Effect of hydrodynamic slippage on electro-osmotic flow in zeta potential patterned nanochannels

Abstract

The effect of hydrodynamic slippage on the electro-osmotic flow in a nanochannel with thick electrical double layers whose wall surface potential has a periodic axial variation is studied. The equations of Stokes flow are solved exactly with the help of the Navier slip boundary condition and the Debye–Huckel linearization of the equation governing the potential of the electrical double layer. Each periodic cell of the flow field consists of four counter-rotating vortices. The cross-channel profile of the axial velocity at the center of the cell exhibits three extrema and a reversed velocity zone near the channel axis of symmetry. The size of the extrema and that of the reversed velocity zone increases with increase in the degree of slippage. In the limit when the wavelength of axial variation in surface potential is much larger than the channel width, the flow characteristics are interpreted in terms of the lubrication approximation. In the limit when the electrical double layer is much thinner than the channel height, the effect of slip is modeled by a Helmholtz–Smoluchowski apparent slip boundary condition that depends on the pattern wavelength.