title: Diffusive behaviors of circle-swimming motors.
abstract: Spherical catalytic micromotors fabricated as described in Wheat et al. [Langmuir 26, 13052 (2010)] show fuel concentration dependent translational and rotational velocity. The motors possess short-time and long-time diffusivities that scale with the translational and rotational velocity with respect to fuel concentration. The short-time diffusivities are two to three orders of magnitude larger than the diffusivity of a Brownian sphere of the same size, increase linearly with concentration, and scale as v(2)/2ω. The measured long-time diffusivities are five times lower than the short-time diffusivities, scale as v(2)/{2D(r)[1+(ω/D(r))(2)]}, and exhibit a maximum as a function of concentration. Maximums of effective diffusivity can be achieved when the rotational velocity has a higher order of dependence on the controlling parameter(s), for example fuel concentration, than the translational velocity. A maximum in diffusivity suggests that motors can be separated or concentrated using gradients in fuel concentration. The decrease of diffusivity with time suggests that motors will have a high collision probability in confined spaces and over short times; but will not disperse over relatively long distances and times. The combination of concentration dependent diffusive time scales and nonmonotonic diffusivity of circle-swimming motors suggests that we can expect complex particle responses in confined geometries and in spatially dependent fuel concentration gradients.
authors.affiliation: Department of Mechanical Engineering, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Nathan A
authors.initials: NA
authors.lastname: Marine
authors.forename: Philip M
authors.initials: PM
authors.lastname: Wheat
authors.forename: Jesse
authors.initials: J
authors.lastname: Ault
authors.forename: Jonathan D
authors.initials: JD
authors.lastname: Posner
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D004735:Energy Transfer; D008956:Models, Chemical; D008958:Models, Molecular; D012212:Rheology / Q000379:methods*; D012399:Rotation; D012996:Solutions / Q000737:chemistry*
chemical_list: D012996:Solutions