Dispersion of Particle-Reactive Elements Caused by the Phase Transitions in Scavenging

A generalized model of scavenging of the reactive radionuclide Pu-239,Pu-240 was developed, in which the sorption-desorption processes of oxidized and reduced forms on multifraction suspended particulate matter are described by first-order kinetics. One-dimensional transport-diffusion-reaction equations were solved analytically and numerically. In the idealized case of instantaneous release of Pu-239,Pu-240 on the ocean surface, the profile of concentrations asymptotically tends to the symmetric spreading bulge in the form of a Gaussian moving downward with constant velocity. The corresponding diffusion coefficient is the sum of the physical diffusivity and the apparent diffusivity caused by the reversible phase transitions between the dissolved and particulate states. Using the method of moments, we analytically obtained formulas for both the velocity of the center mass and apparent diffusivity. It was found that in ocean waters that have oxygen present at great depths, we can consider in the first approximation a simplified problem for a mixture of forms with a single effective distribution coefficient, as opposed to considering the complete problem. This conclusion was confirmed by the modeling results for the well-ventilated Eastern Mediterranean. In agreement with the measurements, the calculations demonstrate the presence of a maximum that is slowly descending for all forms of concentration. The ratio of the reduced form to the oxidized form was approximately 0.22-0.24. At the same time, Pu-239,Pu-240 scavenging calculations for the anoxic Black Sea deep water reproduced the transition from the oxidized to reduced form of Pu-239,Pu-240 with depth in accordance with the measurement data.