In order to design an apparatus for chlorinating titan slag, we must be informed of the following three fundamental data: -the reaction velocity constant (γk_c), the diffusion constant (D_vs) of Cl2 in the ash, and mass transfer coefficient (k_f) of Cl2 in the gas film on the spherically formed sample, composed of coke and slag._vs< During the chlorination of the titan slag at high temperature, the weight loss of the tabletted cylindrical solid sample, composed of coke and slag, was measured by means of a thermobalance. In these experiments, variables of reaction conditions were found to be temperature, velocity of Cl₂ gas, mixing ratio of coke and slag and diameter of coke particles and slag particles.
From these experimental results, we can calculate the above mentioned three fundamental data (γk_c, D_vs, k_f).
In the first place, dW/dt and W can be known from the weight loss of the sample and the time of reaction t. α and β can be obtained by means of Eq. 7, and Dvs and by means Eqs. 8, 9 and 10.
To know γk_c, k_f should be calculated independently of γk_c. In order to obtain the value of kf, the modified equation for the mass transfer in a single sphere reported by Frosessling (Eq. 19) can be resorted to.
The three fundamental data thus obtained are given in the form of Eqs. 26, 16 and 19. Much useful information for the practical design and operation of an apparatus may be got by their application.
(1) The time required for the complete reaction of a spherically formed sample composed of coke and slag with Cl₂……θ₀ (Eq. 28 and 27).
(2) The capacity of the apparatus.
(3) The utility of Cl₂ in the fixed-bed type appratus.
In this report calculated value of θ₀ is employed.

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A graphical method for analyzing liquid-solid systems and an experimental process for obtaining basic data for said analysis to be applicable to one dimensional vertical flow are presented.
1) The graphical method proposed by Kynch (1952) and Lighthill Whitham (1955) for kinematic waves have been modified, taking into account the influence which the liquid flow rate and the mean space-velocity of solid particles have on each other. There are given also several examples as are of use in the practical solution of this kind of problems.
2) As a new experimental process for obtaining a flow-concentration curve on which the graphical analysis is based, the liquid-fluidized-bed method is investigated. Experimental examinations in batch and continuous settling have proved that the method holds good.

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Some methods for the approximate estimations or examinations of the process dynamic characteristics are given below in hopes that they will be of some help when the already known methods are employed.
According to the first method, time constants T₁ and T₂ of 2nd order are estimated from an indicial response curve (Eq. 1) by means of Eqs. (2), (3), and (4). The calculation is easy to make and the results obtained are more accurate than those obtained by other methods. If the time constants T₁ and T₂ are equal to each other, Eqs. (6), (7) and (8) should be employed (Fig. 1).
Ratio of time constants T₂/T₁ depends on the coordinates (x_t, t_t/T₁) of the tangential point from the origin (0, 0), as well as on the coordinates (x_i, t_i/T) of the inflection point on an indicial curve (Eq. 2 & Fig. 2). These coordinates can be obtained from the actual measurements of the results.
Eq. (10) is a criterion formula for 2nd order indicial response, when x=x1, at t=T1, x=x2 at t=T2 and x=x3 at t=T1+T2.
The second method stipulates the estimation of a transfer function of an approximate dead time and 1st order process from proportionally controlled results of the process. Eqs. (14) and (15) are obtained theoretically. Therefore, by means of Figs. 3 and 4, approximate estimations can be made of dead time L and 1st order time constant T, from the process gain M, proportional band P, period of damped cycling τ and subsidence ratio r.

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In our previous paper we reported the influence of physical properties of powder on the mixingdegree and mixing speed in several types of mixers.
The present paper deals with our continued studies on the influence of particle size of powder on the above-mentioned factors observed in several types of mixers.
The experiments were made by mixing three kinds of dry powder system: Na₂CO₃-sand system, having the particle-size distributions shown in Table 1, such as (1) the kind in which both the sample powders have the same size range and comparatively narrow size distributions, (2) another kind in which both the powders have the same size range and wide size distributions, and (3) the other kind in which both the powders have different size range and comparatively narrow distributions.
What we made clear by our researches were:
1) The optimum rotational speed of each mixer Nop was increased as the particle diameter (mean) increased, as shown in Fig. 3 and Eq. (4). The optimum volumes of powder to be charged were almost independent of the particle size in all experiments as shown in Fig. 2-a.
2) The influence of particle size might be divided into two kinds:
a) The influence observed when both the components had the same size.
b) The influence observed when both the components had different size.
In a), when the particle size of the powder was comparatively larger, the values of σs became larger, due to the median diameter of the distribution size as shown in Fig. 4.
But, in b), as the particle size-ratio of the two components was increased, it became more and more difficult to obtain an intimate mixture, as shown in Figs. 6 and 7.

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The velocity distribution of liquid in a cylindrical mixing vessel with flat-plate-baffles like those commonly used was measured by the method similar to the one adopted for the agitator without baffles.1)
Some of the experimental results are shown in Figs. 3, 4, 5, 6, 7, 8 and 9.
Variations of the liquid velocity distributions caused by the baffle-plates inserted in the agitated vessel are shown in Fig. 10. Obviously, the insertion of baffle-plates reduces the circulating flow round the impeller axis (the circumferential component υt of liquid velocity) and promotes the circulation flow in the vertical direction (caused by the discharge flow from the tip of the impeller).
The discharging performance of various impellers is represented by the ratio NP_B/N_q1, which is a dimensionless factor corresponding to the relative power required for a unit quantity discharge. The ratios for various impellers are listed in Table 3 together with those in the non-baffled condition. It is to be noted that, in spite of a considerable increase in N_q1, the circulation efficiency of agitators is lowered by the insertion of baffle-plates.
Furthermore, the power consumption in the neighbourhood of the impeller (NPimp) was calculated and compared with that consumed in the outer region of the vessel (ΔNP) as shown in Table 4.
It may be concluded from above that the improvement in the circulating capacity can be accomplished to a certain extent by a proper design of baffle-plates.

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