Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Pérez, Alberto T.; Vázquez, Pédro A.; Wu, Jian; Traoré, Philippe

doi:10.1017/jfm.2014.537

Cited by 34 publications

(24 citation statements)

References 35 publications

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“…The effect of charge diffusion becomes very small as increases to , thus its linear stability criterion is larger than the former one, and this value also agrees well with from the work of Pérez et al. (2014), in which the charge diffusion effect was neglected. Such an increase of with has verified again the effects of charge diffusion found in the above validation of code for nonlinear equations.…”

Section: Resultssupporting

confidence: 90%

Deterministic and stochastic bifurcations in two-dimensional electroconvective flows

et al. 2021

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Section: Resultssupporting

confidence: 90%

Deterministic and stochastic bifurcations in two-dimensional electroconvective flows

et al. 2021

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“…The results of the linear stability analysis are similar to those obtained in Pérez et al [17]. The no-slip boundary conditions increases the threshold value for injection and changes the structure of the modes.…”

Section: Introductionsupporting

confidence: 85%

“…This nonlinear bifurcation is similar to what happens in one of the most classical problems in EHD, the convection generated by two infinite parallel electrodes immersed in a perfectly dielectric liquid and subjected to a electric voltage applied between the electrodes. However, in two recent papers [16,17] the authors considered a variation of this two-plate problem, with the infinite domain substituted by a finite closed rectangular domain with no-slip boundary conditions applied on all the boundaries. In the first paper, using numerical simulations, the authors showed that the bifurcation may become supercritical for some values of the aspect ratio of the domain.…”

Section: Introductionmentioning

confidence: 99%

Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis

et al. 2018

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We study the linear stability and nonlinear behavior of the electroconvection between two concentric half-cylinders with no-slip conditions on all boundaries. The no-slip condition makes impossible to apply the standard modal approach. Hence, we apply a finite element technique similar to the one we have used in a previous paper about the electroconvection in a rectangular enclosed domain. When compared to the classical problem of electroconvection between two full concentric cylinders, the linear criterion is higher, due to the viscous shear introduced by the lateral walls. As a consequence, the structure of the eigenmodes is very different. There is a repulsion between modes with the same symmetry, forcing pairs of modes to cross each other repeatedly. For inner injection and small value of the ratio between the inner and outer radii the no-slip condition changes the nature of the bifurcation from subcritical to supercritical, while it is always subcritical for outer injection. To understand this behavior, we perform a modal analysis using the eigenfunctions obtained from the linear stability analysis as modal basis. We show that the supercritical branch is originated by the nonorthogonality of the modes when no-slip boundary conditions are imposed. These mechanism explains the previously unexplained appearance of the supercritical branch in the enclosed rectangular configuration.

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“…In the cross-flow with suppressed the transverse structures, the system yields a longitudinal rolling pattern with a constant Ne=1. 41 [88]. Since the longitudinal rolling pattern is two dimensional in the y and z-directions, it does not interact with the bulk cross-flow.…”

Section: Perturbation Of the Hydrostatic Base State Solution Includinmentioning

confidence: 99%

Three-dimensional electroconvective vortices in cross flow

2020

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The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is onedimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number. 1 0 cc c t Fe Pattern transition after cross-flow applicationThis section studies the transitions of 3D to 2D patterns by applying the cross-flow to already developed square vortex structures, as shown in FIG. 3(a). With weak cross-flow, the systems transitions to oblique 3D vortex structures (oblique transverse and regular longitudinal structures coexist). The increased cross-flow yields a longitudinal rolling pattern, i.e., transverse structures are fully suppressed . FIG. 11 shows the time evolution of maximum * z u in Couette cross-flow. For lower cross-flow velocities (e.g., u * wall=2.40) and, therefore, weak shear stress, the maximum * z u decreases to an equilibrium value, that is somewhat greater than that for the rolling pattern flow (u * wall =2.75). Interestingly, with further increase in u * wall (e.g., u * wall=3.20), the equilibrium value of * z u may decrease below the value of the rolling pattern.And with even further increasing u * wall (e.g., u * wall=3.84), the equilibrium solution develops an oblique 3D structure with maximum uz that is greater than that of the rolling pattern. However, at u * wall = 3.88, a bifurcation occurs, and the steady-state solution has only 2D streamwise

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Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Cited by 34 publications

References 35 publications

Deterministic and stochastic bifurcations in two-dimensional electroconvective flows

Deterministic and stochastic bifurcations in two-dimensional electroconvective flows

Electroconvection in a dielectric liquid between two concentric half-cylinders with rigid walls: Linear and nonlinear analysis

Three-dimensional electroconvective vortices in cross flow

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