small). If condition is not met, the slip length is in fact a “stick” length ($\lambda<0$) and the particle goes slower than the liquid. Finally, note that within the Debye-Hückel limit $t_w\ll 1$, the slip length becomes $$\label{slipdebye}
\frac{\lambda}{h}=\frac{2\zeta_w(f(\kappa
a)\zeta_p-\zeta_w)(\e)^2}{2\sigma\mu h^2+(\e\zeta_w)^2\kappa h}
\cdot$$

Discussion
==========

The results presented in the previous section allow one to calculate, for a given set of experimentally determined material and fluid parameters, the amount of apparent slip in the particle velocity which is due to the streaming potential. We present in this section some general observations on formula as well as an estimate for the order of magnitude of the effect in water and a comparison with available experimental slip measurements.

Variations of the slip length
-----------------------------

All the variables in can be made to vary independently except for the screening length $\kappa^{-1}$ and the bulk conductivity $\sigma$ which both depend on the ionic strength of the solution. A simple estimate for the bulk conductivity of a 1:1 solution is $ \sigma= {2 b n_0e^2}$ (see e.g. [@probstein]), where $n_0$ is the bulk ion concentration and $b$ is the ion mobility, which we approximate by the mobility of a spherical particle, $b^{-1} \approx 6\pi \mu 