Uptake of Organic Contaminants from Soil into Vegetables and Fruits - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 379

Change of contaminant mass in soil is deposition from air minus leaching,
run-off, volatilization, degradation and uptake into roots. Division by soil mass, M S ,
results in the concentration in soil:

dC s
dt =

I s
M s −

k s × C s (9.15)

where I S (mg d − 1 ) is input to soil (including deposition from air), and k S (d − 1 )is
the sum of all first-order loss rates from soil. For parameters for the equation, see
other sections of this topic.
The mass balance for thick roots, such as carrots, can be described as follows.
Change of contaminant mass in roots is influx with water minus outflux with
xylem sap. Diffusive uptake is not considered, since it only makes a small
change in the concentration in roots. The root is described with the following
equation:

dm R
dt

= Q × C W − Q × C Xy (9.16)

where m R is the mass of contaminant in roots (mg), Q is the transpiration stream
(L d − 1 ), C W is the concentration in soil pore water (mg L − 1 ) and C Xy is the con-
centration in the xylem at the outflow of the root (mg L − 1 ). If the xylem sap is in
equilibrium with the root, the concentration is C Xy = C R /K RW . K RW (L kg − 1 )isthe

partition coefficient between root and water (Eq. 9.10 ). The concentration in soil
pore water, C W ,is C S × K WS . Substituting these expressions in Eq. 9.16 gives the

following equation:

d ( C R ×

dm R
dt

M R ) Q

K RW ×

= = Q × K WS ×

C S −

C R (9.17)

dt

If plant growth is exponential, and the ratio Q/M R (transpiration stream Q to root
mass M R (kg)) is constant, the growth by exponential dilution can be considered by
a first-order growth rate k R (d − 1 ). If first order degradation or metabolism occurs,
the rate k R is the sum of the loss processes and the growth dilution. Division by mass
of the root results in the concentration in roots:

Q
M R ×

dC R
dt

Q
M R ×

=

K WS × C S −

K RW ×

C R − K R ×

C R (9.18)

The mass balance for leaves can be described as follows.
Change of contaminant mass in leaves is influx with transpiration water plus
gaseous and particulate deposition from air minus diffusion to air. This results in
the following equation:

dm L
dt

Q
K RW

A L × v dep

= C R + A L × g L × (1 − f P ) × C A + × f P × C A

2

(9.19)

1000 Lm − 3
K LA

A L × g L ×

− × C L