  The nonlinear electrokinetic response of ionic solutions is important in
nanofluidics. However, quantitatively understanding the mechanisms is still a
challenging problem because of a lack of analytic approaches. Here, a general
framework for calculating the nonlinear electrokinetic coefficients of strongly
confined electrolytes is constructed using a perturbation scheme of the
pressure and voltage differences across a nanochannel. The theory is applied to
an electrically neutral nanochannel filled with electrolytes, and analytic
expressions for the first- and third-order electrokinetic coefficients are
obtained. We demonstrate that the combination of high hydrodynamic permeability
and ion-wall friction plays an essential role in nonlinear electrokinetics.
Furthermore, we analytically demonstrate that the external flow induces uniform
excess charge inside the nanochannel.
