Hydrodynamic flow in a microchannel due to nanocapillary membrane electro-osmotic flow

A model for hydrodynamic flow in a microchannel terminated by a nanocapillary membrane (NCM) is proposed in which the microchannel electric-double layer (EDL) is treated as a boundary-layer, providing a hydrodynamic slip-velocity at the channel wall, and the NCM electro-osmotic flow (EOF) is treated as fully-developed. Applied pressure gradients and the contribution of the microchannel EDL to both the net charge transport and the back-pressure on the NCM are neglected. The proposed coupling between the NCM EOF and microchannel hydrodynamic response is obtained by arguing that the steady-state Onsager symmetry between linear-response coefficients may be applied to the transient response of the microchannel. The resulting form of the Navier-Stokes equation in the microchannel possesses steady-state solutions that are compatible with parabolic and inverted-parabolic profiles observed in NCM sample concentration experiments.