Hirofumi Miyoshi

Diffusion coefficients of ions through ion excange membrane in Donnan dialysis using ions of different valence

Donnan dialysis with an ion exchange membrane was investigated for ions of different valence. The effective diffusion coefficients (De) of various kinds of ions in the membrane were obtained by fitting of the equation derived from the Nernst–Planck equation to three or more sets of experimental data for Donnan dialysis. It became apparent that the value of De/Ds of monovalent ions (e.g., K+ or Na+ ions) at zA=1 and zB=2 (feed ions are monovalent ones and driving ions are bivalent ones) remained constant at ca. 1/210 and that of bivalent ions (e.g., Ca2+, Cu2+, or Mg2+ ions) remained constant at ca. 1/526 where Ds denotes the diffusion coefficient of ions at infinite dilution in water calculated from the Nernst–Einstein equation, and zA and zB represent the valences of the feed and driving ions, respectively. De/Ds of monovalent ions (e.g., H+, K+, or Na+ ions) at zA=2 and zB=1 (feed ions are bivalent ones and driving ions are monovalent ones) was constant at ca. 1/23.3 and that of bivalent ions remained constant at ca. 1/58.4. It was proved that De/D using De at zA=1 and zB=2 was constant at 1/3.0 and that at zA=2 and zB=1 remained constant at 3.0 where D represents the diffusion coefficient of ions in the membrane at zA=zB (the valences of both feed and driving ions are equal). Therefore, it was found that a large flux of ions could be obtained using the monovalent driving ions in Donnan dialysis. On the other hand, the small flux can be obtained using bi- or higher-valent driving ions.

Diffusion coefficients of ions through ion-exchange membranes for Donnan dialysis using ions of the same valence

The transfer of ions through an ion-exchange membrane during Donnan dialysis was studied theoretically and experimentally. By applying the Nernst-Planck equation to the flux of ions in the ion-exchange membrane, an equation was derived for Donnan dialysis in which feed ions and driving ions were of equal valence. The theoretically derived equation was fitted to the experimental values by adjusting diffusion coefficients. Thus, the diffusion coefficients of ions in the ion-exchange membrane which satisfied all the experimental data were determined. It was clearly shown that the ratio of the diffusion coefficient in the membrane to that in solution remained constant at 70 for a system of monovalent feed and monovalent driving ions, and remained constant at 175 for a system of bivalent feed and bivalent driving ions. The flux of ions in Donnan dialysis was found to be influenced by the concentrations of both feed ions and driving ions. Monovalent ions showed a larger flux than bivalent ions, suggesting that they were better as driving ions. The flux of ions was scarcely affected by the kinds of co-ions. It was necessary to pretreat the membrane with driving ions.

Donnan Dialysis with Ion-Exchange Membranes. III. Diffusion Coefficients Using Ions of Different Valence

Donnan dialysis with ion-exchange membranes was studied under various kinds of experimental conditions using ions of different valences. The diffusion coefficients (D d) of various kinds of ions in the ion-exchange membrane were obtained by curve fitting an equation derived from the mass balance to three kinds of Donnan dialytic experiments. It was found that the value of D d/D s using D d of monovalent ions in Donnan dialysis with a set of monovalent feed ions and bivalent driving ions was 1/175, where D s represents a diffusion coefficient in solution. D s was calculated from the Nernst-Einstein equation substituted by the ionic conductance of ions at infinite dilution in water. Using D d of bivalent ions in Donnan dialysis with the same set led to a D d/D s value of 1/438. Moreover, using D d in Donnan dialysis with the same set, the value of D d/D e was kept constant at 0.4 (D e expresses the diffusion coefficient in the membrane when the valences of the feed and driving ions are equal). On the other ...

Donnan Dialysis with Ion-Exchange Membranes. I. Theoretical Equation

Abstract The transfer of ions through ion-exchange membranes was investigated theoretically for Donnan dialysis. By applying Ficks equation and no electric current to the flux through the ion-exchange membrane on Donnan dialysis, and by changing the valences of feed and drive ions, three kinds of equations were derived: 1) feed ions and drive ions are of equal valence, 2) feed ions are monovalent and drive ions are bivalent, and 3) feed ions are bivalent and drive ions are monovalent. The equations were evaluated by use of a computer by the Runge-Kutta method. The relation between the valence of ions and the characteristic coefficients of the membrane became apparent from the calculated results.

A Method for Estimating the Limiting Current Density in Electrodialysis

Abstract An equation for estimating the limiting current density (LCD) in the electrodialytic equipment with spacers is derived by using the equation of the flow distribution and by assuming that the eddy diffusivity caused by the spacer is proportional to Re. The empirical constants of the eddy diffusivity in the equation were determined by measurement of LCD using spacers, electrolytes, feed concentrations, operating temperatures, and flow velocities. The results obtained show that LCD in the electrodialysis can be estimated from the equation derived here.

Estimation of the Limiting Current Density in Electrodialysis with Both Spacer and Space

Abstract The influence of “space” in the ion-exchange compartment (IEC) on limiting current density (LCD) during electrodialysis was investigated. A general equation to estimate LCD was derived for three types of electrodialytic equipment: 1) with the IEC tilled with spacers, 2) without spacers, and 3) with spacers and space. The theoretical values of LCD calculated from the equation were in good agreement with the experimental values obtained by varying the space thickness and employing various kinds of spacers; it follows that the value of LCD in all three types of electrodialytic equipment can be estimated from the general equation derived here.

Donnan Dialysis with Ion-Exchange Membranes. II. Diffusion Coefficients Using Same Valence Ions

Abstract Donnan dialysis with ion-exchange membranes was investigated experimentally. The equation derived theoretically in the previous paper was fitted to the results of a Donnan dialytic experiment, and the diffusion coefficients of various kinds of ions and in various kinds of ion-exchange membranes were obtained. The flux of monovalent ions in Donnan dialysis was much larger than that of bivalent ions. Thus, monovalent drive ions are the best kind of drive ions to employ. It was found that the ratio of the diffusion coefficient in the ion-exchange membrane to that in the solution remained constant at 70 for monovalent feed and drive ions except for H+ ions, and at 175 for bivalent feed and drive ions. It became apparent that the fundamental equation derived from Ficks equation and no electric current might be used for Donnan dialysis instead of the Nernst-Planck equation.

Influence of the Concentration of Ions in Solution on the Partition Coefficient between Cation Exchange Membrane and Solution

Abstract Partition coefficients of some cations between cation exchange membrane and solution were measured. The reciprocals of the partition coefficients were plotted against the corresponding: dimensionless concentrations of ions in solution. The relations obtained experimentally for monovalent-monovalent and monovalent-bivalent ions systems were in agreement with the respective theoretical equations. For the monovalent-monovalent exchange the relation was linear. While in the monovalent-bivalent case it was non linear. We proposed an empirically obtained linear relation for the monovalent-bivalent system. Therefore, the dependence of the reciprocal of partition coefficients on the dimensionless concentration of solution can be represented by a linear relation for both systems.