In our previous papers, we reported on the optimum operating conditions of several types of mixers, [twin-shell (V^-), double-cone (DC^-), cubic (C^-) and horizontal-cylinder (HC^-) types] for one pair of dry powders, Na₂CO₃-polyvinyl chloride.
In this paper, we make reports of our examination of the influences of the physical properties of powders upon the mixing degree and mixing speed of several types of mixers, as to several powders shown in Table 2 and several pairs of powders shown in Table 1.
What were made clear by our experimental results are:
1) With the same type and size of mixers, the optimum rotational speed of the mixer N_op(=N_s, σ) and the charged volume of the powder (F_b/V)_op are constant for all pairs of powders having the same particle size distribution (as shown in Table 1).
2) The influences of the physical properties of powders upon the mixing degree and mixing speed are described by the difference of characteristic constant C_R (obtained by Equation 7 or Fig.
3) of both powders
a) As ΔC_R increased, the values of σs increased as shown in Fig. 7.
b) As to the mixing degree, V^- & C^-type mixers are not suited to the mixing of the powders whose ΔC_R is big, while HC^- & DC^-type mixers are recommendable for the mixing of the powders whose ΔC_R is big.
c) As to the mixing speed, a good mixing speed is expected of V^- & C^-type mixers for the mixing of the powders whose ΔC_R is big, as shown in Fig. 7 and Table 3.

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Following the previous studies17) on the distillation of the benzene-toluene system in a packed column, experiments were performed for the purpose of studying the effects of operating variables on the distillation of systems as well as the difference in the column performance due to the kinds of systems employed. The apparatus used was the same as in the previous studies, and the systems employed here were methanol-water and ethanol-water systems. The column was 15cm in inside diameter and was packed to a height of 54cm. It was operated as an enriching section and at total reflux. The HOG and KLa values obtained are shown in Figs. 1 and 2. From these figures and others, which are not shown here, it was concluded that both vapor and liquid phase resistances to mass transfer cannot be neglected.
H_P (H.E.T.P.) values were also calculated for all the runs, including the previous data¹⁷⁾ on the benzene-toluene system. The ratio of H_OG to H_P can be fairly well represented by the known Eq. (5), if the average slope of the equilibrium curve, m, as defined by Eq. (3) or (4) is substituted for m in Eq. (5). In general, so far as H_G and H_L are nearly equal, the variation of H_P values with the change of mG_M/L_M is smaller than that of H_OG or H_OL values. This is obvious from Figs. 4 and 5, in which H_P values are plotted against the liquid mass rate, L, with gas mass rate, G, as a parameter. For instance, comparison of Figs. 1 and 4 clearly shows the smaller variation of HP values. Thus, it can be said that H_P is a more practical criterion than H.T.U. for designing packed distillation columns.
H_P values vary with systems, but no general correlation involving physical properties of the systems was obtained.
Experiments were also made for the comparison of the performance of various packings. 25mm and 15mm Raschig rings, 25mm and 12mm Berl saddles, and 25mm and 15mm coke packings were tested. The comparisons between these packings are shown in Fig. 6. For a given type of packing, the HP values are roughly proportional to the 1/3 power of the size of the packing. For a given size, the coke packing shows the lowest HP values, and the difference between Raschig ring and Berl saddle is negligible. The coke packing gives the highest resistance to vapor flow, while Berl saddles show the lowest pressure drop. However, the pressure drop per theoretical plate for coke packings is nearly equal to that for Raschig rings. The Berl saddle has the merit of low pressure drop, while the coke packing has the advantage of very low cost. For the performance of coke packings, refer to the paper by Yoshida and Koyanagi¹⁶⁾.

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Changes in the concentration of a fluid stream and in the bed of adsorbent, where a process of adsorption proceeds intermittently, present formidable difficulties in the mathematical calculation of adsorption, and a practical solution for general use has not yet been arrived at. Under the assumption that the equilibrium-state adsorption is directly proportional to the concentration of the fluid, the author suggests a new approach to the solytion by using differential equations describing the unsteadystate adsorption in stationary packed beds. The final differential equation is shown by Eq. 16, which, when solved numerically, gives Eq. 18.
Eagleton's and the author's experimental data for typical runs showed good agreement with the results obtained from Eq. 18, as presented in Figs. 2 and 3.

