Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

Traoré, Philippe; Pérez, Alberto T.

doi:10.1063/1.3685721

Cited by 109 publications

(90 citation statements)

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“…Such a transition arises due to the nonlinear instability with high values of driving parameters, and it leads to a new bifurcation of the system. The same transition has been confirmed in later studies with different values of M [25,26,28,29]. In this paper we attempt to deepen the study by investigating the route that the two-cell flow structure returns to rest when T is decreased.…”

Section: Introductionsupporting

confidence: 67%

“…Our present results are generally consistent with previous numerical predictions in Refs. [18,22,26,28]. Now it is clear that the discrepancy showed in Table 1 is partly because of the T f eM relationship.…”

Section: Finite Amplitude Instabilitymentioning

confidence: 72%

“…The temporal discretization is also based on the Gear scheme. The interested readers may refer to [26,37] for additional numerical details.…”

Section: Methodsmentioning

confidence: 99%

“…Chic on et al [20] IVF, PIC, one-mode a [5,40], þ∞ 121.4 Cerizza [22] SNS, 4th compact FD scheme 60 110.0 Traor e and P erez [26] SNS, FVM TVD scheme 10 107.5 V azquez and Castellanos [28] SNS, FEM Discontinuous Galerkin 20 108.7…”

Section: Authorsmentioning

confidence: 99%

“…In Ref. [26], all equations were solved with a finite volume method (FVM), and a total variation diminishing (TVD) scheme [27] was applied to the charge equation. For M ¼ 10, they found 155.64 and 107.5 for the linear and finite amplitude criteria, respectively.…”

Section: Introductionmentioning

confidence: 99%

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On two-dimensional finite amplitude electro-convection in a dielectric liquid induced by a strong unipolar injection

Traoré

Pérez

et al. 2015

Journal of Electrostatics

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a b s t r a c tThe hydrodynamic stability of a dielectric liquid subjected to strong unipolar injection is numerically investigated. We determined the linear criterion T c (T being the electric Rayleigh number) and finite amplitude one T f over a wide range of the mobility parameter M. A noticeable discrepancy is shown for T f between our numerical prediction and the value predicted by stability analysis, which is due to the velocity field used in stability analysis. Recent studies revealed a transition of the flow structure from one cell to two with an increase in T. We demonstrate that this transition results in a new subcritical bifurcation. IntroductionElectro-convection induced by the unipolar charge injection into an insulating liquid is a fundamental problem in Electro-HydroDynamics (EHD) [1,2]. The electro-chemical reaction at the interface between liquid and electrode gives rise to injection of ions [3], and the Coulomb force acting upon these injected free charges tends to destabilize the system and induce the flow motion. This type of flow motion plays the center role in several industry applications, such as heat transfer enhancement [4,5] and flow control [6]. However, the inherent strong and complex nonlinear couplings in such a system make the problem difficult to analyze. For homogeneous and autonomous injection between two parallel planar electrodes, there are two basic features in the hydrodynamic stability. First, the hydrostatic state is potentially unstable. When the driving parameter exceeds a critical value, the instability sets in and flow motion takes place. Linear stability analysis shows that the linear criterion, which is a function of the electric Rayleigh number T, is highly dependent on the injection level C but independent on the dimensionless mobility parameter M[7]. Second, the linear bifurcation is subcritical and there exists a nonlinear instability criterion. This feature is due to the ion drift mechanism, which states that charge carriers migrate with a finite ionic velocity under the effect of electric field. The competition between the ionic velocity and the fluid velocity leads to the formation of the so-named charge void region [8]. Since the finite amplitude criterion is lower than the linear one, a hysteresis loop is established between them. The physical mechanism for the subcritical bifurcation was first deduced by F elici with a simplified hydraulic model of 2D rolls in the weak injection regime [9]. In that paper, the author proved that the maximum fluid velocity should be higher than the ionic velocity in order to sustain a stable electro-convective motion. The case of strong injection regime was later discussed by Atten and Lacroix [10]. Both the cellular patterns of 2D rolls and 3D hexagonal cells were considered. With some assumptions, such as the infinite M number and the number of modes retained for the approximation of the velocity field, the nonlinear criteria for various injection levels were determined. For C ¼ 10, the nonlinear criteria for 2D rolls with ...

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Section: Introductionsupporting

confidence: 67%