A general flux-based analysis for spherical electrocatalytic nanomotors

We present a flux-based analysis of the motion of spherical electrocatalytic nanomotors based on an electrokinetic model with general distribution of cation flux over the motor surface. Using the method of matched asymptotic expansions, we find a general expression for the motor velocity to leading order in the Debye length in the limit of weak surface cation flux. The nanomotor velocity is proportional to the first Legendre coefficient of surface cation flux and depends non-linearly on the interfacial potential at the particle surface, inversely on the fluid viscosity and background ion concentration in the electrolyte. The results are consistent with previous experimental observations and numerical calculations. We also provide a scaling analysis that portrays the physical picture of self-electrophoresis at the molecular level based on migration of ions and transfer of their momentum to fluid.