Multicolumn distillation systems are used in many processes and numerous methods have been presented for the solution of such systems. Calculation methods for multicolumn distillation systems can be classified into direct iteration methods, acceleration methods and simultaneous solution methods. The method used in this paper is one type of direct iteration acceleration method. In the case of conventional direct iteration acceleration methods, the θ-method for instance, the correction of errors in the material balance between the individualcolumns is carried out by a material balance equation in which the vapor-liquid equilibrium relationship in each column is not considered. On the other hand, in the method used this time, convergence is accelerated by using a material balance equation in which the vapor-liquid equilibrium relationship in each column is considered. This equation has been derived as a linear equation from the tridiagonal matrix for the material balance in each tray in the column. This method is used for many multicolumn distillation systems including those shown as examples. In all cases, stable solutions are brought about promptly.

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An attempt is made to improve the thermal efficiency of chemical reactions and an endothermic dehydrogenation of alcohol is carried out concurrently with an exothermic oxidation. in one reactor where both reactions produce the same ketone or aldehyde. The dehydro genation rate of 2-propanol over copper oxide-zinc oxide catalyst is expressed by a LangmuirHinshelwood type rate equation in which the effects of oxidation products are taken into account. Oxidation is found to occur in competition with dehydrogenation and, therefore, the reaction rate of 2-propanol is expressed by the sum of the two reactions. Stability analysis of the present reaction system is also made and the resultant steady-state operating temperature range is in accord with experiment.

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The rate of nitric oxide destruction by coal char and activated carbon was measured by use of isothermal diluted fixed-bed reactor over a range of temperature (500845°C). The rate of reaction was found to be first-order with respect to nitric oxide concentration. The activation energy obtained at temperatures less than approximately 680°C coincided with the values reported by previous investigators, but increased activation energy was observed at higher temperatures. The fraction of carbon monoxide in the products distribution was increased with elevated temperature.

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Spherical particles of CaO (4.0 cm in diameter) were carbonated at 730°C in a stream of binary mixtures of CO₂ and inert gases such as N₂, Ar, and He. The variations of pressure and temperature profiles within the sphere and the weight change were continuously measured during the course of reaction.
When the sphere was carbonated by pure CO₂, it was observed that the pressure at the center of the sphere was 535 mmHg lower than the ambient. The pressure decrease ΔP, the temperature rise ΔT, and the overall reaction rate m_A varied remarkably with each inert gas.
These phenomena were satisfactorily analyzed by using a model of non-isothermal and non-isobaric solid-gas reaction with unidirectional flow. It was found that remarkable variations of ΔP, ΔT and m_A with each inert gas were caused by difference in the properties of dynamic effective diffusivity.

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A two-dimensional thermal stress analysis in axisymmetric insulating-refractory materials which has frequent applicability to practical furnaces is performed by the finite-element method taking large deformation into consideration.
Comparisons of the calculated results with the experimental data of a hollow cylindrical sample resulted in the following findings :
(1) The calculated results of temperature profiles and reaction forces are in good agreement with the experimental data.
(2) From the calculated thermal stress profile which breaks out in cracking, it is seen that the tensile stress at the outer surface of the sample almost equals the bending strength of the sample and that at the same time the compressive stress in the inner region of the sample exceeds its compressive strength.
However, visual observation of the cracking position and shape shows that the crack seems to result from the tensile stress.

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Experiments were made of light-induced emulsion polymerization of styrene in an elliptical-type photoreactor with a photosensitizer of uranyl nitrate and a nonionic emulsifier. Micelles were converted to polymer particles at the efficiencies of 0.050.22, which value were much higher than the results obtained previously. Theoretical analyses were made of production mechanism of polymer particle and a simple formula using dimensionless values is introduced. This formula shows three separate regions : the perfect consumption region, the transition region and the Smith-Ewart region. The experimental results agreed well with the calculated values of the transition region.

