Multiply by 1.0....

The conversion from mobility (measured) to zeta potential (inferred) relies on the Henry equation and a term f(k,a) - Henry's function - which relates the thickness of the double layer to the size of the particle itself. Conversion from mobility to zeta potential either involves the Smoluchkowski or Huckel assumptions on the value of f(k,a) - either 1.0 (H) or 1.5 (Smol). Intermediate values for f(k, a) can also be invoked. In electrolytes Smoluchkowski is the usual approximation whereas small particles in low dielectric constant media (e.g. non-aqueous media), f(ka) is assumed to be 1.0. Take a look at the attached and also 'Guidance to improve the scientific value of zeta-potential measurements in nanoEHS'

Environ. Sci.: Nano, 2016, 3, 953-965 DOI: 10.1039/C6EN00136J

Many thanks Alan, your file is really helpful.

Hi,

Zeta potential of particles in dispersion is typically calculated from the electrophoretic mobility of the particles.

In this conversion from mobility (UE) to zeta potential (z), using Henry's equation, includes accountancy for the particle size relative to the Debye length (k):

UE=2 epsilon z f(ka)/2 eta

Where eta is the sample viscosity and epsilon is the dielectric constant.

f(ka) is Henry's function and takes the value of 1.5 in the Smoluchowski model, and 1 in the Huckel model, with the latter describing particles in a non polar media.

So in answer to your question, zeta potential with a different model can be calculated using Henry's equation and the appropriate f(ka) value, however I am not sure what you mean by "normal" zeta potential.

http://www.materials-talks.com/wp-content/uploads/2017/09/mrk654-01_an_introduction_to_zeta_potential_v3.pdf

All calculations of zeta potential are approximations. The more "accurate" the model, the more information you need about your sample and the less likely you are to have it. Henry's function can be very misleading particularly in the situation where the particle diameter and double layer thickness are of comparable size. Unless you know the concentrations and conductivities of all the ionic species in your sample and the particle size then, frankly, just stick with the Smoluchowski or Huckel approximations. But don't make the common mistake of applying Smoluchowski to aqueous and Huckel to non-aqueous that so many people do. There are more factors to consider.

In my personal opinion, a lot of people get so concerned about calculating the zeta potential, they overlook the fact very often you might as well just use the electrophoretic mobility.

To add to my previous comment, here are some data for polystyrene microgel particles dispersed in various concentrations of aqueous KCl. Four different models were used to calculate zeta potential from mobility (Huckel, Smoluchowski, Ohshima, and O'Brien and White. The latter two are much more rigorous than the other two and Henry. As you can see, in the most common range of salt concentrations there is considerable disagreement between Smoluchowski and the more rigorous models. Note also that the lower values at high salt concentrations may be due to electrode polarization issues.

The data were generated for my dissertation:

http://enlightenscientific.com/john-francis-miller-phd-thesis-a4-with-toc/

More information about electrode polarization effects is here:

http://enlightenscientific.com/2018/08/17/next-generation-els/

Thanks to everyone for sharing your knowledge.