92168.pdf

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.

vE.oJE = £e/7j) is derived, the boundary conditions being $ = 0, v =

VE.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.

For non-conducting particles (A = l/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