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A self-scanning one-dimensional photo-diode array (an image sensor), such as is usually used in the card reader of electronic computer or for image analysis, was experimentally employed in the measurement of velocity and turbulence in liquid in a stirring vessel.
Measurement was first performed using a transmitted-light method by which light was focussed at a certain point inside the vessel using the optical system provided. In order to catch precisely the tracers (minute spherical particles) flowing into the measuring area (the focal point), a special circuit was assembled which would be activated only by signals detected simultaneously by the optical systems of both the image sensor and the photo-transistor.
The output signals detected by the image sensor were fed into wave-form memory and processed by mini-computer after A-D conversion. In this way, the diameter of a particle, its speed and two-dimensional direction of motion were obtained. On the basis of these results, velocity and turbulence were calculated.
It is concluded that measurement of liquid velocity and turbulence in a stirring vessel can be performed with high accuracy using the present method.

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Study for mixing process in a stirred tank with paddle-type impeller was carried out with the method of impulse response under the turbulent flow region.
A correlation of circulation time with impeller variables and the effects of measuring positions on response lag were obtained by measuring the period and the response time for the peaks or valleys of observed curves, respectively.
On the other hand, a mixing model with a recirculation process composed of a series of perfect mixing tanks was proposed on the basis of experimental information for the circulation flow patterns.
By making a comparison between model response characteristics and experimental ones, two mixing parameters were decided and the model curves calculated by these parameters agreed approximately with the corresponding experimental curves. It was also shown that the relation between mixing rate and circulation rate could be correlated with power number of impeller.

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The second normal stress difference of a polyethylene melt was measured by flow birefringence in which light axis of the optical system coincided with the direction of flow within nozzles. This method gave the second normal stress difference not from the difference between (P₁₁-P₂₂) and (P₁₁-P₃₃), but directly from the only measured phase difference. The required phase difference occurring only within the fully developed region of flow through the nozzles could be calculated by removing end effect from the measured phase difference, which included the phase differences of the reservoirs in both the entrance and the exit of the nozzles.
The relations between the second normal stress difference and shear stress seemed to grow closer and higher with increasing temperature. The ratios of the second normal stress difference to the first normal stress difference were from -0.1 to -0.2.

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Velocity distribution, V_z of laminar flow in a noncircular duct which has a cross-sectional shape of an annular sector (radius of inner cylinder : R₁, and of outer one : R₂, and opening angle : 2α) has been obtained by an analytical method. Result is shown as
V_z=-R₂²/μ·dP/dZ·2/Inη ∞∑m=1 1-(-1)^mη²/k_m(k_m²+4) sin (k_mInr) · (1-coshk_mθ/coshk_mα)
where r=R/R₂, η=R₁/2₁, k_m=mπ/1nη. Then an equivalent diameter, D_eq, which is defined as
-dP/dZ=32μV_z/D_eq²
by a similar method as for a circular tube, has been given by
D_eq=R₂ [-128/1-(η²)Inη ∞∑m=1 (1-(-1)^mη²/k_m²+4)² (1-tanhk_mα/k_mα)]^1/2
Analytical result of D_eq is confirmed by the experimental result on the pressure gradient for some cross-sectional shapes of ducts.

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The effect of particle-size distribution on axial dispersion of liquids in packed beds was investigated using pulse response measurements, visual observation of liquid flow through two-dimensional packed beds, and pressure drop measurements.
For beds of particles having narrow particle-size distribution (i.e. coefficient of variation of particle diameter η_l less than 8 %), axial dispersion data were correlated by the plots of Peclet number of axial dispersion Pe_zh vs. Péclet number of molecular diffusion Pe_Mh, showing clear dependence on particle diameter.
The values of Pe_zhcan be calculated by use of an agglomeration model associated with whiskers observed from visualization tests. The model parameters were given diagrammatically.
For beds of particles having wide particle-size distribution (η_l> 10 %), the slopes of the plots of Pe_zh vs. Pe_Mh showed slight dependence on η_l and were all less than those in beds of particles having narrow particle-size distribution. This behavior of the plots coincided with the observed results for visualized liquid flow and with the results of pressure drop measurements.

