The shape and the velocity of bubbles in various liquids listed in Table 1 were measured on photographs taken through a stroboscope.
The shape of gas bubbles changed from spherical to ellipsoidal, and then to mushroomlike, as the bubble size increased. The experimental results showed that up to the Reynolds number of 2M^-0.23, the bubble was almost spherical and traveled in a rectilinear path. In the range of 2<ReM^0.23<16.5, ellipsoidal bubbles were formed and as the bubble size increased the shape became flatter. In the range of ReM^0.23>16.5, the bubble was of mushroom shape. These changes in shape are plotted in terms of d/a and ReM^0.23 in Fig. 12, from which experimental equations, Eqs. (12)(15) are derived. These are applicable to bubbles in all solutions except for surface active agent solution. The bubbles in surface active agent solution remained spherical in much bigger size than those in pure water.
Data on the terminal velocity of gas bubbles are shown in Fig. 6. Of spherical and ellipsoidal bubbles, the surface tension and the viscosity were found to be important factors determining the rate of rise. Mushroomlike bubbles rose independently of liquid properties. To correlate the results, dimensionless parameters, C_D, Re and M were employed and experimental equations, Eqs. (9)(11), were obtained for all solutions except for surface active agent solution. These equations agree approximately well with the data of previous investigators summarized in Fig. 16. The presence of certain surface active substances in water served to increase the drag of bubbles, as was made clear by the comparison with the drag of bubbles in pure water.

View full abstract

Taking into consideration the temperature gradient within solid particles, a mathematical analysis is derived on the heat transfer of noncatalytic thermal decomposition in single spheres and packed beds.
The fundamental equations are given by Eqs. 1 and 2 for single spheres and in the case of packed beds, they are given by Eqs. 1, 2 and 11, all on the following assumptions.
1) The specific heat of solid is very small as compared with the decomposition heat.
2) The heat quantity transferred to the decomposition face is all consumed as decompositioh heat.
3) The difference between the surrounding temperature and the decomposition temperature is moderate.
Based on the boundary conditions, the solutions are given by Eqs. 1115 for single spheres and by Eqs. 2123, for packed beds.
Some examples of the solutions are shown in Fig. 17. By means of them, the decomposition rate and the temperature distribution are given as functions of time and distance.
The solutions are applicable to the decomposition of CaCO₃.
The apparatus used in this experiment are shown in Figs. 811, and the mathematical solutions are compared with the result of the experiment.
As shown in Figs. 1623, the solutions coincide fairly well with the results of the experiments in single spheres as well as in packed beds.

View full abstract

In the previous paper it was shown that the rates of extraction, accompanied by chemical reaction, across an unbroken interface, could be reasonably correlated as expressed by Eqs. (1), (2) and (3).
In this papar, mass transfer accompanied by rapid chemical reaction is studied to make clear the liquid-liquid extraction of acetic and butyric acids from solvent drops. Experimental apparatus is made of glass without any rubber, which contains poisonous matter slightly soluble in KOH aqueous solution into which acetic and butyric acids are to be transferred. Conclusions arrived at may be summarized as follows:
(1) In the case of acetic acid transfer from benzene drops, the transfer rates do not increase with the addition of KOH in the aqueous phase, but rather, they decrease at a certain value of q (Fig. 2).
(2) It is made clear that this decrease in transfer rate is not caused by the contamination with the poisonous substances such as reported previously, and that wherever it occurs, the value of q/C_B is found to be constant.
(3) In the case of butyric acid transfer from benzene drops, the extraction rate increases with the increase in the value of q, because the resistance in the aqueous solution decreases with the addition of KOH, but above a certain value of q, the extraction rate decreases for the same reason given above. Therefore, the extraction rates can be expressed by q/C_B in three stages as given in Fig. 6.
a) When the rate is increasing. b) When the rate is decreasing.
c) When the rate is constant.
(4) In the case of other solvents such as hexane, methyl-isobutyl-keton, isopropyl ether and butyl acetate, the extraction rates are classified, according to the value of m (distribution coefficient of the system), into two types described above for acetic and butyric acids transfer.

View full abstract