Environmental Engineering Reference
In-Depth Information
Transport of dissolved solutes in the porewater solely by advective means will progress in
concert with the advective velocity. In situations where the solutes possess kinetic energy
and demonstrate Brownian activity, diffusion of these solutes will occur. Using the pore-
water as the carrier, the solutes will combine their diffusive capability with advective
velocity to produce the combined mass transport. This permits the dissolved solutes to
move ahead of the advective front, i.e., the general tendency is for the diffusion front to
precede the advection front. In situations where tortuosity and pore size differences com-
bine with pore restrictions to create local mixing in the movement of the dissolved solutes,
dispersion results. The degree of dispersion and the resultant effect on mass transport is
not readily quantiied.
The diffusive movement of a particular solute (contaminant) is characterized by its dif-
fusion coeficient. This diffusion coeficient D c is most often considered as being equiva-
lent or equal to the effective molecular diffusion coeficient. In dilute solutions of a single
ionic species, the diffusion coeficient of that single species is termed as the ininite solution
diffusion coeficient D o . The ininite solution diffusion coeficients are dependent on such
factors as: ionic radius, absolute mobility of the ion, temperature, viscosity of the luid
medium, valence of the ion, equivalent limiting conductivity of the ion, etc. A useful list-
ing of these coeficients for a range of solutes and for various sets of conditions can be
found in many basic handbooks and other references (e.g., Li and Gregory, 1974; Lerman,
1979). From a theoretical point of view, the studies of molecular diffusion by Nernst (1888)
and Einstein (1905) show the level of complex interdependencies that combine to produce
the resultant coeficient obtained. From studies dealing with the movement of suspended
particles controlled by osmotic forces in the solution, the three expressions most often
cited, which are
uRT
N
Nernst-Einstein
D
o =
=
uk T
(9.3)
RT
Nr
T
r
21
Einstein-Stokes
D
o =
=
7 166
.
×
10
(9.4)
6
πη
η
o
o
RT
Fz
λ
T
λ
10
Nernst
D
o =
=
8 928
.
×
10
(9.5)
2
z
where D o is the diffusion coeficient in an ininite solution, u is the absolute mobility of the
solute under consideration, R is the universal gas constant, T is the absolute temperature,
N is the Avogadro's number, k' is the Boltzmann's constant, λ o is the conductivity of the
target ion or solute, r is the radius of the hydrated ion or solute, η is the absolute viscosity
of the luid, z is the valence of the ion, and F is the Faraday's constant. A large listing of
experimental values for λ o for major ions can be found in Robinson and Stokes (1959).
We deine a dimensionless Peclet number as Pe = v L d/D o , where v L is the longitudinal low
velocity (advective low). From the information reported by Perkins and Johnston (1963), it
is seen that for Peclet numbers less than 1 ( Pe < 1), diffusive transport of the contaminant
solutes in a contaminant plume travels faster than the advective low of water. For Pe >
10, advective low constitutes the dominant low mechanism for the movement of solutes.
In between the values of 1 and 10, there is a gradual change from diffusion-dominant to
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