104
where R is particle radius, p is sediment porosity, L is the sediment mixing depth (the distance
to which the dissolved phase penetrates the sediment) and ? is a correction factor that takes into
account that part of the sediment particle surface may be hidden by other sediment particles.
This formulation has been successfully used in all modelling works cited above. Real particles
are not spheres, but with this approach it is possible to obtain an analytical expression for the
exchange surface [V-10].
The equation that gives the temporal evolution of pollutant concentration in the dissolved phase,
Cd, is:
?(???)
??
+
?(????)
??
+
?(????)
??
=
?
??
????
???
??
? +
?
??
????
???
??
?
?????
??? + ???????? + ?????? + ????????? (V-14)
where As and Cs are concentrations in the active fraction of bed sediments and suspended matter
respectively.
The temporal evolution of pollutant concentration in suspended particles is given by:
?(????)
??
+ ?(?????)
??
+ ?(?? ??)
??
= ?
??
????
?(???)
??
? + ?
??
????
?(???)
??
? +
??
?????? ? ?????? + ??? (V-15)
where SED expresses the pollutant exchange between suspended particles and the bed sediment
resulting from erosion/deposition:
??? = ???? ? ?? ?? > 0??? ? ?? ?? < 0
(V-16)
where SR is the sedimentation rate calculated by the sediment transport model.
The equation for the temporal evolution of concentration in the bed sediment is:
???
??
= ?????
???
?????
? ????? + ??? (V-17)
where now the exchange due to erosion/deposition of suspended particles is written as:
??? = ?
?????
?????
?? > 0
?????
?????
?? < 0
(V-18)
The total concentration of pollutants in the sediment, Atot, is computed from:
???? = ???? (V-19)
All equations are solved using explicit finite di?erence schemes [V-2]. Second order accuracy
schemes are used for advective and di?usive terms.