The effect of electrical double layer (EDL) on micro-channel flow has been studied widely. Most research focused on flows with typical channel width or pipe diameter much greater than the thickness of EDL (Debye length). In such cases, the influence of EDL on the overall electrical conductivity is small, and a constant bulk electrical conductivity is often used in calculations. In our study of pressure-driven micropipette injection flow, the pipe size is on the same order of magnitude as the Debye length. To elucidate the effect of overlapping EDL the flow inside a micro-channel was analyzed. The governing equations for the flow, the Poisson equation for the electric potential, and the charge continuity equation for the net charge were solved analytically. The effect of overlapping EDL on the electrical conductivity and velocity distribution in the micro-channel and the pressure drop were quantified. The results showed that, the average conductivity of electrolyte solution inside the channel increased significantly, dependent on the channel width. With the modified mean electrical conductivity, the pressure drop for the pressure-driven flow was smaller than that without considering the influence of EDL on conductivity.
Elastic instabilities in pressure-driven channel flow of thixotropic-viscoelasto-plastic fluids
