The authors have obtained the vapor-liquid equilibrium relations in multi-component systems, assuming completely random mixing for molecular distribution and molecular configurations having pairs in liquid phase called the zeroth approximation. The final result obtained with respect to γ_i is as follows:
RTlnγ_i=Σpx_p(1-xi)ω_ip(i p)-Σpqx_px_qω_pq(p q pq i)
The above relation gives an equation similar to Margules' formula of type 2-suffix as wei 1 as to van Laar's formula of type 2 suffix: A_i-j=A_j-i=A_ij, which can be transformed into Aij=ωij/2, 3RT. The result obtained presumably holds well in case L_i⁰=L_j⁰ or L_i⁰≅L_j⁰, where i is 1, 2, ……, n, and symmetrical systems.
Analysis of the multi-azeotrope by means of the equation thus obtained gives the following results:
i) In multi-azeotropes, the following relations must hold:
-ω_ijΔS_j^-1≤T_i⁰-T_j⁰≤ω_ijΔS_i^-1
ii) The values of ω_ij are constant when the components keep homologous series to one another.
iii) Azeotropic compositions x_i are given by linear functions of T.

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Physical properties of some hydrocarbons as separating agents in the dehydration of sec-butanol by azeotropic distillation were studied. Hydrocarbons used in this experiment were iso-octane, n-heptane, methylcyclohexane and two special fractions of gasoline.
Solubility curves of each of the three component systems at 20°C and 40°C were obtained, and the vapor liquid equilibria of the systems-sec-BuOH-water, sec-BuOH-iso-octane, sec-BuOH-n-heptane, and sec-BuOH-methylcyclohexane-were determined. Boiling points of hydrocarbon-water systems may be calculated from the vapor pressure data and the boiling point of each component.
Azeotropic concentrations of the systems-sec-BuOH-water-iso-octane, sec-BuOH-water-n-heptane, secBuOH-water-methylcyclohexane-were determined as listed on page 637, 638.
The result of the investigation suggests that a mixture of hydrocarbons may be used as a separating agent. Two special fractions of gasoline were tested and their batch distillation curves were obtained as given in Fig. 8.

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I. On the stational drying conditions:
The drying rate curves for various materials and methods from which Eq. 1 is derived are shown in Figs. 1-4. It is clear from these that the decreasing drying rate of granular material is proportional to the water content of the material. The heat transfer between air and material is shown by Eq. (2). When the temp. gradient of the material is negligibly small, Eq. (3) is obtained. As shown in Figs. 5 and 6, the temp. gradient can be neglected for the granular material whose diameter is below 2-3mm. Eq. (4) derived from Eqs. (1) and (3) may be solved numerially, e.g., by Runge-Kutta's method. When the sensible heat of water (wc·cw) contained in the material is small as compared with the specific heat of the dried material and r_m≅r_w, Eq. (5) can be solved analytically:(6)In case (w_c·c_w) has a value comparable to the specific heat of the material, Fcrw/(c+cww )(t-tw)>>1 and r_m≅r_w, the following approximate equation, Eq. (8), can be obtained.
(8)
Eqs. (6) and (8) give the relation between tm and w.
II. On the unsteady drying conditions:
The unsteady drying which takes place in a continuous (parallel or counter current) dryer, such as a rotary, pneumatic conveying, spary or fluidized-bed dryer, can be presented by Eqs. (9)-(12). From these are derived Eqs. (13) and (14), whose solutions show the relations among t, tm and w in the dryer.
These equations could be solved numerially. The calculated examples are shown in Table 1 and Figs. 9 and 10.
The drying rate and the drying time in the continuous adiabatic dryer which can be easily calculated by using these relations may help to decide the dryer volume.
The application of this calculation method to the dryer design would be expatiated upon in our report.

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The over-all decontamination factor in the evaporation of radioactive liquid in a natural circulation evaporator reported in the previous paper indicated some disagreement with that obtained by Monowitz et al. The present paper deals with the decontamination factor in an evaporator, a pipe line and a cyclone, pertaining to the pilot plant mentioned in the previous report. According to our experiment, the decontamination factor in the evaporator proves to be mostly independent of the height of vapor space (0.6m and 1.1m, respectively), as shown in Fig. 3. Theoretical calculation from the jet velocity at which a single gas bubble bursts also demonstrates the results obtained experimentally. The results of the studies made on the decontamination factor in the pipe line and the cyclone are shown in Figs. 5 and 6. In our further studies conducted on the system consisting of an evaporator, a pipe line, a cyclone, a glass-fiber-packed tower and a condenser, the over-all decontamination factor ia found to be between 10⁷ and 10⁸. The drag coefffiicient of the glass-fiber-packed bed proves to obey the Langmuir and Iberall's equation.
The decontamination factor without downtake indicates approximately the same value as in a natural circulation type evaporator, when the mass velocity is large. However, the mass velocity at the maximum decontamination factor is larger than in the natural circulation type. Fig. 9 shows the decontamination factor without downtake.
The results obtained by us with the evaporator are, as summarized in Fig. 10, in good agreement with those of the experiment by Monowitz et al, which was conducted in a large scale evaporator. However, taking into consideration the presence of demisters which are usually installed in an industrial scale equipment, the mass velocity at the optimum over-all decontamination factor may be set within the range of 2, 000kg/m²·hr to 3, 000kg/mm²·hr.

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This article refers to the adsorption equilibrium of binary liquid hydrocarbon mixture, i.e. toluenen-hexane by silica gel or activated alumina, studied by means of the direct liquid contacting method. From the experimental data on the adsorption equilibrium were calculated the separation factor, α, in Eq. (1') and the volume of the liquid adsorbed by a gram of adsorbent or the volume of adsorbed phase, z, in Eq. (5).
The results obtained were as follows:
(1) z which was constant over the wide range of liquid concentration for each adsorbent was affected considerably by the preparation temperature.
(2) α, a characteristic constant for each adsorbent, i.e., 14 for silica gel and 7.3 for activated alumina, was not affected by the preparation temperature.
(3) x-y Diagrams calculated by using α in Eq. (1') was in good agreement with that calculated by using z in Eq. (4'), as shown in Fig. (6).

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