92168.pdf

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,

dVc.U.FO e/£ _ g /~r 1^\

(7,32)

dt

or, correcting k 0 to account for the surface conductivity ks,

dVE.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:

dVE. 0 ./df Et (7.34)

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