Surface conductivity and the streaming potential near a rotating disk-shaped sample

Surface conductivity can complicate the determination of a sample's zeta potential from electrokinetic measurements. Correction factors have been derived to mitigate the problem for common systems such as particles, plates, and porous plugs. These factors are functions of the Dukhin number Du given by Ks/Ka where Ks is the surface conductivity, K is the electrolyte conductivity, and a is a length scale appropriate for the sample geometry. Here, the correction factor for the rotating disk geometry, in terms comparable to equations for particles, capillaries, and porous plugs, is shown to be f(Du) is approximately equal to 1 + 1.516Du + 0.135Du(2). The reciprocal of the f(Du) equation expresses the factor by which surface conductivity reduces the measured streaming potential for a given sample's true zeta potential. The theory shows that surface conductivity is negligible in the rotating disk geometry for essentially all ionic strengths because the disk radius is the natural length scale for Du. The correction for surface conductivity for a KCl solution with an ionic strength equivalent to the ionic strength of pure water would be only 1% for a disk 10 mm in diameter. The ohmic resistance to the return of surface current from the disk's periphery through the bulk liquid to the axis is always much smaller than the resistance to the return of surface current back through the diffuse charge cloud of the double layer. The rotating disk geometry is unusual in this regard.