Uptake of Organic Contaminants from Soil into Vegetables and Fruits - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 381

Mass balances for fruit and grain can be set up analogous to Eq. ( 9.20 ). However,
the processes and parameters differ. For grain, we assume no particle deposition and
a lower soil attachment value.

9.4.3 Steady-State Solution for the Root and Leaf Model

The steady-state ( t →∞ ) concentration in roots, C R , with constant concentration in

soil, C Soil , is as follows:

Q

C R =

M R ×

K WS × C Soil (9.22)

Q

K RW +

K R ×

For leaves, the steady state concentration is:

I
a

C L = (9.23)

where I is the sum of all input terms (mg kg − 1 d − 1 ):

Q
M L ×

A L × g L A L × v dep

2 M L

I =

K RW ×

C R + × (1 − f P ) × C A + × f p × C A (9.24)

M L

and a is the sum of all loss processes (d − 1 ):

1000 Lm − 3
K LA ×

A L × g L ×

a = + k L (9.25)

M L

9.4.4 General Solutions for a Cascade Model

The system of three linear differential equations (Eqs. 9.15 , 9.18 and 9.20 ) can be
solved analytically or numerically for continuous or pulse input. Continuous input
occurs from atmospheric deposition to soil and leaves, whereas pulse inputs vary,
e.g. inputs from accidents, pesticide spray application and application of manure or
compost.
The differential equations for the contaminant concentration in soil, root and
leaves can be treated as a diagonal matrix, so that:

dC 1
dt

=− k 1 C 1 + I 1 / M 1 (9.26)

dC 2
dt

=+ k 12 C 1 − k 2 C 2 + I 2 / M 2 (9.27)

dC 3
dt

=+ k 23 C 2 − k 3 C 3 + I 3 / M 3 (9.28)