Theory for finite-phase traveling-wave boundary-guided transport of triboelectrified particles

Numerical simulations 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 dimensionless frequency Ω=(ω/k)/(bE₀), mass M=(m/q) (kb) (bE₀), and gravitational acceleration G=mg/qE₀, where k and ω are the wavenumber and angular frequency of the imposed wave and E₀=kV, where V is the peak voltage. The effects of having a finite number of phases consisting of discrete electrodes covered by a semi-insulating layer are highlighted. The time-average velocity in the direction of wave travel is found to be synchronous (have velocity ω/k) for 0<Ω<Ω*<1, where Ω* is reduced by having finite phases. Because the discrete electrodes result in hops of higher magnitude, they tend to result in a conversion to asynchronous hopping and `certain´ modes at a lower frequency than with a sinusoidal wave. At low M, they can also result in the stalling of particle pumping as the frequency is raised. Predicted effects of image forces, dielectric layer thickness, bulk conductivity, and surface conductivity as well as particle sticking and slipping are discussed