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Axial mixing of liquid phase in three-phase fluidized beds was measured in columns of 6 and 10 cm in diameter. Glass beads of six different sizes (diameter, 0.216 6.9 mm), alumina beads (2.0 mm) and Raschig rings (5.2 mm) were used as fluidized particles. Superficial liquid and gas flow rates were varied over the range of 0.6016.8 cm/sec and 030 cm/sec, respectively.
Flow pattern in the three-phase fluidized bed was classified into three regions : coalesced bubble flow (u_L0< 8 cm/sec, u_g0 < 10 cm/sec), dispersed bubble flow (u_L0> 8 cm/sec, u_g0<10 cm/sec) and slug flow (u_g0> 10 cm/sec).
The coalesced bubble flow region appeared in the bed of small particles (d_p≤1 mm). Modified Péclet number Pe_L (=u_LD_t/E_z) was correlated by the following equation :
Pe_L=1.07 (u_L0) ^0.738 (u_g0) ^-0.167 (D_t)^-0.583 (coalesced bubble flow)
The dispersed bubble flow appeared in the bed of large particles (d_p >2 mm) and at lower gas flow rate. Pe_L was correlated as a function of the ratio of the particle to the column diameter :
Pe_L=26 (d_p/D_t) ^1/2
(dispersed bubble flow, 0.02 < d_p/D_tL< 0.12)
In the slug flow, the behavior of Pe_L was similar to that in the coalesced bubble flow.

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The process of breakup of a liquid drop in a shear field is irreversible and discontinuous, and the deformed shape of and the flow behavior in the drop at the step of breakup are too complex to analyse.
As the first approach in this paper, the macroscopic balance of mechanical energy, taking into account the changes of surface and kinetic energies and energy dissipation, is applied to the deformation process and conservation of mechanical energy in the dispersed phase during the breakup process is assumed. From this analysis, it is found that under a shear stress changed stepwise the minimum loaded time, θ₂, required for breaking up a drop into two droplets is inversely proportional to the excess shear rate ΔG (=G -GB).
However, the state of drop at the natural breakup under shear stress continuously loaded cannot be shown as a singular state in the first approach. Thus, as the second approach, the catastrophe theory is applied to the breakup process.
In the cusp-type catastrophe, if the excess shear rate ΔG and the loaded time θ · ΔGas two external variables, and the state of drop as the internal variable are chosen, the process of de-formation and breakup can be well interpreted. The dependencies of the loaded time and the number of droplets at the natural breakup process on the excess shear rate, predicted by the theory, have been proved by the experimental data.

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Dust explosion has hitherto been studied experimentally for specific materials, but there are few works on the theoretical aspect. Mitsui and Tanaka studied theoretically the ignition temperature and the minimum explosible concentration based on a simple model. But their theoretical treatment involved some doubts in expressing the emissivity, so the authors have refined them for predicting the above characteristics of dust explosion. The results agree satisfactorily with past experimental data. Another interesting phenomenon-that there may be a particle diameter to give the minimum ignition temperature-is suggested.

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In the ultrafine grinding operation of graphite, the rate of grinding, morphological and structural changes of the ground product were found to be heavily dependent on the gas atmosphere and grinding method. In vibration ball mill grinding, cleavage breaking occurred in oxygen and gave flaky products, whereas in helium, noncleavage breaking took place and produced cubes. The rate of grinding, dS_w/dE, in helium was about 8 times that in oxygen. These results were explained by the different coefficients of friction of graphite in different gas atmospheres. Structural changes accompanying grinding corresponded well with net grinding energy consumed, E. Jet mill grinding produced flakes in both nitrogen and air. Formation of bended planes and microcracks and an abnormal increase in rhombohedral structure were observed. In terms of the dislocation theory of graphite crystal, the grinding mechanism was explained as follows : Graphite particles broke under a stress acting perpendicularly on the plane in a jet stream. In mechanical agete mortar grinding in air, cleaving occurred under a shear stress parallel to the plane.

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The settling velocities of floc particles, which were made from dispersed microcellulose by using aluminum sulfate as a coagulant, were measured, and their buoyant densities were calculated by Stokes' equation. As a result, it was found that (1) the floc-density function, ρ_e=ad^-Kρ, proposed by Tambo et al., holds, (2) floc density increases with increase in agitation rate, (3) there exists a hysteresis phenomenon in the floc density with respect to the agitation rate, and (4) all the Kρ values observed in this system are nearly equal to 1. And it was shown that when the Kρ value is larger (smaller) than 1, the total projected area of flocs by light beam is increased (decreased) in the coagulation progress, and therefore, the Kρ value can be estimated by following the light-transmittance variation in the coagulation process.

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