Electrohydrodynamic Stability of Space‐Charge‐Limited Currents in Dielectric Liquids. I. Theoretical Study
TL;DR: In this paper, an analysis of the steady cellular convection which results when charge is injected uniformly into the free surface of a film of an insulating liquid is discussed; the method of exchange of stabilities is assumed to be valid; velocity and potential perturbations on the initial steady state lead to a characteristic equation which determines the conditions for onset of instability.
Abstract: Liquid motion is often observed when an electric field is applied to a dielectric liquid. An analysis of the steady cellular convection which results when charge is injected uniformly into the free surface of a film of an insulating liquid is discussed. The initial, steady‐state current is space‐charge‐limited. The method of exchange of stabilities is assumed to be valid; velocity and potential perturbations on the initial steady state lead to a characteristic equation which determines the conditions for onset of instability. This characteristic equation is of the seventh order and has nonconstant coefficients. A numerical integration has been performed on the equation and the resulting solutions show that a critical potential exists above which convection will occur. The condition for instability is R = 99 = eV0/μη., where η is the dynamic coefficient of viscosity, μ is the charge carrier mobility, and e is the permittivity. The dimensionless number R is analogous to the Rayleigh number in hydrodynamics....
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TL;DR: In this article, an electrokinetic instability (EKI) micromixer is used to effect active rapid stirring of confluent microstreams of biomolecules without moving parts or complex microfabrication processes.
Abstract: A novel electrokinetic instability (EKI) micromixer and method takes advantage of the EKI to effect active rapid stirring of confluent microstreams of biomolecules without moving parts or complex microfabrication processes. The EKI is induced using an alternating current (A/C) electric field. Within seconds, the randomly fluctuating, three-dimensional velocity field created by the EKI rapidly and effectively stirs an initially heterogeneous solution and generates a homogeneous solution that is useful in a variety of biochemical and bioanalytical systems. Microfabricated on a glass substrate, the inventive EKI micromixer can be easily and advantageously integrated in molecular diagnostics apparatuses and systems, such as a chip-based “Lab-on-a-Chip” microfluidic device.
632 citations
TL;DR: In this paper, a unified asymptotic picture of the electric double-layer undercurrent, encompassing all regimes from quasi-equilibrium to the extreme non-equilibria, is developed and employed for derivation of a universal electro-osmotic slip formula.
Abstract: Electric conduction from an electrolyte solution into a charge selective solid, such as ion exchange membrane or electrode, becomes unstable when the electrolyte concentration near the interface approaches zero owing to diffusion limitation. The sequence of events leading to instability is as follows: upon the decrease of the interface concentration, the electric double layer at the interface transforms from its common quasi-equilibrium structure to a different, non-equilibrium one. The key feature of this new structure is an extended space charge added to the usual one of the quasi-equilibrium electric double layer. The non-equilibrium electro-osmotic slip related to this extended space charge renders the quiescent conductance unstable. A unified asymptotic picture of the electric double-layer undercurrent, encompassing all regimes from quasi-equilibrium to the extreme non-equilibrium one, is developed and employed for derivation of a universal electro-osmotic slip formula. This formula is used for a linear stability study of quiescent electric conduction, yielding the precise parameter range of instability, compared with that in the full electroconvective formulation. The physical mechanism of instability is traced both kinematically, in terms of non-equilibrium electro-osmotic slip, and dynamically, in terms of forces acting in the electric double layer.
336 citations
Cites background from "Electrohydrodynamic Stability of Sp..."
...The same term relates to the flow of liquid dielectrics caused by the action of an electric field on the space charge of ions of the appropriate sign injected into a low quantity into the fluid (see Schneider & Watson 1970; Castellanos & Velarde 1981; Perez & Castellanos 1989)....
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TL;DR: In this paper, a survey of different aspects of fluid motion induced by the Coulomb force exerted by the electric field on an injected space charge is given, and the instability problem in highly symmetrical electrode configurations is considered with positive coupling between velocity and charge perturbations, linear and nonlinear criteria and phenomena during the transient regime of unipolar injection.
Abstract: A survey is given of different aspects of fluid motion induced by the Coulomb force exerted by the electric field on an injected space charge. The instability problem in highly symmetrical electrode configurations is considered with positive coupling between velocity and charge perturbations, linear and nonlinear criteria and the phenomena during the transient regime of unipolar injection. Then the features of electroconvection are described for both strong and weak injection and also in the case of coaxial cylinders. The last part deals with the liquid motion induced by injection from very restricted areas, as occurs in configurations of low symmetry with particular attention devoted to charge plumes.
197 citations
TL;DR: In this paper, the authors considered two asymptotic states of convection: one where the whole motion is dominated by viscosity, and one where inertial effects dominate, and they derived the dependence of the current density ratio I/I0 on the stability parameter T = M2R = eϕ0/Kρν, and on 1/R = ν/Kϕ 0, which is an equivalent Prandtl number.
Abstract: The problem of electric charge convection in a dielectric liquid layer of high ionic purity, when subjected to unipolar injection, is in many ways analogous to that of thermal convection in a horizontal fluid layer heated from below, although no formal analogy can be established. The problem treated is intrinsically more nonlinear than the thermal problem. We consider two asymptotic states of convection: one where the whole motion is dominated by viscosity, and one where inertial effects dominate. In each state, two or three spatial regions are distinguished. From the approximate equations that hold in the different regions, information about the variation of the different quantities with distance from the injector is obtained, and further approximations permit us to establish the dependence of the current density ratio I/I0 (called the electric Nusselt number) on the stability parameter T = M2R = eϕ0/Kρν, and on 1/R = ν/Kϕ0, which is an equivalent Prandtl number (e is the permittivity, ρ the fluid density, K the mobility, ν the kinematic viscosity, and ϕ0 the applied voltage). In the viscous state, the analysis gives I/I0 ∞ T½; in the inertial state the law I/I0 ∞ (T/R)1/4 = M½ is obtained. Since M is independent of the applied voltage, the latter law shows the saturation in the electric Nusselt number observed in earlier experiments. The transition in the states is associated with a transition number (MR)T [gap ] 30, which is an electric Reynolds number, related to an ordinary Reynolds number of about 10.The experimental results, obtained in liquids of very different viscosities and dielectric constants, verify these theoretical predictions; further, they yield more precise numerical coefficients. As for the transition criteria, the experiments confirm that the viscous and inertial effects are of the same order when Re [gap ] 10. It was also possible to determine roughly the limits of the viscous and inertial states. The viscous analysis remains valid up to a Reynolds number of about 1; the inertial state can be considered valid down to a Reynolds number of 60. Schlieren observations show that the motion has the structure of very stable hexagonal cells at applied voltages just above the critical voltage, which are transformed into unstable filaments when the voltage is increased further. At even higher voltages, the motion finally breaks down into turbulence. It may be of interest to point out that, when M < 3, the electric Nusselt number approaches 1, which is equivalent to the situation in thermal convection at low Prandtl numbers.
196 citations
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