration and temperature.

In the course of the mathematical development unknown quantities such as the partition function of a liquid molecule were introduced. It was necessary to make pragmatic assumptions concerning the form and magnitude of these functions in order to proceed. The justification of these assumptions rests upon analogy, "reasonable" estimates and the apparently successful final result.

Application of the equations to electrolytes in aqueous solution gave agreement within about 30 per cent except for sulfates. The search for the reasons behind the anomalous behavior of the sulfates led to a correction term which takes into account the ion-association and other factors involved in non-ideal behavior of electrolytes. With this correction factor applied to all the electrolytes, sulfates and non-sulfates, the experimental data and calculated predictions were generally within approximately 30 per cent of each other. Based on these results, it would appear that the equations derived will be useful in predicting Soret coefficients, where no data are available. It is suggested that the equations be further tested with the view of extending the concepts to mixed electrolyte solutions.

The scarcity of reported Soret coefficients prompted a new design for a Soret cell, incorporating two cellophane du Pont PT-600 membranes. The membranes do not permit a macroscopic flow of solution. In addition, the apparently do not affect the distribution of components under conditions of no net transfer and hence do not alter the Soret coefficient. The membranes partitioned the cell so that the "differential" volumes contiguous to the hot and cold zones offered a .050-inch diffusion path with the remainder of the cell offering a .350-inch diffusion path. The entire "differential" volume could be removed as a sample without disturbing the rest of the cell.

With this cell, the CuSO4,-H2O, CoSO4-H2O and CuSO4-CoSO4-H2O systems were investigated over a 0.1-0.6 molar range, with temperature gradients of 159°-59°F, 140°-40°F, and 100°-40°F.

Soret coefficients increased monotonically from 9.0-10.3x10-3 °C-1 over a 0.1-0.6 molarity range for CuSO4 and 7.0-7.4x10-3 °C-1 for CoSO4 over the same molarity range. For the mixed salt system, no significant change in Soret coefficient of each component was detected as a result of the mixing. These results are about 10 per cent higher than Bosanquet (2) reported for the same experimental conditions, but with a cell partitioned in two equal halves, separated by a cellophane membrane. Average values of concentration and temperature for each half were assumed.

At higher temperatures it was found that the Soret coefficient for CuSO4 was essentially constant but at the lower temperatures the Soret coefficient decreased with decreasing average temperature. The high temperature behavior is generally in accord with the predicted results, based on the mathematical derivation.

With a membrane life of approximately one month, the cell, once assembled, was operated continuously without dismantling between runs. Such ease of operation is a very attractive feature in conjunction with the effective isolation of the bulk solution by the membranes when removing the samples. It is therefore recommended that further data be obtained, as a function of temperature difference, mean temperature and concentration so that a satisfactory statistical analysis maybe undertaken. It is further suggested that a more durable membrane be found and integrated into the design of the cell used in this investigation. A thorough investigation should also be launched to study the effect of this membrane on Soret coefficients.

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