Page 213 - Introduction to Colloid and Surface Chemistry

202 Charged interfaces
It follows from this expressioin that the electrophoretic mobility of a
non-conducting particle for which KO is large at all points on the
surface should be independent of its size and shape provided that the
zeta potential is constant.
If electro-osmosis is being considered, a similar expression (i.e.
v
E.oJE = £e/7j) is derived, the boundary conditions being $ = 0, v =
V
E.O. at JT = oc and fy = £,v = 0 at the surface of shear, where V E 0 is
the electro-osmotic velocity.
The Henry equation

Henry 187 derived a general electrophoretic equation for conducting
and non-conducting spheres which takes the form

i)] (7.25)
.
where ¥(KO) varies between zero for small values of KU and 1.0 for
large values of KO> and A = (& 0-~*i)/(2&o+/Ci), where k 0 is the
conductivity of the bulk electrolyte solution and ki is the conductivity
of the particles. For small KO the effect of particle conductance is
negligible. For large KU the Henry equation predicts that A should
approach — 1 and the electrophoretic mobility approach zero as the
particle conductivity increases; however, in most practical cases,
'conducting' particles are rapidly polarised by the applied electric
field and behave as non-conductors.
l
For non-conducting particles (A = /2) the Henry equation can be
written in the form

% =~il-f(Kfl) (7,26)
1.57J
where f (KO) varies between 1.0 for small tea (Hiickel equation) and
1.5 for large KO (Smoluchowski equation) (see Figure 7.12). Zeta
potentials calculated from the Hiickel equation (for KO = 0.5) and
from the Smoluchowski equation (for KM — 300) differ by about 1 per
cent from the corresponding zeta potentials calculated from the
Henry equation.
The Henry equation is based on several simplifying assumptions:

1. The Debye-Huckel approximation is made.
2. The applied electric field and the field of the electric double layer