  Traveling wave charges lying on the insulating walls of an electrolyte-filled
capillary, give rise to oscillatory modes which vanish when averaged over the
period of oscillation. In this paper we show that they also give rise to a zero
velocity mode which does not vanish. The latter is a nonlinear effect caused by
continuous symmetry-breaking and the commensurate fluid velocity varies
quadratically with respect to the electric field generated by the charge
distribution, in contrast to the linear field dependence present in
conventional electroosmosis formulations. As the effect becomes more pronounced
by reducing the characteristic lengthscale of the system, it can be employed
for unidirectional transport of electrolytes in small capillaries. Certain
results from the literature are recovered as special cases of our formulation.
The hydrodynamic theory developed here is based on a semi-infinite space, on a
finite channel and on cylindrical capillary configurations. General relations
derived, expressing the zero mode velocity in terms of the electric potential
only, are independent of the boundary conditions imposed on the charge and
potential and can thus be adopted to suit alternative experimental conditions.
