 Velocity maximum in a one-charged-wall channel

Differentiating the screened-channel velocity gives $x_{\max }=d-{\kappa }^{-1}\mathrm{arsinh}[(\cosh \kappa d-1)/(\kappa d)]$. For $\kappa d\gg 1$, $x_{\max }\simeq \log (\kappa d)/\kappa$. The outer flow declines almost linearly to the passive no-slip wall rather than forming a symmetric plug.