Ionic current magnetic fields in a two dimensional nanoslit

Internal and external magnetic fields due to pressure-driven ionic currents inside a two- dimensional nanoslit are obtained theoretically and numerically by finite element solution of governing equations, i.e. , Poisson-Nernst-Planck, Ampere, and Navier-Stokes equations. The transport governing equations in this study are non-dimensionalized by Debye screening length, and discretized in a two dimensional finite length nanoslit. The magnetic field components have opposite signs above and below the nanoslit due to opposite directions of the Amperian closed path. Within the nanoslit the non-uniformity of ionic currents resulted in non-uniform magnetic fields however outside the nanoslit, magnetic fields remain relatively constant, independent of the distance from a sufficiently long and wide nanoslit. It is anticipated that non-invasive ionic/streaming current measurements can be conducted by external magnetic fields readouts in sufficiently long and wide nanoslits. For instance, to estimate electrical properties (zeta potential) of solid-liquid interface, and to accurately sequence DNA and biomolecules.