  We propose a method to model metallic surfaces in Lattice Boltzmann
Electrokinetics simulations (LBE), a lattice-based algorithm rooted in kinetic
theory which captures the coupled solvent and ion dynamics in electrolyte
solutions. This is achieved by a simple rule to impose electrostatic boundary
conditions, in a consistent way with the location of the hydrodynamic interface
for stick boundary conditions. The proposed method also provides the local
charge induced on the electrode by the instantaneous distribution of ions under
voltage. We validate it in the low voltage regime by comparison with analytical
results in two model nanocapacitors: parallel plate and coaxial electrodes. We
examine the steady-state ionic concentrations and electric potential profiles
(and corresponding capacitance), the time-dependent response of the charge on
the electrodes, as well as the steady-state electro-osmotic profiles in the
presence of an additional, tangential electric field. The LBE method further
provides the time-dependence of these quantities, as illustrated on the
electro-osmotic response. While we do not consider this case in the present
work, which focuses on the validation of the method, the latter readily applies
to large voltages between the electrodes, as well as to time-dependent
voltages. This work opens the way to the LBE simulation of more complex systems
involving electrodes and metallic surfaces, such as sensing devices based on
nanofluidic channels and nanotubes, or porous electrodes.
