Mass transport and separation of species in an oscillating electro-osmotic flow caused by distinct periodic electric fields

In this work, we theoretically analyze how a passive solute is transported by an oscillating electro-osmotic flow along a parallel flat plate microchannel connecting two reservoirs with different concentrations. Three distinct periodic functions of the applied external electric field are considered: sawtooth, square, and parabolic waveforms, which are expressed as Fourier series. For each case, the dimensionless velocity and concentration fields are found analytically and, subsequently, the transport of the solute was obtained numerically. We distinguish four dimensionless parameters that govern the studied phenomenon: an angular Reynolds number, the Schmidt and Péclet numbers, and an electrokinetic parameter, this latter representing the ratio of the half-height of the microchannel to the Debye length. As has been reported in the specialized literature, the mass transport and separation of species in oscillating flows under the effect of an oscillatory pressure gradient can be increased with the angular frequency. For the present study, instead of a pressure gradient, we use oscillatory electro-osmotic forces, together with symmetric and asymmetric wall zeta potentials in the microchannel. For this condition, we prove that the transport of the solute is affected notably. In this paper, we show that controlling the type of the external electrical signal can also improve the mentioned tasks, depending on the Schmidt number, the electrokinetic parameter, and the angular Reynolds number.