Abstract
“Electrohydrodynamics” refers to fluid flows triggered by electric fields. Various mathematical models, geared towards explaining apparently distinct phenomena over a range of scales and materials, have evolved almost independently. Three important classes of phenomena are:
(i) Electrokinetics: Flows driven by the action of electric fields on nanometric “electrical double layers”, which are characteristic of solid-electrolyte interfaces. Such flows are observed on the micron-scale, typically in the form of channel flow or electrophoretic particle migration. They are regularly employed in both colloid-science applications and microfluidic devices.
(ii) Electrocapillarity: The effective surface tension reduction measured for electrified interfaces. The effect is fundamental to electrochemistry, and enables electrowetting technologies. For a surface polarised by an applied field, the surface-tension reduction is non-uniform whereby flow is inevitable.
(iii) Leaky-dielectric electrohydrodynamics: Field-driven flows associated with charged interfaces separating poorly conducting fluids. The leaky-dielectric model was originally put forward by G.I. Taylor towards explaining perplexing observations of drops deforming to an oblate shape under an electric field. It has
since become omnipresent in electrohydrodynamic modelling.
The mathematical model underlying electrokinetics (Poisson-Nernst-Planck-Stokes equations) is unique in that it explicitly describes the transport of the charge-carrying ions, instead of assigning the fluids a set of bulk electrical properties. I will present a systematic asymptotic methodology for coarse-graining the electrokinetic equations, leading to “macroscale models” wherein electrical double layers are represented by a set of effective boundary conditions. In contrast to classical electrokinetic analyses, these nonlinear models are limited to neither weak fields nor weakly charged surfaces. Their usefulness will be demonstrated by presenting novel nonlinear solutions to the classical electrokinetic problem of electrophoresis, of both solid and fluid particles. In the latter case, electrocapillarity, and leaky-dielectric electrohydrodynamics, emerge in appropriate asymptotic limits. These linkages provide surprising interpretations for the lumped parameters appearing in these models, and reveal why “standard” electrokinetic effects are subdominant in these scenarios.