103
??? = ????1 ?
|??? |
???
? (V-8)
where ? is the bottom friction stress (whose components are given by Eq. V-4) and ?cd is a
critical deposition stress above which no deposition occurs since particles are kept in suspension
by turbulence. The settling velocity of particles is obtained from Stokes’ law as mentioned
above:
?? =
????
??
???
???
(V-9)
where ? and D are suspended particle density and diameter respectively and ? is the kinematic
viscosity of water.
The erosion rate is written in term of the erodability constant E:
?? = ??? ?
|??? |
???
? 1? (V-10)
where fp gives the fraction of fine particles in the bed sediment and ?ce is a critical erosion stress
below which no erosion occurs. The model can also calculate sedimentation rates (SR) as the
balance between the deposition and erosion terms.
V-3. RADIONUCLIDE TRANSPORT
The dispersion model includes three phases, i.e. water, suspended matter in the water column
and bed sediments. An advection–di?usion equation is solved in order to simulate the transport
of radionuclides in the water column. Interactions between the dissolved phase and solid phases
(suspended matter and bed sediments) are described through a dynamic approach, in terms of
kinetic transfer coe?cients. Thus, assuming that adsorption–release reactions are described by
a single reversible reaction, a coe?cient k1 characterizes the transfer from the liquid to the solid
phase and a coe?cient k2 characterizes the inverse process. Dimensions of these coe?cients
are [T]?1.
The adsorption process is a surface phenomenon that depends on the surface of particles per
water volume unit. This quantity has been denoted as the exchange surface [V-6–9]. Thus in
general:
?? = ?(?? + ??) = ??
??? + ????? (V-11)
where Sm and Ss are the exchange surfaces for suspended matter and bottom sediments
respectively (dimensions [L]?1). ? is a parameter with the dimensions of a velocity. It is denoted
as the exchange velocity [V-6–9].
Assuming spherical particles, the exchange surfaces are written as [V-6–9]:
?? =
??
??
(V-12)
and:
?? =
????(???)?
??
(V-13)