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z
D
C
H
G
G
A
B
∆
z
∆
x
E
F
∆
y
y
x
FIGURE 3.1
Rectangular volume element in the soil. (From Selim and Amacher, 1997. With permission.)
Similarly, if
J
x
+Δ
x
is the solute flux in the
x
direction for solute leaving the
face EFGH, the total mass of solute leaving EFGH per unit time, that is, the
solute outflow rate, is
Solute
ouflowrate=J
yz
(3.3)
x+
x
From elementary calculus
J
x
+Δ
x
can be evaluated (approximately) from
∂
∂
J
x
(3.4)
J
= J
+
x
x
x+
x
x
where Μ
J
x
/Μ
x
is the rate of change of
J
x
in the
x
direction. From Equation
3.4, the net mass of solute flow (inflow minus outflow) per unit time in the
volume element from solute movement in the
x
direction is
Solute inflowrateSoluteoutflowrate=( J
−
−
J
)yz
x
x+x
(3.5)
J
x
−
∂
∂
=
x
xyz
Similarly, the net mass of solute flow per unit time from solute movement
in the
y
direction is
−
∂
∂
J
y
y
xyz
(3.6)
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