92168.pdf

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,

QEE =

E

where QE 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, VE 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 +(2E of the electrokinetic unit and — QE 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),

ME = -^- (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

require an electrolyte concentration as low as 10~^5 rnol dm"^3 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