A theoretical treatment is prcsented which attempts to quantify the benefits obtained by using smaller bubbles or larger particles in dispersed air flotation. The limited experimental data obtained so far suggest that the theory is sound, particularly in its prediction of the effect of bubble size.any liquid effluents contain particles which are M too small to be removed economically in sedimentation tanks or by conventional filters. The diameters of such particles are normally less than 20 microns. Dispersed air flotation removes them by adsorbing them on small rising air bubbles, typically of diameters up to 0.1 mm. The bubbles may be generated either by electrolysis, or by forcing air through a porous plate or through spargers. As they rise through the liquid they contact particles either by collision or by Brownian diffusion, depending on particle size. An example of an industrial application is Saint Gobain's Electro-flotation process"', designed initially for removing oil-covered iron dust particles from rolling mill effluents.In dissolved-air flotation, a technique long established in industry, the bubbles are formed by nucleation on the particles'e', For this to happen a substantial portion of the clarified effluent must be recycled, compressed to 4 to 6 atmospheres and saturated with air. Dispersed air flotation has the advantage of eliminating the need for recycling and compression. However, bubble-particle contacting is necessarily less efficient and contacting efficiency becomes an important design parameter. This paper explores the effect of bubble size and particle size on contacting efficiency. Previous workThe removal of suspended solids from effluents by dispersed air flotation is obviously similar in many ways to the froth flotation process used in mineral dressing. The mineral flotation literature records little or no quantitative work on the effect of bubble size, although it is known qualitatively that smaller bubbles tend to increase the flotation rate and a subsidiary function of frothers (long-chain alcohols) is t o reduce bubble size"). Many empirical studies have been made on the effect of particle size in mineral flotation without any clear-cut relation emerging. If the first order flotation rate constant is k, and the particle diameter is d, then Morris") found k, a In dp; Bushell"' found ?c, independent of d, ; Tomlinson and On prksente un traitcment thhriqne par lequel on cherche A dkterniiner quantitativement les avantages qu'on obtient en employant des bulles plus petites ou des particules plus grosses flottant disperdxs dam l'air. Les rksultats maigres qu'on a obtenus expkrimentaleriient jusqn'ici tendent 8 indiquer que la thCorie est bien fondke, surtout en ce qui a trait i sa prkdiction de I'effet des dimensions des bulles.Fleming'" found kl a d,? for easily floated minerals and kl a d, for poorly floated minerals; Gaudin et a P found k1 to be independent of d, for d, = 1 to 4 microns and kl a d , for d , = 4 to 20 microns. Only Tomlinson and Fleming reported the bubble size us...

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Flotation rates of glass beads and of latex particles have been measured as a function of particle size using very small bubbles. With glass beads the observed rate versus size relationship agreed quite well with the prediction of a simple hydrodynamic collision model, but that found with latex particles did not. It is suggested that electrical forces may have to be taken into account when the particles have a significant zeta potential. With both types of particle, the relationship between flotation rates measured at two different bubble sizes is consistent with the model's predictions.

A modified group solution model for liquid mixtures is presented. The model differs from previous models in that the Bronsted‐Koefoed congruence principle is used to describe the effect of molecular size. The model has been tested for mixtures involving paraffin hydrocarbons, alcohols and water at low pressures. Such systems involve binary mixtures of the groups methylene and hydroxyl, and are reasonably represented by the model. Data presented enable the approximate equilibrium properties of such solutions at low pressures to be predicted at 40°C and 90°C. Interpolation and reasonable extrapolation from these temperatures should be satisfactory.

The Gillespie-type still used by Lu was modified to provide a better approach to equilibbrium. It was tested by comparing experimental and literature data for binary mixtures of ethanol-benzene and methanol-water. Isothermal vapor-liquid equilibrium data were then determined for acetone-n-heplane mixtures at 65°C. Redlich-Kister constants were evaluated by a weighted least-squares fit and are presented.

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Group solution models of liquid mixtures have been used previously to predict thermodynamic properties of non-ideal systems. A model of this type has been developed which enables the viscosities of liquid mixtures to be predicted. The concept of an "ideal viscosity" is introduced, and allowance made for the interaction between the groups present and for the structural contributions of differing molecules. Predictions require a knowledge of only the viscosities of the pure components of a mixture. It has been tested for mixtures of alkanes, alcohols and water at 2 5 O C , and gives good agreement with experiment. Experimental viscosities for ethanol/n-hexane, for n-propanol/ water, and for four multi-component mixtures at 2 5 O C are presented. hile many models have been developed relating ConclusionsThe group solution model presented gives a reasonable representation of liquid mixtures containing the Manuscript

The diffusion of various inert and of hydrogen-bonding solutes into aliphatic alcohois was considered. The diffusivities of benzene, p-dichlorobenzene, biphenyl, and triphenyl methane in methanol, ethanol, n-prapanol, n-butanol, n-pentanol, and n-heptanol were measured a t 25°C. for low solute concentrations. An equation was developed for the limiting values of the binary mutual diffusion coefficient in complex-forming mixtures. This equation, used in conjunction with the Wilke-Chang correlation, gave a considerable improvement over existing predictive methods for the diffusivity of inert solutes, mono-and polyhydroxy olcohols, and water in aliphatic alcohols. alcohols, and for water. The experimental data were taken from Tables 1, 2, and 3. The association parameters for methanol and ethanol were taken as 1.9 and 1.5, respectively (1 ) . From Figure 1 it can be seen that the predicted diffusivities for inert solutes are consistently low, often by more than 20%. On the other hand, the predicted diffusivities for mono-and polyhydroxy alcohols and water are always higher than the observed values. This is so because hydrogen bonding between solute and solvent hydroxyl groups tends to retard the diffusional motion of these latter types of solutes-a factor which is not taken into account in the correlation.Thus the Wilke-Chang equation, which was developed using data for at1 types of solutes ( I ) , performs best for mixtures where moderate solute-solvent interactions are present. However, where interactions are either fairly weak or very strong, this equation can give large errors in the