Ternary Ion Exchange Kinetics

Few studies have appeared on ternary exchange kinetics, even though in most soil systems exchange processes involve three or more ions. Bajpai etal. (1974) studied Mn-Cs-Na, Ba-Mn-Na, and Sr-Mn-Cs exchange on a resin. Nernst-Planck equations were used to study the ternary systems, and when FD effects were included in the equations they described the data well. Other ternary kinetic studies were conducted by Wolfrum et al. (1983) and Plicka et al. (1984). 

Plicka et al. (1984) studied Mg-U02-Na exchange on a resin using the kinetic model described below. If one assumes that ions A and B are sorbed by a resin in the C form and that the exchange reactions begin at time / = 0, then 

This is a three-component (A, B, C) system, and the transport or diffusion of each component can be described using the Nernst-Planck equation. The relation of the diffusion flux of the i component (i, j, k = A, B, C) can be obtained by combining three Nernst-Planck equations, for the respective components, under the conditions of zero electric current inside the resin particle  

A complicated second-order differential equation is obtained by substitut- 

The time concentration profiles Cft, rd) of the components (A, B, C) in the particle of the resin were found by the solution of the system consisting of three respective equations [Eq. (5.34)]. The total quantity of each component in the particle, which is related to the volume of the particle in time t, can be evaluated by substitution of the Ct(t, rd) values into Eq. (5.35)  

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Exchange on Soils and Inorganic Soil Constituents 117 Exchange on Humic Substances 119 Ternary Ion Exchange Kinetics 122... 

Fig. 11. Examples of ternary ion exchange kinetic measurements within the Na/Ca/Mg-A system. The dashed lines which bound the experimental data represent the simple binary exchange rates (viz, Na/Ca and Na/Mg). When magnesium is added to the system in progressively larger amounts (i. e. O > ) a progressive slowing of the Na exchange rate is seen. Taken with permission from [21]...

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