Self-similar nested sequences on a chaotic attractor for traveling-wave electrophoresis

Oscillating electric potentials are applied to interdigitated arrays of cylindrical electrodes above and below a stationary conducting viscous fluid. The phases of these potentials are chosen to produce a longitudinal traveling wave that traps high-mobility ions and partially traps intermediate-mobility ions in periodic and narrowband chaotic attractors with average velocities that are commensurate with the wave speed. Stable periodic attractors have periods up to 101 times the wave period. Incommensurate broadband chaotic attractors are described by one-dimensional iterated contact-angle return maps, which feature self-similar nested sequences that converge geometrically at unstable trapped orbits. Sequences of singular angles and sequences of step transitions are characterized by distinct convergence factors. A criterion for allowed interelectrode orbits is developed. Experiments are suggested to evaluate the applicability of the theory to microfluidic separations.