- Electroosmosis
Movement of water through a solid matrix under an electric field - Electrophoresis
Movement of suspended particles through water under an electric field - Streaming potential
Small electric field caused by the movement of water through a soil matrix - Sedimentation potential
Small electric field caused by movement (sedimentation) of solid particles through water - Ion Migration
Movement of cations and anions under an electric field
Of these phenomena, electroosmosis and electrophoresis are the most relevant to the commercial application of EKG. Electroosmosis generally occurs in soils, and electrophoresis tends to occur in slurries and colloids. The boundary between the two processes is somewhat gradational but can be related to Atterberg limits.
When a D.C. voltage is applied across a wet soil mass, ion migration takes place. Positive ions (cations) are attracted to the cathode and repelled from the anode and negative ions (anions) are forced in the opposite direction. As the cations migrate along the porewater / solid boundary layer they drag with them their water of hydration and exert a viscous drag upon the free pore fluid around them. The Helmholtz-Smoluchowski theory (Helmholtz, 1879; Smoluchowski, 1914) is the generally favoured theory of electroosmosis, and the condenser analogy it adopts assumes that the soil capillaries have charges of one sign on or near the surface of the wall (negative) and countercharges (positive) concentrated in a double layer protruding a small distance from the wall, the remaining void is assumed to be filled with free pore fluid, as shown below.
Helmholtz-Smoluchowski Model for electroosmotic flow (After Mitchell, 1993).
The Helmholtz-Smoluchowski theory states that upon the application of an
electrical potential difference across the system the mobile shell of counter-ions
drags water through the capillary by plug flow, resulting in a high velocity
gradient between the two plates of the ‘condenser’. The rate of
water flow is controlled by the balance between the electrical force causing
water movement in one direction and friction between the liquid and the wall
in the other. The overall flow (qA) generated by the
application of a potential difference (D) may be expressed as (Mitchell, 1993):
where ke is the electroosmotic permeability of the soil; V/ L is the electrical
potential gradient; and A is the cross-sectional area of the soil sample across
which the potential difference is applied. As such this is analogous to Darcy's
Law of hydraulic flow. Where Q is the flow rate; kh is the hydraulic permeability;
ih is the hydraulic gradient and A is the cross sectional area of the soil.
The overriding benefit of electroosmosis is that Ke is independent of pore
size and has a relatively constant value in soils. This is in stark contrast
to hydraulic permeability (kh) which decreases markedly with pore size as
shown below.
Electroosmotic performance over a range of soils.
This means that as soils become finer and more impermeable, the relative
benefit of electroosmotic flow increases. The net result is that electroosmosis
can cause significant flow of water in materials that under normal circumstances
are effectively impermeable. This result has profound ramifications for engineering
disciplines.
