Non-antiperiodic electric fields with zero time-average yield net electrophoresis

We report that multimodal periodic electric fields with time asymmetry but zero time average induce controllable net electrophoretic motion of colloids. Net motion is observed both experimentally and numerically if the electric field has two frequency modes that are the ratio of odd and even numbers (e.g., 3 Hz and 2 Hz). Furthermore, the direction of motion is reversed by changing the sign of the applied waveform, for example by swapping which electrode is powered and grounded. We provide generalized theoretical arguments indicating that non-antiperiodic force excitations will yield net motion in isotropic media, provided there is a nonlinear component in the equation of motion, and we show how similar ratchet-like responses occur in other mechanical systems involving nonlinearities.