Vertical random variability of the distribution coefficient in the soil and its effect on the migration of fallout radionuclides.

In the field, the distribution coefficient, K-d, for the sorption of a radionuclide by the soil cannot be expected to be constant. Even in a well defined soil horizon, K-d will vary stochastically in horizontal as well as in vertical direction around a mean value. The horizontal random variability of K-d produce a pronounced tailing effect in the concentration depth profile of a fallout radionuclide, much less is known on the corresponding effect of the vertical random variability. To analyze this effect theoretically, the classical convection- dispersion model in combination with the random-walk particle method was applied. The concentration depth profile of a radionuclide was calculated one year after deposition assuming (1) constant values of the pore water velocity, the diffusion/ dispersion coefficient, and the distribution coefficient (K-d = 100 cm(3). g(-1)), and (2) exhibiting a vertical variability for K-d according to a log- normal distribution with a geometric mean of 100 cm(3). g(-1) and a coefficient of variation of CV = 0.53. The results show that these two concentration depth profiles are only slightly different, the location of the peak is shifted somewhat upwards, and the dispersion of the concentration depth profile is slightly larger. A substantial tailing effect of the concentration depth profile is not perceivable. Especially with respect to the location of the peak, a very good approximation of the concentration depth profile is obtained if the arithmetic mean of the K-d- values (K-d = 113 cm(3). g(-1)) and a slightly increased dispersion coefficient are used in the analytical solution of the classical convection- dispersion equation with constant K-d. The evaluation of the observed concentration depth profile with the analytical solution of the classical convection- dispersion equation with constant parameters will, within the usual experimental limits, hardly reveal the presence of a log- normal random distribution of K-d in the vertical direction in contrast to the horizontal direction

Transport of fallout radiocesium in the soil by bioturbation : A random walk model and application to a forest soil with a high abundance of earthworms.

It is well known that bioturbation can contribute significantly to the vertical transport of fallout radionuclides in grassland soils. To examine this effect also for a forest soil, activity-depth profiles of Chernobyl-derived Cs-134 from a limed plot (soil, hapludalf under spruce) with a high abundance of earthworms (Lumbricus rubellus) in the Olu horizon (thickness=3.5 cm) were evaluated and compared with the corresponding depth profiles from an adjacent control plot. For this purpose, a random-walk based transport model was developed, which considers (i) the presence of an initial activity-depth distribution, (ii) the deposition history of radiocesium at the soil surface, (iii) individual diffusion/dispersion coefficients and convection rates for the different soil horizons, and (iv) mixing by bioturbation within one soil horizon. With this model, the observed Cs-134-depth distribution at the control site (no bioturbation) and at the limed site could be simulated quite satisfactorily. It is shown that the observed, substantial long-term enrichment of Cs-134 in the bioturbation horizon can be modeled by an exceptionally effective diffusion process, combined with a partial reflection of the randomly moving particles at the two borders of the bioturbation zone. The present model predicts significantly longer residence times of radiocesium in the organic soil layer of the forest soil than obtained from a first-order compartment model, which does not consider bioturbation explicitly

Kinetics of Film Diffusion Controlled Ion Exchange Processes, Theory and Applications.

A differential equation describing the kinetics of film diffusion controlled ion exchange processes is derived on the basis of the theory of irreversible thermodynamics. This equation is solved subsequently with the boundary conditions of infinite solution volume and applied to some experimental results involving differential ion exchange reactions. In case of the boundary conditions of a finite solution volume, the kinetics of dissolution of a sparingly soluble salt by an ion exchanger is considered

Kinetics of Ion Exchange in a Stirred Flow Cell.

The kinetics of ion exchange in a stirred-flow cell have been investigated experimentally and theoretically in the concentration range where film diffusion is the rate-determining step. To obtain detailed information, the ratio of the two counterions A and B in the inflow solution, as well as that of the ions initially in the ion exchanger, was selected in such a way that the ion exchanger was converted in successive steps from the pure A form to the pure B form, and back to the A form. The kinetics of the total conversion of the ion exchanger from the pure A form to the pure B form in one step were also determined. The experiments (exchange Cs+-H+) show that: (i) for partial conversions and for the forward reaction (uptake of the preferred ion, here Cs+), the half-life, t1/2, of the ion exchange decreases considerably if the initial fraction of the preferred ion in the ion exchanger is increased; (ii) at a given initial ionic composition of the ion exchanger, the half-life is shorter when the preferred ion is taken up rather than released; (iii) compared with a process where the ion exchanger is converted only partially from the H+ form to the Cs+ form, the half-life for the total conversion of the ion exchanger from the H+ to the Cs+ form in one step is much shorter. The theory describes all observations quantitatively, with only two adjustable parameters (rate coefficient, R, and the ratio of the diffusion coefficients DA/DB) for the whole set of experiments. The calculations reveal that the strong dependence of t1/2 on the initial ionic composition of the ion exchanger is only to a small extent due to the kinetic properties of the ion exchanger, but is rather a result of its selectivity (i.e. non-linearity of the ion-exchange isotherm). This restricts the usefulness of the stirred-flow technique for investigating the kinetics of ion exchange