Determination of forced convection effects on the response of membrane-based ion-selective electrodes via numerical solution to the Navier-Stokes-Nernst-Plank-Poisson equations

Ion selective electrodes (ISEs) enable measurements via the build-up of a phase boundary potential at the surface of a sensing membrane. While a framework exists to understand the performance of ISEs in stagnant samples, the influences of fluid flow on ISEs are less studied. We model the transport of ions in solution occurring near interfaces between ISE membranes and aqueous samples when subject to an external flow. We developed a numerical model extending the Pressure-Implicit with Splitting of Operators (PISO) algorithm to incorporate the Navier-Stokes-Nernst-Plank-Poisson system of equations. We find that external flow distorts the aqueous side of the formed double layer at the ISE membrane and aqueous sample interface, leading to an increase in the phase boundary potential. The change in potential is shown to be a function of a novel set of dimensionless numbers, most notably the Debye Length Reynolds number, i.e., the Reynolds number with the Debye Length as the system dimension.