Thickening operation consists of three major processes, -classification in settling, flocculation of suspended particles and simple thickening, the last of which should be considered independently of the other two. This presents a difficulty in analyzing the experimental results, which give them in mixture.
In order to solve the problem, simple thickening and classification in settling were treated separately. In this way, theoretical analysis and the presumption of the behavior of flocculation were made possible to some extent, by making a comparison of these theoretical results with the experimental data.
As the results of our recent study of the improvement of the structure, the flow pattern of the industrial thickeners, which had been too complicated for the results of the theoretical analysis to be applied to, was simplified, and the results of the theoretical study became applicable to the calculation of practical thickening operation.
Basic problems in simple thickening were studied from the viewpoint stated above, and the results as given below were obtained.
1) The graphic methods for predicting the behavior of batch settling obtained empirically by Work-Kohler and Yoshioka-Hotta-Tanaka were verified and explained theoretically.
2) The physical conception of compression point on the batch settling curve was modified.
3) The essential difference, in kinematic mechanism, between batch and continuous thickening was proved.
4) The elementary calculations for the scheme of thickening process were set forth.

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(1) An easy and reliable method for determing the diffusivities of CO₂ in liquids was obtained from the experiment in which the so-called bell-shaped nozzles as shown in Fig. 2 and the jet-receiver calibrated in degrees of absorption were employed, while the pressure in the absorption chamber was held as high as 2-3mm H₂O.
(2) To practice the above method, the stationary range of the jet, i.e., the minimum jet length (l_min) and the maximum jet length (lmax), was determined as in Figs. 6 and 8 and lmax/d was confirmed to be proportional to We^0.5.
(3) The diffusivities of CO₂ in glycerine and cane sugar aqueous solutions were measured. The results shown in Figs. 9 and 11 proved to be in good agreement with the values obtained from the correlation of Othmer & Thakar, ¹³⁾ by calculation.
(4) The diffusivities of CO₂ in ethanol were measured in the temperature range of 6.4-20°C. The results are shown in Figs. 12 and Table 1.
(5) The diffusivities of CO₂ in NaOH and KOH solutions were measured at 20°C. The results are shown in Table 2. Their values of DLμ are mostly constant and accord with the value (1.79×10^-5cm²·c.p./sec) in H₂O.
(6) Dependence of the concentration of CO₂ on the diffusivity of CO₂ in H₂O was investigated at 20°C. The results are shown in Fig. 14.

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As the expression of the vertical pressure in columns of powders, Janssen's equation has been accepted. But as previously pointed out by Shaxby, the static pressure in the powder bed is a function not only of the depth but of the state of packing. In this paper many factors which affect the vertical pressure of non-cohesive granular matcrials packed in the cylindrial vessel are discussed.
The values obtained by the measurement of the powder pressure differ greatly according to the state of packing. In the state of packing which is characterized by the state of powder bed just beginning to slide down the vessel, and where the balance method, illustrated in Fig. 3 is employed, the values obtained are somewhat lower than those obtained in the case which is characterized by the vertical pressure of the bed in the completely static state and where the gauge method, consisting of diaphragm and strain gauge as shown in Fig. 5 is employed. In the case of loose packing formed by rapid pouring of the material, the vertical pressure of the bed in the static state is lower than that of the closely packed one, formed by gradual accumulation of particles. On the other hand, in the state of powder bed just beginning to slide down, the relation of vertical pressure is reverse to the above.
Consequently, Janssen's equation may be used only to estimate the approximate vertical pressure, because the tendency to form an arch is some cases of packing, including that of the non-cohesive materials, contributes markedly to lessen the pressure, especiany in the case of balance method.
As the result, the authors have come to the following conclusion:
(1) Janssen's equation should be rewritten as follows, where the factor α is taken in.
(2) The factor α is a function of the kind of material, of the diameter of the cylinder, of the state of packing and of the method of measuring. When the standard sand is used, the dfect of cylinder diameter on α is negligible but the effect of the state of packing on it is remarkable, as shown in Table 2. Hower, in the case of millet and rape whose shape factors are each nearly equal to l, the effect of the state of packing is small and α varies with the diameter of the vessel, as shown in Table 3.
(3) The values obtained by the balance method are useful for handling the problems of the granular material flowing out through the bottom of the vessel or at the arch formed in the vessel, while the values obtained by the gauge method should be used for calculating the strength of the vessel and the particles.

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