Electrokinetic self-propulsion by inhomogeneous surface kinetics

Electrokinetic self-propulsion was conceptually proven in recent experiments wherein bimetallic nano-rods were observed to migrate when placed in aqueous solutions. We present here a systematic theoretical model of the self-propulsion mechanism, analysing the steady-state transport occurring about an autonomously moving inhomogeneous particle. The non-uniform catalysis on the particle surface is modelled via position-dependent cation redox coefficients. The particle shape is axisymmetric but otherwise arbitrary, as are the distributions of the (possibly discontinuous) kinetic coefficients along its boundary. We formulate the mathematical problem governing this electrokinetic transport. In the thin-Debye-layer limit, the microscale description is transformed into a macroscale one, applying in the electro-neutral bulk. Effective boundary conditions represent asymptotic matching with the Debye-layer fields. A linearized model is derived for weak variation of the kinetic coefficients and is solved for a spherical-particle geometry. With a view towards understanding existing experiments, the macroscale model is used for analysing slender particles. Matched asymptotic expansions provide the particle velocity as a functional of its shape and kinetic-coefficient distributions. The predicted self-propulsion is in the direction observed in nanorod experiments.