On the competition between streaming potential effect and hydrodynamic slip effect in pressure-driven microchannel flows

The competition between streaming potential effect and hydrodynamic slip effect in pressure-driven microchannel flows is elucidated. The treatment is performed analytically in the framework of the Debye–Hückel linear approximation and the Navier slip boundary condition. As compared with pressure-driven flows in nonslip microchannels, pressure-driven flows in microchannels with hydrodynamic slippage are found to experience severer flow reduction (streaming potential effect). An apparent viscosity ratio is also defined to identify the competition between streaming potential effect and hydrodynamic slip effect in pressure-driven microchannel flows. It is shown that the streaming potential effect predominates when this ratio is larger than unity and the slip effect predominates when this ratio is smaller than unity. More importantly, we derive a formula for the critical slip length which provides a guideline for designing hydrophobic surfaces over which the effect of hydrodynamic slip exactly counteracts that of streaming potential.