Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis

Mitchell originally proposed that an asymmetric ion flux across an organism's membrane could generate electric fields that drive locomotion. Although this locomotion mechanism was later rejected for some species of bacteria, engineered Janus particles have been realized that can swim due to ion fluxes generated by asymmetric electrochemical reactions. Here we present governing equations, scaling analyses and numerical simulations that describe the motion of bimetallic rod-shaped motors in hydrogen peroxide solutions due to reaction-induced charge auto-electrophoresis. The coupled Poisson-Nernst-Planck-Stokes equations are numerically solved using Frumkin-corrected Butler-Volmer equations to represent electrochemical reactions at the rod surface. Our simulations show strong agreement with the scaling analysis and experiments. The analysis shows that electrokinetic locomotion results from electro-osmotic fluid slip around the nanomotor surface. The electroviscous flow is driven by electrical body forces which are generated from a coupling of a reaction-induced dipolar charge density distribution and the electric field it creates. The magnitude of the electroviscous velocity increases quadratically with the surface reaction rate for an uncharged motor, and linearly when the motor supports a finite surface charge.