Abstract of thesis (PH. D.) - University of Michigan, 1944. / An article, by J.O. Osburn and D.L. Katz, reprinted from Transactions of American institute of chemical engineers, v. 40, no. 5, 1944. Literature cited: p. 531.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1955. / Typescript. Vita. Includes (as Part I): A study of the diffusion of glycolamide in water at 25⁰ with the Gouy interference method / By Peter J. Dunlop and Louis J. Gosting. Reprinted from Journal of the American Chemical Society, vol. 75 (1953), p. 5073-5075. Includes bibliographical references.

Inaug.-diss.--Leipzig. / Vita.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M.S.)--University of Wisconsin--Madison, 1963. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 29-30)

Smith and Storrow [J. Appl. Chem. (London) 2: 225, (1952)] and Hammond and Stokes [Trans. Faraday Soc. 40: 890, (1953)], using their individual modifications of the diaphragm-cell method for measuring liquid diffusivities, reported diffusion coefficients on the ethanol-water system that disagreed by as much as 100 per cent. It was apparently in view of this disagreement that Johnson and Babb gave a very reserved summary opinion on the diaphragm-cell method in a comprehensive review article [Chem. Rev. 56: 387, (1956)]. In the present work a diaphragm cell was designed which, unlike prior designs, is suitable for use with practically all organic liquids. A compact machine, accommodating and stirring a battery of six such cells, was designed and used. The precision of the cell constant determinations, using aqueous KC1 solutions, was ± 0.1%, a scatter completely accounted for by the errors arising from a standard gravimetric analysis of the solutions which, in this case, was improved in accuracy by one order of magnitude over hitherto reported analyses. Using this apparatus, the diffusivity results obtained by Hammond and Stokes were confirmed within the accuracy of the ethanol-water measurements (± 2%). Critical experiments on an apparatus similar to that used by Smith and Storrow revealed that there was a possibility of distillation through a wetted ground glass joint from the one solution into the other. The apparent higher diffusivities obtained by these authors were attributed to this phenomenon. Detailed derivation of the general equation of diffusion, using the methods of the thermodynamics of irreversible processes, and discussion of the question of the various frames of references and the various diffusivities defined by some authors is given. Using the general equation of diffusion in a binary system new formulae which apply regardless of volume changes on mixing were derived for use with the diaphragm cell method. It was shown that, in the case where the density of the solution is linear in the volume concentration, the general equation of diffusion reduces to Fick's first law and the various formulae based upon the general equation reduce to the corresponding simple formulae. The trial-and-error procedure used with electrolytes by R. H. Stokes was generalized and used to compute the true differential diffusivities from the measured integral values and it was shown that, contrary to the contention of Stokes, this type of procedure is applicable in the case of systems where the limiting values of the diffusivity are not known and the diffusivity changes strongly with concentration. Also, an alternate procedure, based on the differentiation of the integral diffusivities, is suggested. It was noted that the minimum of the diffusivity-concentration curve and that of the relative volume decrease-concentration curve, and the maximum of the viscosity-concentration curve are at a composition corresponding to one molecule of ethanol and three molecules of water. This coincidence may be evidence for the existence of a molecular complex. It was found that the activity-based diffusivity is practically constant over some 70% of the composition range. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

This investigation was undertaken primarily for the purpose of collecting reliable experimental data on binary gaseous diffusion coefficients of polar systems. The binary gas pairs investigated were the A - SO₂ , A - HCI , and SO₂ - HCI systems. Diffusion through, a porous solid in a flow apparatus was adopted for the diffusion measurement. The diffusion cell was standardized by making diffusion runs using the N₂ - CO₂ system at 5 different temperatures, room temperature, 70°C, 120°C, 200°C, and 250°C, and using also the N₂ - H₂ system at room temperature. Thermal conductivity cells and chemical methods, alone or in combination, were used for analysis of the gas streams. The results in all these three systems could be represented by straight lines on logarithmic plots of diffusion coefficient against temperatures from 20°C - 250°C. In the first two pas pairs, the experimental coefficients appeared to be 25.3% and 29.2% less at room temperature, and 20.0% and 12.1% less at about 250°C than the respectively predicted values obtained by using the Stockmeyer potential function in the Hirschfelder diffusion equation. The slopes of the lines were 1.988 and 2.42, respectively. It was found that the A - SO₂ system could be represented by a potential function of the Lennard-Jones type, although the molecular force parameters determined from the diffusion data did not agree with those calculated from the pure component values and the usual empriical combining rules. The system A - HCI could not be represented by a function of the Lennard-Jones type. The third system, SO₂ - HCI, was also found to behave more or less the same way as A - HCI system. However, the slope of the line obtained from a Log D vs Log T plot (2.22), was smaller than that of the A - HCI system, although still greater than that predicted by using the Monchick and Mason . (12-6-3) potential function. The magnitudes of the diffusion coefficients within the range of temperatures studied were found to be within 11.0% of the predicted ones. Nevertheless, the system did not conform completely to the Monchick and Mason model. Some qualitative reasons are given for the inadequacies of present potential functions and combining rules for use in predicting binary diffusion coefficients in mixtures containing polar molecules. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

