Fundamentals of electrokinetics - In-Situ Remediation of Arsenic-Contaminated Sites - page 88

Figure 5.1. Empirical relation between pH and zeta potential ( ζ ).

5.2.1.2 Electroosmosis or electroosmotic advection
During electrokinetic processing, pore water is transported by electroosmosis, which together
with electromigration, provides an important mechanism for removing contaminants from porous
media. Electroosmotic velocity on a plane surface, V eo [m s − 1 ], is expressed as (Mitchell and
Yeung, 1991; Mitchell and Soga, 2005; Pamucku and Wittle, 1994; Probstein, 2003; Shapiro,
1990):

V eo =− ( εζ/µ ) E (5.4)

where ε is the permittivity of the medium [C V − 1 m − 1 ], ζ is the zeta potential [V], E is the electric
field strength or electrical potential gradient [V m − 1 ] in a direction parallel to the electroosmotic
flow, and

is the viscosity of the medium [N s m − 2 ]. The zeta potential is defined as the electrical
potential at the shear or slipping plane between the moving and stationary phases (Dzombak and
Morel, 1990; Mitchell and Soga, 2005). This formula for electroosmotic velocity on a charged
plane surface is known as the Helmholtz-Smoluchowski relation. According to this equation, the
electroosmotic velocity ( V eo ) is significantly affected by the electric field strength ( E ) and the
zeta potential ( ζ ). The magnitude and sign of ζ depend on the interfacial chemistry, and it can be
expressed by a complex function of the chemistry of both liquid and solid phases (Eykholt and
Daniel, 1994). An example of the relationship between the zeta potential and pH of a kaolinite
medium has been empirically determined (Eykholt and Daniel, 1994; Kim et al ., 2003; Lorenz,
1969):

µ

281e − 0 . 48pH ζ [mV] =− 38 . 6 + (5.5a)

194e − 0 . 41pH ζ [mV] =− 29 . 9 + (5.5b)

The empirical relations between pH and ζ are presented in Figure 5.1 , which are compared
to those suggested by Lorenz (1969) and Kim et al . (2003). In addition, the effect of electrolyte
concentration on zeta potential is represented by Kruyt (1952) and Alshawabkeh (1994):

ζ = A − B log C (5.6)