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The work required for crushing or grinding a given amount of material may be expressed by the amount of energy of the nature of statical and dynamic compressions given to said material, the work shown by the area of stress-strain diagram multiplied by the volume of the material But this is not the net work required for crushing the material into fragments or separating it into small pieces. It would be proper to consider the net work to be proportional to the magnitude of the increased surface of the crushed material.
Whereupon, the author derived, theoretically, the following equation as an expression for the net work expended during crushing: A_r=C log A/C in which A is the energy applied, Ar the net work performed and C a constant for the given magnitude of the material. From this, A=Ph, where P is the weight of the falling hammer and h the height of fall. Consequently, P^*h=C·(P^*<P). This is the work necessary for reducing the material to the desired particle size.
Again the author obtained an expression showing a relation between the net work required for crushing a given amount of material and the number of blows of the falling hammer, as follows:
A_z=A_1z^e-(z-1)/zm
where A^z stands for the net work which the z th blow imparts, and z^m the number of the order of blows at which the maximum net work is given. This equation shows good agreements with the results of the experiments by many investigators as well as by the author.

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Mass transfer rates from solid particles to water in packed bed were measured for spherical and cylindrical β-naphthol particles.
Data at low water velocities show that Sh tends to approach 2.0 with decrease of R_ep, as shown in Fig. 2. The effect of Sc on Sh was examined and plotted as in Fig. 4. It was found that Sh-2 was proportional to Sc^1/3.
The present data and the previonsly published data of other investigators for spherical and cylind rical particles are shown in Fig. 5. The solid lines drawn in the figure correspond to the equations:
(3)
(4)
The data for flakes¹¹⁾ and broken solids⁴⁾, which are shown in fig. 6 for the experimental range of R_ep>1, agree with the results obtained from Equations (3) and (4).

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The mixing characteristics of the fluid flowing through reactors are industrially important for the purpose of designing reactors and estimating the yield of the product. Recently several studies have been made on the mixing characteristics of the homogeneous and heterogeneous reactors. These mixing characteristics usually cover the field of turbulent diffusion whose coefficient is obtained on the assumption that the turbulent mass diffusion is superimposed on the convective flow with the uniform velocity.
Studies on fluid mixing in the fluidized bed were made by Wilhelm et al for the liquid-solid system and by Gilliland et al for the gas-solid system. Wilhelm et al⁴⁾ measured the turbulent diffusion coefficient by measuring the spreading of the methylene blue dye from a point source in water-fluidized bed of glass beads. Gilliland et al carried out the diffusion experiment on helium gas from a point source²⁾, and employed the technique of the residence time curve³⁾ for the fluidized bed of gas-solid system.
The present authors have obtained the axial turbulent diffusion coefficients by measuring axial concentration gradients in the water-fluidized beds of β-naphthol cylindrical particles.
When the concentration in the bed is very small as compared with the saturation concentration, the dissolution rate approximates to the zero-order reaction as expressed by Equation (1'). By using the boundary conditions at the inlet and outlet of the bed, that is by using Equations (2) and (3), Equation (4) can be derived from Equation (I').
The experimental apparatus used for this work is shown in Figure 1. The inside diameter of the column is 52.1mm. City water is used as the fluid. The water, before entering the fluidized bed, passes through the calming section of fixed bed packed with glass beads. The water in the fluidized bed is slowly taken out by means of the injectors thrust along the tube wall at intervals of 5cm. The concentration of this water is measured by the spectrophotometer at the wave length of 2, 735 A and 2, 850 A.
From the measured concentration gradients, the axial diffusion coefficient Ez is calculated with the help of Equation (4) at three points: η≡l/L=1/4, 1/2, 3/4.
The results derived are presented in Table I, Figures 2 and 3. Figure 2 shows the relative axial Peclet number (Pe=D_pμ₀/E_z) plotted against fractional void ε, and the relative Pe vs. Rep is shown in Figure 3. From these figures we know that the turbulent diffusion coefficient Ez increases with the increase of fractional void and reaches the maximum value of about 70cmcm²/sec in this system.

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