In our previous paper, ⁴⁾ a report was made on the adsorption equilibrium (x-y diagram) of binary liquid hydrocarbon mixture, i.e., toluene-n-hexane-silica gel system, and on the separation factor, α, in Eq. (1) which was determined, based on the constant adsorbed phase volume, z.
This paper deals with the adsorption fractionation of binary liquid hydrocarbon mixture with the constant separation factor, α, and adsorbed phase volume, z.
The results obtained are as follows:
(1) Based on the material balance given by Eq. (2), which is analogous to Vermeulen's constant pattern, ³⁾ the second stage-fractionating curve may be represented by Eq. (5) or (6), where t_s' is given by V(1-x₀₁)/l and xs can be calculated from Eq. (8) or (9).
(2) Experimental results obtained with toluene-n-hexane-silica gel (desorbent-methanol) system are summarized in Table 1. As shown in Fig. 3, curves derived from Eq. (17) give a good x-t' correlation over a wide range of x. Rate coefficient K_s can be determined by Eq. (18) from the observed half-point slope (dx/dt')_x=0.5.
Rate coefficient for the first stage-fractionating curves as summarized in Table 2 have been calculated using Eq. (19) from the observed half-point slope, (du/dt')_u=0.5. Curves obtained from Eq. (12)' are in good agreement with the observed results as shown in Fig. 8.
The above-mentioned K_s for the first-and-second stage fractionating curves are plotted against the liquid flow rate, 1/S. In Fig. 9, these show approximately good agreement with each other.

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Mass-transfer process on a tray has been discussed theoretically, together with the influence of longitudinal dispersion of vapor (gas) and liquid phases. Reducing the overall mass-transfer behavior of the system to that of a continuous flow system with a homogeneous first-order rate process (Eqs. 7-10), a general relation has been derived to give the rate of mass-transfer (Eq. 15) and the tray efficiency (Eq. 18). In the derivation, the concept of a "model" has been eliminated entirely. (Sect. 1).
From this general standpoint the theories presented previously by various authors have been proved to differ from one another only in the process of approximating E_x(φ) included in Eq. 15, by an alternative function of φ obtained from the behavior of a proper model adopted. All these theories developed before have been generalized, applying suitable functions for E_x(φ). It is concluded that three kinds of figures as stated in 1-5-B are enough to determine the tray efficiency to include the combined effect of longitudinal dispersion of each phase and other variables. (Sect. 2).

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In previous papers, the relation between the decontamination factor and the boiling condition in evaporation was discussed. For industrial use, however, the apparent decontamination factor by evaporation has been considered more important than the actual decontamination factor.
In this paper, the actual and the apparent decontamination factors are given by Eqs. 1 and 2, respectively. The relation between the actual and the apparent decontamination factors by various evaporation processes has been studied, too. The equations obtained are as follows:-
I. Single stage evaporation (Cf. Fig. 1)
II. Multi-stage evaporation (Cf. Figs. 5 and 7)
Comparison of various operations in a single evaporator is given in Table 1. In an extreme case, it is found that the exponent of the apparent decontamination factor is reduced by nearly 2.

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To obtain information concerning residence time of particles in fluidized bed, the effects of gas velocity on hold-up and concentration of smaller-sized particles in fluidized bed were observed and the following results were obtained.
1) Particle hold-up in bed decreases as gas velocity increases. (See Fig. (a)-(c)). Specific contact area is correlated to modified Reynolds number, as shown in Fig. 4 (a) and (b).
2) Fluidized bed consisting of particles of two sizes tends to give a higher percentage of coarse particles than that given by the feed. This tendency becomes remarkable with the increase of gas velocity and decrease of feed rate, as shown in Fig. 5 (a). But it diminishes in case the fluidized bed is placed higher than L, the height of overflow pipe, as seen in Fig. 5 (b).

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