scholarly journals Instability of a planar fluid interface under a tangential electric field in a stagnation point flow

2021 ◽  
Vol 931 ◽  
Author(s):  
Mohammadhossein Firouznia ◽  
Michael J. Miksis ◽  
Petia M. Vlahovska ◽  
David Saintillan
Keyword(s):  
Stability Analysis ◽  
Electric Field ◽  
Stagnation Point ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stagnation Point Flow ◽  
Immiscible Fluid ◽  
Charge Dynamics ◽  
Tangential Electric Field ◽  
Interfacial Charge

The interface between two immiscible fluids can become unstable under the effect of an imposed tangential electric field along with a stagnation point flow. This canonical situation, which arises in a wide range of electrohydrodynamic systems including at the equator of electrified droplets, can result in unstable interface deflections where the perturbed interface gets drawn along the extensional axis of the flow while experiencing strong charge build-up. Here, we present analytical and numerical analyses of the stability of a planar interface separating two immiscible fluid layers subject to a tangential electric field and a stagnation point flow. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a local linear stability analysis in the vicinity of the stagnation point to study the behaviour of the system in terms of the relevant dimensionless groups of the problem. The local theory is complemented with a numerical normal-mode linear stability analysis based on the full system of equations and boundary conditions using the boundary element method. Our analysis demonstrates the subtle interplay of charge convection and conduction in the dynamics of the system, which oppose one another in the dominant unstable eigenmode. Finally, numerical simulations of the full nonlinear problem demonstrate how the coupling of flow and interfacial charge dynamics can give rise to nonlinear phenomena such as tip formation and the growth of charge density shocks.

Linear stability analysis of an electrified incompressible liquid sheet streaming into a compressible ambient gas

2016 ◽  
Vol 231 (10) ◽  
pp. 1849-1858 ◽  
Author(s):  
Yuxin Liu ◽  
Chaojie Mo ◽  
Lujia Liu ◽  
Qingfei Fu ◽  
Lijun Yang
Keyword(s):  
Stability Analysis ◽  
Electric Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Density Ratio ◽  
Sheet Thickness ◽  
Liquid Sheet ◽  
Wave Number ◽  
Liquid Density ◽  
Ambient Gas

This article presents the linear stability analysis of an electrified liquid sheet injected into a compressible ambient gas in the presence of a transverse electric field. The disturbance wave growth rates of sinuous and varicose modes were determined by solving the dispersion relation of the electrified liquid sheet. It was determined that by increasing the Mach number of the ambient gas from subsonic to transonic, the maximum growth rate and the dominant wave number of the disturbances were increased, and the increase was greater in the presence of the electric field. The electrified liquid sheet was more unstable than the non-electrified sheet. The increase of both the gas-to-liquid density ratio and the electrical Euler number accelerated the breakup of the liquid sheet for both modes; while the ratio of distance between the horizontal electrode and the liquid-sheet-to-sheet thickness had the opposite effect. High Reynolds and Weber numbers accelerated the breakup of the electrified liquid sheet.

scholarly journals 235th ECS Meeting: Linear stability analysis of time-dependent electrodeposition in charged porous media

2019 ◽  
Author(s):  
Edwin Khoo ◽  
Hongbo Zhao ◽  
Martin Z. Bazant
Keyword(s):  
Stability Analysis ◽  
Electric Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Electrode Surface ◽  
Time Dependent ◽  
Pore Surface ◽  
Surface Charges ◽  
Negative Surface ◽  
Overlimiting Current

We study the linear stability analysis of time-dependent electrodeposition in a charged random porous medium, whose pore surface charges can generally be of any sign, that is flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero pore surface charges, the voltage and electric field at the cathode diverge when the bulk electrolyte concentration there vanishes at Sand's time. The same phenomenon happens for positive surface charges but at a time earlier than Sand's time. In contrast, negative surface charges allow the electrochemical system to sustain an overlimiting current via surface conduction past Sand's time, keeping the voltage and electric field bounded. Therefore, at Sand's time, negative surface charges greatly reduce the electrode surface instabilities while zero and positive surface charges magnify them. We compare theoretical predictions for overall electrode surface stabilization from the linear stability analysis with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also use the linear stability analysis as a tool to analyze how the crystal grain size changes with duty cycle during pulse electroplating.

Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

2007 ◽  
Vol 583 ◽  
pp. 347-377 ◽  
Author(s):  
F. LI ◽  
O. OZEN ◽  
N. AUBRY ◽  
D. T. PAPAGEORGIOU ◽  
P. G. PETROPOULOS
Keyword(s):  
Stability Analysis ◽  
Electric Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Surface Charges ◽  
Two Fluids ◽  
Long Wave ◽  
Normal Electric Field ◽  
Two Fluid

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

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