  Electrokinetic flows of an aqueous NaCl solution in nanochannels with
negatively charged surfaces are studied using molecular dynamics (MD)
simulations. The four transport coefficients that characterise the response to
weak electric and pressure fields, namely the coefficients for the electrical
current in response to the electric field ($M^{jj}$) and the pressure field
($M^{jm}$), and those for the mass flow in response to the same fields
($M^{mj}$ and $M^{mm}$), are obtained in the linear regime using a Green--Kubo
approach. Nonequilibrium simulations with explicit external fields are also
carried out, and the current and mass flows are directly obtained. The two
methods exhibit good agreement even for large external field strengths, and
Onsager's reciprocal relation ($M^{jm} = M^{mj}$) is numerically confirmed in
both approaches. The influence of the surface charge density on the flow is
also considered. The values of the transport coefficients are found to be
smaller for larger surface charge density, because the counter-ions strongly
bound near the channel surface interfere with the charge and mass flows. A
reversal of the streaming current and of the reciprocal electro-osmotic flow,
with a change of sign of $M^{mj}$ due to the excess co-ions, takes places for
very high surface charge density.
