slip length reaches a maximum $\lambda^*$ for $\zeta_w=\zeta_w^*$. Right: maximum value of the apparent slip length $\lambda^*$ as a function of the particle zeta potential $\zeta_p$ for $\kappa h=10$, $\kappa a \ll 1$ and three values of the ionic strength: $n_0=10^{-6}$ mol l$^{-1}$ (pure water, $\kappa^{-1}\approx 300$ nm, solid line), $n_0=10^{-4}$ mol l$^{-1}$ ($\kappa^{-1}\approx 30$ nm, dashed line), $n_0=10^{-2}$ mol l$^{-1}$ (tap water, $\kappa^{-1}\approx
3$ nm, dotted line).[]{data-label="maximum"}](maximum.eps "fig:"){width=".48\textwidth"} ![Left: variation of the apparent slip length $\lambda$ for pure water as a function of the wall zeta potential $\zeta_w$ for $\zeta_p=50$ mV, $n_0=10^{-6}$ mol l$^{-1}$ (pure water), $\kappa h=10$ and $\kappa
a \ll 1$; the slip length reaches a maximum $\lambda^*$ for $\zeta_w=\zeta_w^*$. Right: maximum value of the apparent slip length $\lambda^*$ as a function of the particle zeta potential $\zeta_p$ for $\kappa h=10$, $\kappa a \ll 1$ and three values of the ionic strength: $n_0=10^{-6}$ mol l$^{-1}$ (pure water, $\kappa^{-1}\approx 300$ nm, solid line), $n_0=10^{-4}$ mol l$^{-1}$ ($\kappa^{-1}\approx 30$ nm, dashed line), $n_0=10^{-2}$ mol l$^{-1}$ (tap water, $\kappa^{-1}\approx
3$ nm, dotted line).[]{data-label="maximum"}](variation.eps "fig:"){width=".48\textwidth"}

Order of magnitude for water
----------------------------

Let us address here the case of water at room temperature (T=300C, $\epsilon$=80, $\ell \approx 2$ Å). We have calculated 