Theory for Pure-Traveling-Wave Boundary-Guided Transport of Tribo-Electrified Particles

Numerical simulations and limiting analytical solutions are used to picture synchronous and asynchronous domains of traveling-wave pumping of charge-conserving particles (having mass m, charge q, radius a and mobility b) in terms of the dimensiouless frequency Ω = (w/k)/(bE0), mass M = (m/q)(bE0)(bE0) and gravitational acceleration G= mg/qEo, where k and w are the wavenumber and angular frequency of the imposed wave and Eo is the peak electric field intensity. One- dimensional motions, which can be synchronous for o < Ω < 1 (have velocity w/k), have a subsynchronous velocity that decreases rapidly with increasing frequency for Ω > 1. Both synchronous and asynchronous motions can exist over a range Ω < Ω < 1, where Ω → 1 as M → 0. Similar identification of domains for two-dimensional pumping brings in the additional parameters G and an image force parameter I = q[(e/e0) − l]/[(ε/ε0 + + 1)]16πc2ε0E0 where c is the closest distance of the particle charge center from a dielectric of permittivity, ε, coating the electrodes. Masuda's electric curtain mode is fitted into the general picture. As the frequency is raised, synchronous hopping motions give way to an asynchronous mode which can be the “slow curtain mode”. It is shown that the “fast curtain mode” (which would also be asynchronous) does not exist. Depending on M, there is a range of frequencies over which both the synchronous and asynchronous modes can exist, depending on the initial conditions. For the one-dimensional and the curtain asynchronous modes, simple models are used to show that even at relatively low particle densities, the effect of fluid entrainmenl on the pumping is significant, generally tending to increase the velocity of asynchronous modes.