Reduction of Contaminants in Soil and Water By Direct Electric Current - Electrokinetics for Petroleum and Environmental Engineers - page 38

(e.g., electric double layer for which Debye length is the width of the layer),
electroneutrality can be achieved considering Nernstian boundaries and
Faradaic reactions.

2.2.2 Theoretical Considerations: Transport of Water and Its

Constituents - Electroosmosis

In 1809, Reuss observed the electrokinetic phenomena when a DC current
was applied to a clay-water mixture. Water moved through the capillary
towards the cathode under the electric field. When the electric potential
was removed, the flow of water immediately stopped. In 1861, Quincke
found the electric potential difference across a membrane resulted from
streaming potential. Helmholtz first treated electroosmotic phenomena
analytically in 1879, and provided a mathematical basis. Smoluchowski
(1921) later modified it to also apply to electrophoretic velocity, also known
as the H-S theory. Helmholtz-Smoluchowski (H-S) theory describes the
migration velocity of one phase of material dispersed in another phase
under an applied electric potential. The electroosmotic velocity of a fluid of
certain viscosity and dielectric constant through a surface-charged porous
medium of zeta or electrokinetic potential ( ζ ), under an electric gradient,

E is given by the H-S equation as follows:

=⋅ ∂
∂

ez
h

Φ

(2.4) v

s

= kE

eo eo

x

where, v eo = electroosmotic (electrophoretic) velocity

e s = permittivity of the solvent or the pore fluid

h = viscosity of the solvent or the pore fluid

k eo = coefficient of electroosmotic conductivity

∂Φ / ∂ x = E = electric field

) potential in equation 2.4 has been shown to vary with
pH and ionic concentration of the pore fluid, as well as the electric field,
therefore is not constant during electroosmotic transport in clay media
(Probstein and Hicks, 1993). This makes it difficult to assess a velocity
term for temporal and spatial distribution predictions of the electroos-
motic transport. The nonlinearity and nonuniformity associated with the
electroosmotic velocity became apparent when experiments showed that
v e /E increased with E , hence rendering the other parameters of equation
2.4 to be functions of the electrical field (Ravian and Zaslavsky, 1967). In
a given clay deposit in the field, pore cross-sections, the electrical double

he zeta ( ζ