Abstract
The electroviscous effect has been widely studied to investigate the effect of surface charge-induced electric double layers (EDL) on the pressure-driven flow in a micro/nano channel. EDL has been reported to reduce the velocity of fluid flow and increase the fluid drag. Nevertheless, the study on the combined effect of EDL with large zeta potential up to several hundred millivolts and surface charge depenedent-slip on the micro/nano flow is still needed. In this paper, the nonlinear Poisson–Boltzmann equation for electrical potential and ion distribution in non-overlapping EDL is first analytically solved. Then, the modified Navier–Stokes equation for the flow considering the effect of surface charge on the electrical conductivity of the electrolyte and slip length is analytically solved. This analysis is used to study the effect of non-overlapping EDL with large zeta potential on the pressure-driven flow in a microchannel with no-slip and charge-dependent slip conditions. The results show that the EDL leads to an increase in the fluid drag, but that slip can reduce the fluid drag. When the zeta potential is large enough, the electroviscous effect disappears for flow in the microchannel under a no-slip condition. However, the retardation of EDL on the flow and the enhancement of slip on the flow counteract each other under a slip condition. The underlying mechanisms of the effect of EDL with large zeta potential on fluid drag are the high net ionic concentration near the channel wall and the fast decay of electrical potential in the EDL when the zeta potential is large enough.
Highlights
With the development of advanced fabrication techniques, micro/nano electro-mechanical systems (MEMS/NEMS) have been realized and widely used
Deionized (DI) water is chosen as the electrolyte, and the diffusion constants of OH− and H+ are that many more counter-ions are attracted to the channel wall and there is a larger net local ionic concentration near the channel wall, and the two separate electric double layer (EDL) are more difficult to overlap with each other
Considering the effect of non-overlapping EDL on the electrical conductivity and slip length, the effect of nonoverlapping EDL with large zeta potential up to several hundred millivolts on the pressure-driven flow is introduced into the Navier–Stokes equation to study the electroviscous effect in a one-dimensional microchannel with no-slip condition and charge-dependent slip condition at the channel walls
Summary
With the development of advanced fabrication techniques, micro/nano electro-mechanical systems (MEMS/NEMS) have been realized and widely used. The adsorbed layer, a thin layer consisting of immobile ions strongly attracted to the solid surface because of electrostatic interaction, is formed next to the solid surface. The diffuse layer, a thin layer consisting of mobile ions, is formed because of loose electrostatic force and thermal diffusion Both the adsorbed layer and the diffuse layer constitute an electric double layer (EDL) [5,14,15,16]. To characterize the EDL, zeta potential is defined, and it refers to the electrical potential at the shear plane separating the immobile fluid layer strongly attracted to the solid surface from the rest of the liquid. Debye length κ−1 is the characteristic thickness of EDL, and is given by [5],
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