Benedikt Sabass, Udo Seifert
A small, bimetallic particle in a hydrogen peroxide solution can propel
itself by means of an electrocatalytic reaction. The swimming is driven by a
flux of ions around the particle. We model this process for the presence of a
monovalent salt, where reaction-driven proton currents induce salt ion
currents. A theory for thin diffuse layers is employed, which yields nonlinear,
coupled transport equations. The boundary conditions include a compact Stern
layer of adsorbed ions. Electrochemical processes on the particle surface are
modeled with a first order reaction of the Butler-Volmer type. The equations
are solved numerically for the swimming speed. An analytical approximation is
derived under the assumption that the decomposition of hydrogen peroxide occurs
mainly without inducing an electric current. We find that the swimming speed
increases linearly with hydrogen peroxide concentration for small
concentrations. The influence of ion diffusion on the reaction rate can lead to
a concave shape of the function of speed vs. hydrogen peroxide concentration.
The compact layer of ions on the particle diminishes the reaction rate and
consequently reduces the speed. Our results are consistent with published
experimental data.
View original:
http://arxiv.org/abs/1202.3797
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