Isothermal vapor-liquid equilibrium measurements were made at 50°C. for the ternary systems acetone-methanol-chloroform, acetone-methanol-carbon tetrachloride, and acetone-methanol-methyl acetate, by means of an improved vapor-recirculation type of apparatus. The complete range of concentrations was investigated, including six of the seven constituent binary systems. Chemical methods, supplemented by density and refractive-index measurements, were used for analysis.Results are presented in the form of activity coefficients Y as a function of various concentrations. Binary and ternary constants for the three-suffix Margules equations were determined by plots of (log y ) / ( l -x ) a as a function of the mole fraction x. Such equations have been found to represent both the binary and the ternary data adequately except in the system containing both methanol and carbon tetrachloride. For these mixtures a simplified four-suffix equation, including a single ternary constant, correlates binary and ternary equilibrium data.The data indicate that reliable estimates of ternary equilibria can be based on the assumption that the ternary constant C* is zero for mixtures in which all deviations from Raoult's Law are positive. This is interpreted as indicating that the probability of existence of trimolecular aggregates, two-or three-component, in ternary solutions is no greater than the average of probabilities of existence of trimolecular aggregates in the constituent binary systems. Based on equations of the Margules type, a procedure is outlined for determining binary constants rapidly and for planning experiments whereby a ternary system may be completely investigated with the aid of very few measurements.The composition changes that the accompany differential distillation of the three ternary mixtures are described qualitatively in terms of the shape of the vapor-pressure-composition surfaces.

X x = Martinelli momentum transfer parameter [ ( d P / = mole fraction solute in liquid, dimensionless = mole fraction solute in gas, dimensionless d2) L / ( d p / d ) G] l ' ' , dimensionless y y* = composition of vapor in equilibrium with annular liquid; defined by Equation ( 6 ) , dimensionless p p Subscripts u = annular liquid film e = entrained liquid G = gas phase L = liquid phase LITERATURE CITED = fluid viscosity, lb. mass/(ft.) (hr.) = fluid density, lb. mass/cu.ft.

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A theoretical study has been mode of longitudinal dispersion mechanisms during steady flow of o fluid through unconsolidated spherical beads. The mathematical model utilizes a step function input of thermal energy and presents the solution for the transient behavior of the system. The longitudinal dispersion of the step input is considered the result of eddy mixing of the fluid, molecular conduction within the fluid, and a finite time log for heat transfer to occur between fluid and particle. The latter mechanism is characterized by both a fluid film resistance and on intraparticle resistance. The exact solution, involving on infinite integral,

The U n iv e r sity of O klahom a, P h.D ., 1964 E n g in eerin g , c h e m ic a