90 III-4. RADIONUCLIDE TRANSPORT The submodel of radionuclide transport describes the specific water–sediment sorption processes. It includes the advection–di?usion equations for dissolved, ???, and adsorbed by suspended sediment of i?th fraction, ???? , radioactivity in the water column, and the equations for concentration of the dissolved, ???, and adsorbed, ???? , radioactivity in the bottom deposits: ???? ?? + ???? ? ?? + ???? ? ?? + ???? ? ?? = ? ?? ???? ???? ?? ? + ? ?? ??? ???? ?? ? + ? ?? ??? ???? ?? ? ? ???? ? ???(???? ???? ? ??? ??? ? ? ???) (III-15) ???? ? ?? + ????? ? ?? + ????? ? ?? + ?(?????)??? ? ?? = ? ?? ???? ???? ? ?? ? + ? ?? ??? ???? ? ?? ? + ? ?? ??? ???? ? ?? ? ? ???? + ???(??????????? ? ????) (III-16) ?(????? ? ) ?? = ?????????? ??? ? ???? ? ? ? ??(???) ???????? ? ???? ???? (III-17) where ??? = ????? ???? and ? is the radionuclide decay constant. Adsorption and desorption of radionuclides between the liquid and solid phases are described by the radionuclide exchange rates, a12 and a13, and by the distribution coe?cients ???? and ???? [III-14, III-15, III-16], which are defined, under equilibrium conditions, as: ??????? ? = ??? ??? ??? ? ??? (III-18) ??? ? ? ???? = ?????? ??? ? ??? (III-19) The dependence of the distribution coe?cient on sediment particle size can be written for the water column as [III-17]: ???? = ? ??? ? ?? (III-20) and for bottom sediment as: ???? = ? ??? ?? ???? (III-21) where Ri is sediment particle radius (m), ? is an exchange velocity (m/s), ? is a correction factor that takes into account that part of the sediment particle surface may be hidden by other sediment particles. At the free surface z = ? the boundary conditions are: ?? ???? ?? = ???? (III-22) ?? ????????? ? ?? ???? ? ?? = 0 (III-23) The ?uxes into the bottom z = ?h + zo are: