A method to determine zeta potential and Navier slip coefficient of microchannels

The no-slip boundary condition for liquid flows in microchannel has been applied successfully although it has no theoretical foundation. Liquid molecules, however, can slip at the liquid-solid interfaces if the liquid has a lower wettability. The velocity slip at the solid wall, called the Navier slip, is proportional to the velocity gradient at the wall for given wall physicochemical properties. Since the electroosmotic flow has a sharp velocity variation at the wall, the Navier slip of electroosmotic flow can be appreciable in a microchannel where there may be negligible Navier slip for a purely pressure-driven flow which has a smoother velocity variation at the wall. The Navier slip affects the volumetric flow rate and streaming potential significantly in electrokinetic flows and, therefore, one must be cautious about the possible occurrence of Navier slip in the design and operation of various microfluidic devices. In the present work, we have devised a simple method of estimating both Navier slip coefficient and zeta potential by measuring both the volumetric flow rate under a given pressure gradient after eliminating streaming potential and streaming potential under a given pressure gradient. Instead of streaming potential, one may adopt volumetric flow rate under a given external electric field. The method relies on a semi-analytic formula derived in the present work, which allows evaluation of streaming potential and volumetric flow rate without the necessity of numerical solution of nonlinear partial differential equations. The present method is found to estimate both slip coefficient and zeta potential reasonably accurately even using contaminated experimental data.