Page 211 - Introduction to Colloid and Surface Chemistry

200 Charged interfaces

The Huckel equation (small KO)

Consider KO to be small enough for a spherical particle to be treated
as a point charge in an unperturbed electric field, but let the particle
be large enough for Stokes' law to apply. Equating the electrical force
on the particle with the frictional resistance of the medium,
Q EE =

E
where Q E is the net charge on the particle (i.e. the electrokinetic
unit), E is the electric field strength, 17 is the viscosity of the medium,
a is the radius of the particle, V E is the electrophoretic velocity and « E
is the electrophoretic mobility.
The zeta potential is the resultant potential at the surface of shear
due to the charges +(2 E of the electrokinetic unit and — Q E of the
mobile part of the double layer - i.e.

r. QE QE

QE (7-22)
4irea(l + KO)
where 6 is the permittivity of the electrolyte medium (see footnote on
page 179). Therefore (neglecting Ka compared with unity),

M E = -^- (7.23)
1.51?
The Huckel equation is not likely to be applicable to particle
electrophoresis in aqueous media; for example, particles of radius
10~ 8 m suspended in a 1-1 aqueous electrolyte solution would
5
3
require an electrolyte concentration as low as 10~ rnol dm" to give
KO = 0.1. The equation, however, does have possible applicability to
electrophoresis in non-aqueous media of low conductance.
The Smoluchowski equation (large KO)

Consider the motion of liquid in the diffuse part of the double layer
relative to that of a non-conducting flat surface when an electric field