Continuous countercurrent ion exchange was studied with the cationic system of magnesium and hydrogen ion, using an exchange column, 2cm in internal diameter and 5 to 30cm in height, where the bed of resin particles moved downward.
The data were correlated by an equation so as to relate the overall volumetric coefficient of mass transfer based on fluid film to operating variables and the properties of the ionic system.
The results indicated that film resistance of each phase was of the same order of magnitude. Overall volumetric coefficient based on the fluid film was found to be about 0.03 [1/sec].
Non-dimensional constants, α and β, appearing in the correlation equation, and related to film resistance of each phase, were 2.4 and 0.2, respectively. These values were smaller than those, 4.7 and 0.9, respcctively, obtained by Hiester et al., for the monovalent system of lithium, potassium and hydrogen ion. These differences may be attributable to the colum diameter differences, i.e., 9cm diameter in the Hiester's equipment and 2cm diameter in the authors'. More studies will be required, however, to know what factors participate in this phenomenon. Some considerations were made on the mutual relation between the degree of the exchange adsorption of magnesium in the solution and the ratio of the fluid flow rate to the resin particles flow rate.

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Ion exchange equilibrium in the solution of a salt was studied by many investigators, but few papers have been published on ion exchange equilibrium in the mixed solution of salts of strong acid and weak acid.
The authors measured Na⁺-H⁺ exchange equilibrium in the solution of these salts in different equivalent ratios. NaCl as a salt of strong acid and CH₃COONa, CH₂ClCOONa, CCl₃COONa, HCOONa or Na₂C₂O₄ as a a salt of weak acid were used. Taking into consideration the dissociation of weak acid, these equilibriums were represented by an equation, independently of equivalent ratios, and the result was found to agree with equilibrium in NaCl solution.
In the mixed solution of these salts, c₀ in Eq. (4) which was applied by Bieber and others to equilibrium given by Eq. (1) had to be substituted for c₀', sum of c_A and [H⁺], because of dissociation of weak acid. The value of c₀ was given by Eq. (9) for monovalent weak acid and [H⁺] is represented by Eq. (13) for divalent weak acid. A plot of c_Na/c₀ and q_Na/q₀ as shown in Figs. 1, 3, 4 and 5 gives different equilibrium curves with the change in equivalent ratios. A plot of c_Na/c₀' and q_Na/q₀ (Figs. 2, 3, 4 and 5) gives only an equilibrium curve without any dependence on equivalent ratios and it agrees with a curve for NaCl solution.

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Binary ion exchange reactions were investigated by many workers, but very few studies have been made on ternary systems.
Passing mixed solution of Na ion and Ca ion through the resin bed of strongly acidic, H-form cation exchanger under conditions of various equivalent ratios of the salts and flow rates, the authors measured the heights of the exchange zone for these salts. From the operation of Na ion separation which was performed by passing mixed solution through the resin bed, the authors derived the equations for calculating the degree, S, of Na ion-separation (Eq. (17)), the separation efficiency, η, (Eq. (19)) and the minimum height, Z_m, of the resin bed capable of Na ion separation (Eq. (20)), by using the height, H, of the exchange zone; and they compared these calculated values with the observed ones.
Equilibrium isotherms for Na⁺-H⁺ and Ca⁺⁺-H⁺ are shown in Fig. 3. The heights of the exchange zone for Na ion and Ca ion as shown in Fig. 4 are proportional to U^0.55 and independent of the equivalent ratio within the experimental range. These heights are represented by Eqs. (21) and (22), respectively.
The calculated values which are obtained by introducing Eq. (22) into Eqs. (17) and (19), respectively. agree comparatively well with the observed values.
When Eqs. (21) and (22) are introduced into Eq. (20), Z_m is given by Eq. (23).

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重力下にある乾いた非凝集粒子の特性について簡単にのべてある。粒子径,形状,密度,表面特性および粒度分布が静止層の充填特性および粒子群の流動特性に及ぼす影響を説明してある。粒状物質の流量を予測するのに必要な関係も一括して与えてあるし,流動粒子の興味はあるが,相関のえられていない特性についての検討も含まれている。

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