In natural fluids, stratification of density is common. Observations of natural turbulence in the presence of a density stratification are difficult since the stratification usually occurs in regions not readily accessible. In the laboratory, maintenance of a stratification in a shear flow presents equal difficulties. Observations were made of isolated puffs of fluid injected vertically downwards into a uniform fluid of the same density, and into a stably stratified fluid of greater density. The observations demonstrate that such isolated puffs in uniform fluid are subject to the same decay laws as is the turbulent energy in an extended turbulent fluid. This implies that a turbulent field, made up of randomly oriented puffs of fluid of varying volumes and velocities, would display many of the characteristics of a fluid in which the turbulence is a result of shear flow, and that observations made on such puffs can be applied with some confidence to natural turbulence. The apparatus was so constructed that the detailed mixing between the injected fluid and the surrounding fluid resulted in the formation of a finely divided precipitate which rendered the puffs visible, and permitted measurements of their path by means of moving picture photographs. The results demonstrate that mixing with the surroundings occurs throughout the puff, which retains its identity and a relatively uniform density. Measurements of the rate of formation of precipitate permit an estimate of the rate at which the injected fluid became mixed with the entrained fluid. The density stratification had very little influence upon this rate until after the puff had reached its maximum penetration. The rate of horizontal spreading of the puff during its motion also showed little effect of the stratification. Measurement of the penetration and ultimate position of the center of a puff in a density stratification together with measurements of the position of the center of a puff in uniform fluid permit the calculation of a number of dimensionless ratios. These are displayed graphically as a function of a dimensionless number made up from the initial conditions of velocity, volume, density gradient, density, and the acceleration of gravity. This number resembles the reciprocal of a Richardson's number and is referred to as 1/Ri. The maximum conversion of initial kinetic energy to potential energy observed was 20 percent, being greatest for small values of 1/Ri. The portion of the initial energy which contributes to the breakdown of the stratification was found to be approximately 3 percent and nearly independent of 1/Ri. Some writers have thought the loss to density stratification would be much greater than this. A figure representative of the transport of properties during the history of a puff varied by a factor 35 over the possible range of initial conditions, being greater for high values of 1/Ri. An estimate of the possible effect of density stratification upon the production of turbulent energy shows that production is reduced by as much as a factor 10 for small 1/Ri. This arises from the reversal and rebound of the puff of fluid in the stratification. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The diaphragm cell technique for measurement of diffusion coefficients has been subjected to detailed analysis with the particular view to obtaining measurements on the various solutions involved in solvent extraction of uranium and its compounds. Consideration of types of cells used previously has led to an improved diaphragm cell design. An apparatus accommodating and magnetically stirring six cells simultaneously was designed and constructed. The result of errors of analysis of solutions on the diffusion coefficients has been determined as a function of the experimental conditions. The effect that volume changes occurring in real solutions during diffusion have on the value of the diffusion coefficient D, as computed by the standard logarithmic formula, was considered. Computations carried out in a first approximation showed that although the error committed by the neglect of volume changes is appreciably larger than estimated by previous workers it is not large enough to account for the full amount of some discrepancies reported in the literature. A numerical procedure is given for pursuing the analysis in a second and a third approximation involving decreasing dependence on the simplifying assumptions always made in previous calculations using this technique. This procedure can be programmed on an electronic computer. It is proposed that in situ concentration determinations at the beginning and end of a diffusion experiment be used based on comparison with an outside standard. Combined with the numerical method suggested this will allow considerable reduction in the concentration difference between the two solutions in the cell without significant loss in accuracy or increase in experimental time, and also make the measured diffusion coefficient a more "true" value. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate