Environmental Engineering Reference
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the classical treatise of “electrokinetic phenomenon” in colloidal systems
(Hunter, 2001; Lyklema, 1995), it is this interface, known as the electric
double layer (EDL) or diffuse double layer (DDL) which plays a critical role
in the coupling between the ion motion and the fluid flow. The double
layer intrinsically connects the solid and the liquid phase, and mediates the
relative motion between the liquid and solid phase through (i) accumula-
tion of charge density; (ii) transport of charge and ions along surface; and
(iii) passage of charge to the surrounding electrolyte (Bard and Faulkner,
1980).
The bulk transport of ions in electrochemical systems without the con-
tribution of advection by water is described by Poisson-Nernst-Planck
(PNP) equations (Rubenstein, 1990). The well-known Nernst-Planck
equation describes the processes of diffusion, the process that drives the
ions from regions of higher concentration to regions of lower concen-
tration; and electromigration (also referred to as ion-migration ), the pro-
cess that launches the ions in the direction of the electric field (Bard and
Faulkner, 1980). Since the ions themselves contribute to the local electric
potential, Poisson's equation that relates the electrostatic potential to local
ion concentrations is solved simultaneously to describe this effect. The
electro-neutrality assumption simplifies the mathematical treatise of bulk
transport in most electrochemical systems. Nevertheless, this “no charge
density accumulation” assumption does not hold true at the inter-phase
regions of electric double layer between the solid and liquid, hence the
cause of most electrokinetic phenomenon in clay-electrolyte systems.
The analysis of mass transport by diffusion under chemical ( C/ x )
gradient and by migration under electrical ( ∂F / x) gradient in dilute
solutions - for which the interactions between individual species can be
neglected - is described by the Nernst-Planck [Eq. 2.1] and the Poisson's
[Eq. 2.2], together referred to as the PNP equations:
C
t
(
)
*
i
=∇
DCuzFC
+
Φ
(2.1)
i
i
i
i
i
−∇
e
2
Φ
= =∑
r
zFC
(2.2)
s
i
i
i
where, C, D * , u and z are the concentration, diffusion coefficient, mobility
and charge number of a single species i , respectively, and F is the Faraday's
constant (i.e., a mole of charge);
is the electrostatic potential; e s is the
permittivity of the solvent, and r is the charge density.
For many electrochemical systems the local electroneutrality condi-
tion is used, which sets the left-hand side of equation 2.2 to zero for zero
Φ
 
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