Laboratory scale ball mill tests were carried out with 3 kinds of binary mixtures of potasiumdichromate with silica sand, with dolomite and with limestone of the same initial size. These materials are supposed to be of the same density and of similar shape of particle and have different values of Hardness from that of potasium-dichromate. The latter in the specified amount of the sample taken after each 5 minutes interval run was separated by dissolving, washing and filtering from the other material, from whose specific surface and weight the specific surface area of dissolved potasium-dichromate and the variation in the mixing degree of the system can be calculated.
Five ideal models for preferential grinding were proposed, whose empirical data showed that, in general, depending upon “Relative Hardness” which was tentatively defined as the ratio of Mohs' Hardness, there was a definite ratio of particle sizes between the harder and softer constituents, where only the harder material became crushed selectively. This critical size ratio was practically correlated with mass ratio and Relative Hardness, and was found to depend upon the grinding “Probability, ” not upon the orientation of the acting force.
The degree of preferential grinding η was quantitatively defined and its numerical values based upon empirical results showed that η varied periodically with grind-time, ranging from zero to unity, whose magnitude and frequency appeared to depend upon the mass ratio of each component and upon Relative Hardness.
Pursuing the variation of the critical size ratio at the introduction of the grinding probability, a quantitative conclusion was obtained as follows: the critical size ratio should change with time duration as shown in Fig. 10, depending on the probability P. From this pattern, it is suggested that the crushing machines having larger probability and longer residence time would be of great use for the purpose of obtaining comparative uniformity in the finished product.

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The axial mixing characteristics of gas and liquid flowing through gas-liquid packed beds (in which bubbles rise up through a descending continuous liquid phase among packings), and liquid packed beds (through which liquid flows through packings without gas flow) are determined, by employing the methods of the transient response and the frequency response.
The transient response curves of gas or liquid, obtained experimentally were plotted against (√τ-1/√τ) on normal probability papers, after having eliminated the end effects. Then, the straight lines were obtained, as suggested by Eq.(9). From the slope of the line, M=uL/2E or Pe=d_pU/E were determined for each run. On the other hand, from the frequency response curves, the ratio of inlet to outlet amplitude and the phase lag of the sinusoidally-varying acid concentration were determined, and M and Pe were calculated, according to Eqs.(12) and (13).
Dimensions of the experimental apparatus used and a range of variables studied are as follows:
Tower; 10.0cm I. D., 110cm height
Packings; 1.0, 1.5, 2.0cm ceramic Raschig rings
Gas (air) flow rate;0-10l/min
Liquid (water) flow rate;0.45-11l/min
Period of concentration wave; 63, 127, 253 sec
Tracer; He, HCl Under these conditions, the experimental results indicate that
i) The velocity of rising up and the mixing coefficients of bubbles in liquid packed beds are kept constant and independent of the gas flow rate.
ii) In liquid packed beds, the Peclet number for liquid, (Pe)_L, increases slightly from 0.65 to 1.3, as the Reynolds number for liquid, (Re)_L is increased from 100 to 2000, as illustrated in Fig. 5.
iii) In gas-liquid packed beds, the Peclet number for liquid varies over a wide range, as a function of the liquid flow rate and independent of gas flow rate. The generalized correlation for it is given by Eq.(20)

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The rate of approach to equilibrium of a packed distillation column with finite hold-up of liquid in the still was analysed in a case of top liquid feed, top vapor discharge and no reflux liquid. From the strict results, the following simplified approximate solution was derived.
(23) where
This equation means that the time required for 99% approach to equilibrium is proportionate to the amount of liquid hold-up in the still and is inversely proportionate to the rate of liquid flow. Prerequisite conditions for the derivation of approximate solution were summerized in Eq.(26) and Eq.(27).
An experiment of the enrichment of heavy water in the flow sheet shown in Fig. 5 was conducted under atmospheric pressure. The calculated values by the use of approximate equation showed a fairly good agreement with the observed values, as shown in Fig. 6 and Fig. 7.

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Knowledge concerning the location of azeotropic points is essential for the quantitative design of azeotropic distillation apparatus. In most cases of azeotropic distillation the ternary systems are employed. Some of them have a ternary azeotropic point. Recently J. Holl proposed a method by which the ternary azeotropic saddle point can be found semiempirically. Using three binary vapor-liquid equilibrium data, P. J. Horvath tackled this problem theoretically.
Before performing these works it is therefore useful to know previously the range of existence of the ternary azeotropic point. In the case of a system which has three binary azeotropic points, the following method is presented to predict the range of existence of the ternary azeotropic pointusing the Ewell's liquid classification.
Connecting three binary azeotropic points in a ternary system as shown in Fig. 1, four triangles are formed; that is, triangle II_A III_A, indicated as [I], triangle II I_A II_A as [II], triangle III II_A III_A as [III], and triangle I_A II_A III_A as [IV], where I, II, and III refer to each pure component and I_A, and III_A to binary azeotropic points. The position of the ternary azeotropic point is classfied II_A into the following three cases; in the triangle IV (Case A), on the side of the triangle IV (Case B) and outside of the triangle IV (Case C).
Using the data from literature, the above classification of 42 ternary systems are made and shown in Table 1. Most systems belong to Case A. Case B and Case C are comparatively few and further classification of these cases are carried out in Table 2. In Case B the location of azeotropic point is on the base of the triangle whose apex has the lowest number in Ewell's classification or is related to the component of the strongest hydrogen bonding ability.
In Case C these points are lying within the triangle whose base is formed by the triangle [IV] and whose apex has the lowest number in Ewell's classification. Furthermore in this case points are near the base of that triangle.
The above are based on the composition triangle of weight fraction and the same is true for the case of mole fraction. This fact can be proved mathematically.

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Narrow-cut spherical particles are often desirable for handling solid materials in chemical process and other industries. This paper deals with the granulating operation to solidify dispersed droplets. of fused materials in air flow. The schematic diagram of experimental apparatus is shown in Figs.(1) and (2). The operating condition covered the range of nozzle (straight pressure type) diameter from 0.48 to 1.25mm, and that of discharge pressure from 0.1 to 5.0Kg/cm².
The results obtained are summarized as follows:
1) For the straight pressure nozzle as shown in Fig.(2), discharge pressure is correlated in Fig.(3) and can be calculated from equations (2) and (3).
2) Mean droplet diameter is calculated from equations (6) and (7).
3) Examples of relation between size distribution curve and discharge pressure are shown in Fig.(7). The log-probability function fits well the data as shown in Fig.(8).
4) The time necessary to cool and solidify dispersed droplets can be found from equations (22), (23) and (24) assuming constant air temperature. Experimental data and calculated results are shown in Table 3.

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