Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients

Abstract

The interface between two miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium tangential electric field is studied experimentally and theoretically. A bulk-coupled electrohydrodynamic instability associated with the diffusive distribution of fluid conductivity at the interface is experimentally observed.The configuration is modelled using a layer of exponentially varying conductivity spliced on each surface to a constant-conductivity fluid half-space. Over-stable (propagating) modes are discovered and characterized in terms of the complex growth rate and fastest growing wavenumber, with the conductivity ratio and an inertia-viscosity time-constant ratio as parameters. In the low inertia limit, growth rates are governed by the electric-viscous time τ = η/εE2. Instability is found also with the layer of varying conductivity bounded by rigid equipotential walls. A physical mechanism leading to theoretically determined fluid streamlines in the form of propagating cells is described.At relatively high electric fields, large-scale mixing of the fluid components is observed. Photocell measurements of distributions of average fluid properties demonstrate evolution in time on a scale determined by τ.

Convective and absolute electrokinetic instability with conductivity gradients

“…An important comparison to this work is the temporal stability analysis of an electrohydrodynamic instability with zero base flow (Hoburg & Melcher 1976, 1977. The mechanism proposed by Hoburg & Melcher is qualitatively similar to that described in figure 17.…”

“…The correct internal velocity scale is the electroviscous velocity scale, U ev , which is obtained by balancing viscous and electric stresses. The electroviscous velocity scale is similar to that defined in Hoburg & Melcher (1976) and Melcher (1981). Our definition strives to account for all the relevant physical parameters involved in the electroviscous balance of our problem.…”

“…Electrohydrodynamic instability has been a subject of extensive research since Taylor and Melcher's pioneering leaky dielectric model (Melcher & Taylor 1969;Saville 1997). The core of the leaky dielectric model is the Ohmic model, and the essence of the electrohydrodynamic instability mechanism is charge accumulation at material interfaces and its coupling to fluid motion through electric body forces (see, for example, Melcher & Schwartz 1968;Hoburg & Melcher 1976). The natural velocity scale in this instability is the electroviscous velocity that results from a balance between the viscous and electric stresses (Melcher 1981).…”

Convective instability of electrokinetic flows in a cross-shaped microchannel

“…The charge density term ρ e in (3.10) forms in the bulk regions of the flow containing conductivity gradients, and couples with the applied field to generate electrical body forces in the bulk liquid. In a seminal paper on electrohydrodynamic instabilities of so-called 'leaky-dielectrics', Hoburg & Melcher (1976) showed that the accumulation of free charge ρ e in regions of conductivity gradients and collinear applied fields is described by the conservation of the electromigration current (3.4) and Gauss's law (3.5). This coupling can be quantified as…”

“…These instabilities are caused by a coupling of electric fields and ionic conductivity gradients that results in an electric body force (per unit volume) of the form ρ e E = ( E · ∇σ )E, where , E and σ are the local permittivity, electric field and ionic conductivity, respectively. In a seminal paper on EHD instability, Hoburg & Melcher (1976) showed that applying electric fields transverse to conductivity gradients in low-conductivity corn oil always results in unstable flows. Baygents & Baldessari (1998) performed a linear stability analysis of fields applied parallel to a linear conductivity gradient in high-conductivity electrolyte solutions.…”