the induced electric field: if one were to conduct an experiment in such conditions without considering any important electrical effects, these particles would go faster than the expected Poiseuille pressure-driven profile, leading to the incorrect conclusion that the velocity profile has a non-zero slip velocity at the wall. Thus, even if the flow satisfies the no-slip condition, measurements of particle velocities would lead to non-zero apparent slip lengths. We shall quantify this mechanism in the following sections.

Particle velocity
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![Schematic representation of the flow between two parallel plates with charged surfaces (zeta potential $\zeta_w$) and a charged suspended particle (zeta potential $\zeta_p$); in the case illustrated, $\zeta_w<0$ and $\zeta_p<0$. The channel height is $2h$, the particle radius is $a$, the smallest wall-particle distance is $d$ and the screening length $\kappa^{-1}$.[]{data-label="figure"}](channel.eps){width=".7\textwidth"}

We consider the presence of a single solid spherical particle of radius $a\ll h$ suspended in a two-dimensional channel of height $2h$ where a pressure-driven flow occurs, as illustrated in Figure \[figure\]; the particle is located at a distance $d=h-|z|$ from the closest wall. We also assume for simplicity that the presence of the particle does not modify the nature of ionic groups in solution (1:1 monovalent ions), so 