Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 73

and that of Rao et al. (1976):

D= D ( +λ τ v )

(3.27)

o

More general regression formulas were proposed, including those of De
Smedt and Wierenga (1984) and Wierenga (1977):

D=ab +

(3.28)

and

D=ab v + (3.29)

where a and b are constants, with a much greater than D o . Another regression
formula is also used (Bond and Smiles, 1983; Rose, 1977; Bond, 1986):

( )

b

(3.30)

D= D Γ+ aP

m e

where I is a constant and P is the particle Peclet number defined as:

Pl D o =υ /

(3. 31)

where the term l is a characteristic length of the porous medium.
Besides water flow velocity, D or D o is also affected by the degree of water
saturation. D is usually much larger in unsaturated soils (De Smedt and
Wierenga, 1984; Laryea et al., 1982). In a horizontal infiltration study with a
silty clay loam, Laryea et al. (1982) estimated increased D values as the soil
water content increased. Moreover, D depends on porosity and pore size dis-
tribution. Koch and Fluhler (1993) found that D values were much larger in
porous beads than in spherical solid beads.
Combining Equations 3.13, 3.14, and 3.16 yields the following simplified
solute flux expression in the z direction:

J =D C
z

∂
∂

−Θ + q C (3.32)

z z

which incorporates the effects of mass flow or convection as well as diffusion
and mechanical dispersion. Incorporation of the flux Equation 3.19 into the
conservation of mass Equation 3.13 yields the following generalized form for
solute transport in soils in one dimension:

q C
z

∂θ
∂

C
t

ρ ∂
∂

S
t

∂
∂

∂
∂

C
z

− ∂

+ = θ D

z

(3.33)

z ∂