Environmental Engineering Reference
In-Depth Information
medium is a solid framework of cation exchange surfaces with the pore
space occupied by chemically reactive species in aqueous solution, (iii) all
fluxes are linear homogeneous functions of all driving forces (or poten-
tial gradients), (iv) isothermal conditions prevail (coupled heat transfer is
neglected), (v) all the applied voltage is effective in fluid and charge trans-
port, (vi) electrophoresis is not present, (vii) soil particles are treated as
electrically nonconductive (insulators), (viii) surface conductance and
streaming potential are negligible, and (ix) hydraulic conductivity, coef-
ficient of EO permeability, and coefficient of volume compressibility are
constant in time and space (Alshawabkeh, 1996).
Several mechanisms contribute to the transport of mass in porous geo-
media under applied electric field including hydraulic or fluid flow, ion,
compound, and charge transport. In the following section a description
of these transport mechanisms under the aforementioned assumptions is
provided.
5.3
Fundamental Governing Equations
5.3.1 Fluid Flux
Fluid flux in a porous medium due to applied hydraulic gradient is given
by Darcy's law as:
(
)
(5.1)
h
J
=∇−
k h
w
h
where,
k
h
is the coefficient of hydraulic conductivity (LT
-1
), and
h
is the
hydraulic head (L). Microstructure, fabric, porosity, and pore size distri-
bution of the fine grain soils are the main factors that affect
k
h
and sig-
nificantly influence fluid transport under applied hydraulic gradient. Fluid
flux due to the applied electrical gradient in a porous medium is given by
the Helmholtz-Smoluchowski theory as:
(
)
e
(5.2)
J
=∇−
k
E
w
eo
ex
m
where,
k
eo
is electroosmosis permeability coefficient (L
2
V
-1
T
-1
), ε is
permittivity of the medium (Farad.L
-1
),
x
is zeta potential (V),
E
is elec-
tric potential (V), and
m
=
is dynamic viscosity of pore fluid (FTL
-2
).
Electroosmosis (EO) permeability coefficient depends mainly on porosity
and zeta potential of the soil. The total fluid flux due to applied hydraulic
and electrical gradients is given by:
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