Introduction to Electrokinetics - Electrokinetics for Petroleum and Environmental Engineers - page 6

where ε is the dielectric constant (relative permittivity, dimensionless);
ε o is the permittivity of free space [8.854×10 -12 C 2 /J.m=C 2 /N.m 2 ]; k B is the
Boltzmann constant (1.3806488×10− 23 J/K); T is the absolute temperature;
ρ i is the number density of ions in the solution; z is the valency; e is the elec-
tron charge (1.602 × 10 -19 C); 1/κ is the Debye length; and C is the electrical
charge (Coulomb: ampere second). Eq. 1.2 also shows that the charge den-
sity of the surface (σ c ) is proportional to the surface potential (ψ s ) .
With respect to an ionic solution, the Debye length is the distance
from the shear plane of the Stern layer to the bulk fluid. The Debye length
depends on the specific properties of the ionic solution. For aqueous solu-
tions (Donaldson and Alam, 2008):

1
k =

B
M

(1.3)

where B is a constant specific to the type of electrolyte. B is equal to
0.304 for monovalent cations and anions (NaCl); 0.176 where either the
cation or the anion has a valency of two (CaCl 2 or Na 2 CO 3 ); and 0.152
when both ions have a valency equal to two (CaCO 3 ). M is the molarity of
the pore solution (see Donaldson and Alam, 2008).
The composition of the Stern layer varies with respect to the nature
of the surface charge and ionic constituents of the electrolyte (Castellan,
1971):

1. The double layer may be entirely diffuse (no Stern layer) if
ions are not adsorbed on the solid surface (Fig. 1.5). In this
case the Stern layer does not exist and the potential differ-
ence declines exponentially from the solid surface to the
bulk solution.
2. If the concentration of ions in the electrolyte is sufficient to
exactly balance the surface charges of the solid, the poten-
tial will decrease linearly within the Stern layer to zero at
the shear plane. Thus, the zeta potential is zero (equal to the
potential of the bulk fluid).
3. If the adsorption of ions does not completely balance the
surface charge density, the zeta potential has a finite value
with respect to the bulk fluid.
4. If the surface charge is very strong, the Stern layer may con-
tain an excess of ions from the electrolyte. Thus, the zeta
potential will have a charge opposite to the surface charge.