Introduction to Electrokinetics - Electrokinetics for Petroleum and Environmental Engineers - page 2

1.1 Factors Influencing Electrokinetic Phenomena

The theoretical development of electrokinetic phenomena and electro-
chemical transport has been studied historically as far back as 1879 by
Helmholtz that led to the introduction of the first analytical equation.
Helmholtz described the motion of the charged ionic solution from the
anode to the cathode and explained it by the presence of a double layer.
This double-layer theory is illustrated in figure 1-1, where the negatively
charged surface of the clay attracts the positive ions of aqueous medium,
forming the immobile double layer. This immobile double layer is followed
by a thick mobile layer with a predominance of positively-charged ions
(cations), with a few diffused negatively-charged ions (anions).
Later, the analytical solution was further modified by Smoluchowski in
1921 to arrive at the Helmholtz-Smoluchowski's equation for electroki-
netic permeability:

D

z
p

(1.1)

k =

e

4 F

where D is the dielectric constant; z is the zeta potential; and F is the
formation factor.

Cathode Anode

P

Rock

I

II IV

III

Rock

Figure 1.1 Schematic diagram of electrokinetics double layer (I: Immobile Double Layer,
II: Mobile Double Layer, III: Free Water, IV: Velocity Profile) as envisioned by Dr. George
V. Chilingar. Solid curved line - velocity profile in a capillary. P=DC current power
supply. Rock is negatively charged.