In our previous papers, we reported that all mixing curves, even of different shapes of mixers under different conditions, had similar features, and that each of them might be divided into three regions, I, II, and III, as shown in Fig. 1.
In the present paper, we analysed the mixing curve and discussed the effect of various factors on the coefficient of mixing velocity, φ, given by Eq. (1) which was obtained from the slope of the mixing curve in region II mentioned above.
Experimental results obtained are summarized as follows:
(1) Even if the shape and the working capacity of the mixers, as well as the combinations and the particle size of powders, were different, the plots of φ vs.N showed similar curves and gave the maximum values φ_m and (N)φ_m for all cases, as shown in Figs. 2-a, 3-a, 4-a and Eq. (2).
(2) Furthermore, the plots of φ vs. F/V gave a straight line which had various negative inclinations, though it was not applicable to the horizontal cylinder type mixer, as shown in Figs. 2-b, 3-b, 4-b and Eq. (3).
(3) The results obtained might be summarized as in Eq. (5); the experimental coefficients in Eq. (5) had different values depending on the operating conditions, as tabulated in Table (1).

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Using the apparatus shown in Figs. 1 and 5, we studied the torque characteristics of a paddle-type solid mixer. The materials used were Toyoura and Soma standard sands. Their particle size distribution and other properties are shown in Fig. 2 and Table 1, respectively. Typical data on agitating torque of the paddle blade are shown in Figs. 7 and 8. Torque curves are divided into four ranges, according to the speed of the blade as illustrated in Fig. 9, where, ranges B and C are important in practical use.
In range B, the whole upper part of the particle bed (part (1) in Fig. 12) is rotating slowly and the torque becomes the least throughout the whole revolution.
While, in range C, as the result of the increasing speed, the effect of the centrifugal force appears and the upper part of the particle bed moves in a manner similar to that of liquid in a tank agitated by a flat blade paddle with no baffle.
For range B, assuming the motion of the upper part of the particle bed to be a rotating motion of solid body, the equations of the theoretical torque T_L0 and actual torque T_L are obtained as follows:
For range C, by use of the pump theory, the effect of centrifugal force is introduced and the following equations are obtained:

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A new apparatus for determing vapor-liquid equilibria of miscible mixtures is designed and is illustrated in Fig. 1. It is a modification of the Othmer's still, but differs practically from this in that the volume of liquid in the overflow vessel below the condenser can be changed in six steps. This feature enables us to take six point-measurements, at the maximum of vapor-liquid equilibrium from one single feed of original mixtures, as shown in Table 2 and Fig. 3.
To determine the dependability of the still, two kinds of mixtures are selected, one of which, i.e. methylethylketone-toluene, nearly obeys Raoult's law, while the other, i.e. methanol-toluene, greatly deviates from the ideal behavior. The agreement of the new data with those in literature shows that the new equilibrium still yields reliable results.

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Ribbon-type mixers, one of the fixed-type mixers, havc been employed in various industrial processes, but few experimental studies are reported on them.
We studied the performances and the operational conditions of this type of a mixer, and, using the coefficient of mixing velocity φ, analyzed the results obtained.
The powders used were of two-component system, Na₂CO₃-sand, of four different particle sizes.
The degree of mixing was defined by means of the standard deviation σ.
The results obtained were summarized as follows.
(1) The mixing curvebtained of the ribbon-type mixer were similar to those of the rotational-type mixer, i.e.a twin-, a double-cone and a cubic-mixer, as shown in Fig. 3. Therefore, we might consider that the mixing processes were fundamentally similar with both the types of mixers, though in the case of the ribbon-type mixer, the first stage of mixing curves were different from that in the case of the rotational-type mixer, as shown in Fig. 3.
(2) In the ribbon-type mixer the influence of the rotational speed on the number of revolution required was smaller than in the case the rotational-type mixer.
(3) The optimum volme ratio of charged powder to inner volume of mixing vessel (F/V)_op. was about 17.3%, as shown in Fig. 5 (a), (b) and (c), corresponding to about 40% of appearent volume ratio of the powder.
(4) As particle size increased, the velocity of mixing increased, with the degree of mixing, σ, becoming larger, as shown in Fig. 6 (a), (b) and (c).
(5) The influences of the rotational speed, charged volume ratio of powder and particle size on the coefficient of the mixing velocity might be expressed by an empirical equation (4).

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