Page 220 - Introduction to Colloid and Surface Chemistry

Charged interfaces 209

Electro-osmosis

Experimentally, it is the volume flow rate which is measured. For a
single capillary of cross-sectional area A and with large Ka, this flow
rate is given from the Smoluchowski equation by

df 1
and since (by Ohm's law) AE - I/k 0, where k$ is the conductivity of
the liquid and / the current,
e/£
dV FO g
c.U. _ /~r 1^\
(7,32)
dt
or, correcting k 0 to account for the surface conductivity k s,
dV E. Q. d{
(7.33)

Equation (7.32) can be shown by a more general derivation 90 to
apply also to porous plugs, but, as in the case of streaming potential,
there is no satisfactory method of allowing for surface conductance.
Combination of equations (7.30) and (7.32) gives a general
relationship between electro-osmosis and streaming potential, Saxen's
equation, which, by a more general derivation, can be shown to apply
independent of plug structure and surface conductance:

dV E. 0./df E t
(7.34)
P