Electro-hydrodynamic particle levitation on electrodes

The thin-Debye-layer model is utilized to analyse the electro-hydrodynamic flow about a colloidal particle which is exposed to a direct ionic current, emitted by a proximate reactive electrode. This flow is driven by electro-osmotic slip on the particle, as well as a comparable slip on the electrode itself. The small particle–electrode separation allows for the use of singular perturbation. Thus, the electro-neutral bulk-fluid domain is decomposed into an ‘inner’ gap region, where the electric field and shear rate are large, and an ‘outer’ region, consisting of the remaining bulk domain, where they are moderate. Matched asymptotic expansions in both regions provide the requisite flow field. The intensive shear rate in the narrow gap region is associated with a lubrication-type pressure build-up, which is responsible for the leading-order hydrodynamic force on the particle. This force acts to repel the particle away from the electrode, thereby supporting it against gravity. Its magnitude is inversely proportional to the gap width. At large distances from the particle the fluid velocity decays with the third power of distance, while near the electrode it decays with the fourth power. The inward pointing flow near the electrode tend to entrain neighbouring particles, thereby resulting in two-dimensional particle clusters. For equal values of particle and anode zeta potentials, this process is dominated by the particle-slip contribution.