An empirical equation for specific surface of several ceramic materials brought about by permeation method is obtained by correlating two constants k and n with each other, generally used in the Rosin-Rammler's exponential law:
From the computation of the lower limit value of size distribution of powder for wider ranges of fineness, it is pointed out that the exponential law, generally accepted for ball mill grinding, is never essential but only apparent, and that the correct one should be expressed as a "reversed-S-forming" curve on a log-log plot.
The reversed-S-form distribution shows that the fundamental mechanism of comminution could be classified into two types, which are termed "uniformity-Grinding" and "Probability-Grinding, respectively.
The physical explanation of the "Comminution Coefficient", formerly proposed by the author, is given qualitatively by means of the different mechanisms of development of cracks or fissures through a solid structure which occur as a result of different stress distribution, depending on whether the force acting is normal or tangential.

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Original data have been obtained on various factors that should be considered for the design purpose of multiple fluidized beds, by the authors observing the performance of the triple beds unit in a 7cm. I.D. tube equipped with visible glass sections. This work is divided into two parts, one dealing with critical conditions on which unstable states take place, the other with fluidization under a stable state.
Any local irregularity in the flow of fluidizing medium into the downspout would tend to cause a change in steady state operation, but this change can be reduced by inserting an orifice-type plate at the bottom of the downspout.
Variations of values of dimensionless ratios, (a'/a) and (l/l'), affect definitely the value of the critical Froude number of particles on which slugging, caused by air by-passing in the downspout, occurs. Probably the most satisfactory expression concerning phenomena of slugging in the downspout is given in Eq. (1).
In order to maintain the steady effluent of particles from the downspout, the maximum diameter of a particle which can be employed must be smaller than d'/6, approximately.
From the experiments conducted to determine the boundary condition on which the clogging of the downspout, caused by the increase in the solid rate, occurs, it is recognized that the solid rate in the gravitational flow of particles from the orifice may be substituted for this critical rate, and an empirical equation for a powder orifice is derived, as Eq. (3).
The increase in the height of the downspout projecting above the plate increases the pressure differential across the plate, and when ΔP_i>(ΔP_b)_sl, the slugwise motion on the plate occurs.
Suitable sizes of d, d', l and l' can be determined by the use of these boundary conditions.
The approximate height of the solid column in the downspout may be calculated from the various factors contributing to pressure differentials in the flow paths according to Eqs. (7) and (8).
Attempts to correlate the bed density in continuous and batch fluidizations by using our results plus other data have found expression in Eq. (10). For usual operating conditions the bed heigkt may be represented by Eq. (11).
By the use of Eqs. (7) to (11), we can determine the magnitudes of the total length of the downspout and the plate spacing.

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[in Japanese]

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