Electrohydrodynamic Phenomena

Abstract

This work is a review article focused on exploring the interactions
between external and induced electric fields and fluid motion, in the
presence of embedded charges. Such interactions are generally termed
electrohydrodynamics (EHD), which encompasses a vast range of flows
stemming from multiscale physical effects. In this review article we shall
mainly emphasize on two mechanisms of particular interest to fluid dynamists
and engineers, namely electrokinetic flows and the leaky dielectric
model. We shed light on the underlying physics behind the above
mentioned phenomena and subsequently demonstrate the presence of
a common underpinning pattern which governs any general electrohydrodynamic
motion. Hence we go on to show that the seemingly unrelated
fields of electrokinetics and the leaky dielectric models are indeed
closely related to each other through the much celebrated Maxwell
stresses, which have long been known as stresses caused in fluids in
presence of electric and magnetic fields. Interactions between Maxwell
Stresses and charges (for instance, in the form of ions) present in the
fluid generates a body force on the same and eventually leads to flow
actuation. We show that the manifestation of the Maxwell stresses itself
depends on the charge densities, which in turn is dictated by the underlying
motion of the fluid. We demonstrate how such inter-related dynamics
may give rise intricately coupled and non-linear system of equations
governing the dynamical state of the system. This article is mainly
divided into two parts. First, we explore the realms of electrokinetics,
wherein the formation and the structure of the so-called electrical double
layer (EDL) is delineated. Subsequently, we review EDL’s relevance to
electroosmosis and streaming potential with the key being the presence
and absence of an applied pressure gradient. We thereafter focus on
the leaky dielectric model, wherein the fundamental governing equations
and its main difference with electrokinetics are described. We limit our
attentions to the leaky dielectric motion around droplets and flat surfaces
and subsequent interface deformation. To this end, through a rigorous
review of a number of previous articles, we establish that the interface
shapes can be finely tailored to achieve the desired geometrical characteristics
by tuning the fluid properties. We further discuss previous studies,
which have shown migration of droplets in the presence of strong
electric fields. Finally, we describe the effects of external agents such as surface impurities on leaky dielectric motion and attempt to establish a qualitative connection between the leaky dielectric model and EDLs. We finish off with some pointers for further research activities and open questions in this field.