the wall would hinder some component of the measured slip velocity. Note that if walls were not present, a correction to the velocity accounting for the finite size of the particle and the spatial variations of the fluid velocity would also be present, but only at second order in the ratio of the particle size to the length scale over which flow variations occur [@hinch].

#### Electrical contribution

In general the particle will be charged, with a zeta potential $\zeta_p$ which we assume to be uniform. Consequently, its velocity will include a contribution from electrical forces, ${\bf
U}_{\rm elec}(z)$. This velocity has two components $$\label{}
  {\bf U}_{\rm elec}(z)={\bf U_{\rm EPH}}+U_{\rm drift}(z)\,{\bf
  e}_z,$$ where ${\bf U_{\rm EPH}}$ is an electrophoretic velocity due to the presence of an external electric field and $U_{\rm drift}(z)$ is a vertical drift due to the electrostatic interactions between the charged particle and the charged walls. Such drift will only be significant if the double layers around the particle and along the channel walls overlap, and will be exponentially screened otherwise [@saville]. We will assume that such requirement is met in practice $\kappa d \gtrsim {\cal O}(1)$, so that it can be neglected.

When the electric field 