This paper deals with the influence of the structure and shape of the vcssel and pipe line on the fluidization quality of fluidized bed as it is investigated by the author.
The quality of fluidized bed was measured by means of non-uniformity index (fluidization index) proposed by W.W. Shuster. As the result, it was found out that the arrangements of the holes in the bottom plate of the bed and the length of the pipe line had a considerable influence on the quality of fluidization, and that divergent type reaction vessels had better quality than ordinary cylindrical ones.

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Many studies have been made toward, though indiiectly, the quantitative evaluation of heat and mass transfer as well as other phenomena in agitation. Most of these studies are characterized by the fact that these phenomena have been experimentally studied and dimensionally analysed, solely from the standpoint of clarifying its operational and geometrical effects. Stress may be placed upon the fact that little attention has been paid to the more intrinsic factor, …… for instance, to the liquid flow pattern, …… to which each study of agitation must be intimately related. Referring to the representative reports which had been published, the author investigated the interrelation between the quantitative measure for representing the effect of agitation and the concept of its intensity which should define the measure, irrespective of geometrical specifications. At the outset, it was defined as an "operational condition" that the intensity of agitation would affect the quantitative measure which is represented by factors including heat, mass transfer coefficients and so on, corresponding to each. particular case under study.
The literature survey was conducted as follows :
(1) Mass transfer data in agitation:
In Figs.1 and 2, experimental results in solid-liquid agitation system are quoted. Referring to other data in liquid-liquid and gas-liquid system, (Fig.4, 5 and 6), the author noticed many cases in which the effect of agitation, K, K' and others could be defined by its intensity represented by the power per unit volume of liquid as indicated by Eqs.(7) and (8) under geometrically similar systems;.... in other words, β=0.75 in Eq. (6) when physical properties of liquid were constant... or by Fig.3 under geometrically dissimilar system, apart from the liquid flow pattern. However, as was already pointed out, the intensity thus presented is considered to be far from its general criterion.
(2) Heat transfer data:
The conclusion mentioned above applies to the heat transfer data in solid-liquid system quoted in Fig.7. The heat transfer from the jacket or coil in a mixing vessel was summarized as shown in Fig.8. Considering that the intensity in this case should be intrinsic Reynolds number on the coil or jacket surface, the author assumed the liquid velocity on each surface, in lieu of the modifier Reynolds number of impeller, by conducting the flow pattern measurement, following the procedure already reported. Rearranging the modified Reynolds number as shown in Eqs.(10) and (11), and using the experimentally determined liquid velocity as indicated in Eq.(9), Fig.8 was recal culated, resulting in Fig.9.
The heat transfer data from vertical tube tanks are quoted in Fig.10. In this case the power data tabulated in the original paper and the assumed pumping action of the turbine type impeller were employed in the calculation of the discharge rate, after the same procedure as described in the previous paper. Introducing the factor of Q/V, (reciprocal of the time needed to make one circulation of the whole liquid throughout the tank) Fig.10 was rearranged to obtain Fig.11. In Figs.9 and 11, the effect of geometrical dissimilarity is less indicative of the possibility of defining Reynolds number or the liquid circulation rate as the intensity of agitation.
(3) Other data:
The study of suspending particulate particles in highly viscous liquid by way of agitation is quoted. In this case, as shown in Fig.12, which was obtained by recalculating the original data, the energy input per unit mass of liquid possibly corresponds to the measure of agitation which is shown by the ratio of the height of uniformly distributed suspension and liquid depth under a certain condition for minimum impeller speed at which all solids are in suspension.

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Power delivered be impeller into liquid in a mixing tank is dissipated, in due course, into irreversible form of heat energy by the shearing force of liquid. Broadly speaking, the mechanism of energy dissipation is first found in velocity gradient of the stationary flow (principal contribution is seen in the boundary film along the tank wall, bottom and so on) and secondly, in velocity fluctuations superposed on the former. Since the energy lost by the latter mechanism is considered to be intrinsic in mixing, the quantitative estimation of this energy (temporarily defined as the effective mixing energy) was carried out, following the flow pattern studies reported by the author in the previous papers.^1).2)

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New equations for the calculation of Bingham plastic flow through circular pipes have been derived by rearrangement of McMllen's equations as follows.
Total volume of flow rate: (1)
Average Nelocity in the pipe: (2)
Velocity at the central plug (maximum velocity):
(3)
Velocity at any point from pipe wall to central plug boundary:
(4)
In constructing the curve indicated by Equation(4), use is made of parallel displacement of the "imaginary velocity distribution curve" indicated by the following equation.
(5)
Apparent viscosity is represented by:
(6)
where
(7)
(8)
(9)
(10)
Another method has been proposed for computing pressure loss during laminar flow of Bingham plastic materials.
The equations used in this method are as follows:
(11)
(12)
(13)
In determining pressure loss in a pipe of radius R, when Bingham plastic material flows at a given average velocity ua, it is recommended to apply either Equation (11) to a/φ or Equation (12) to φ/a, so as to obtain φ by the use of Fig.2 or a-φ table, which will be published in full shortly⁸⁾.
When φ is known, the pressure loss can be calculated by means of Equation (13).
One more method is given for the evaluation of the two plastic constants.
In two pairs of p and V the following equations hold:
(14)
(15)
where
(16)
(17)
By means of a simple trial-and-error procedure, a1, a2, φ1 and φ2 can be easily obtained.
When a₁ and φ₁ are known, yield value, τ_y, and plastic viscosity, η, can be calculated by means of the following equations.
(18)
(19)
It is supposed that the use of a-φ table⁸⁾ together with the equations derived by the author is more convenient than that of the method previously proposed by E.L. McMillen⁶⁾ and developed by B.0.A. Hedstrom⁴⁾.

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