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.

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.

A Linear Stability Analysis for an Improved One-Dimensional Two-Fluid Model

2003 ◽  
Vol 125 (2) ◽  
pp. 387-389 ◽  
Author(s):  
Jin Ho Song
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Model ◽  
Two Phase ◽  
One Dimensional ◽  
Proposed Model ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

A linear stability analysis is performed for a two-phase flow in a channel to demonstrate the feasibility of using momentum flux parameters to improve the one-dimensional two-fluid model. It is shown that the proposed model is stable within a practical range of pressure and void fraction for a bubbly and a slug flow.

scholarly journals Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

2014 ◽  
Vol 26 (12) ◽  
pp. 127101 ◽  
Author(s):  
Sukhendu Ghosh ◽  
R. Usha ◽  
Kirti Chandra Sahu
Keyword(s):  
Fluid Flow ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Two Fluid ◽  
Double Diffusive

LARGE-SCALE DISTORTIONS OF SQUARE PATTERNS

1994 ◽  
Vol 04 (05) ◽  
pp. 1147-1154 ◽  
Author(s):  
ALEXANDER NEPOMNYASHCHY
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Large Scale ◽  
Instability Threshold ◽  
Amplitude Equations ◽  
Wave Disturbances ◽  
Long Wave

Stationary square patterns are typical in several instability problems. Near the instability threshold, the evolution of long-wave disturbances can be described by a system of amplitude equations resembling the Newell-Whitehead-Segel equations. These equations are used for the linear stability analysis and the investigation of the defects.

scholarly journals On the porosity influence on stability of flow over porous medium

2020 ◽  
Vol 30 (1) ◽  
pp. 134-144
Author(s):  
K.B. Tsiberkin
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Short Wave ◽  
Wave Instability ◽  
Plane Parallel ◽  
Long Wave ◽  
The Stability ◽  
Critical Wavenumber

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

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.

Three Dimensional Film Stability and Draw Resonance

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Zahir U. Ahmed ◽  
Roger E. Khayat
Keyword(s):  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Physical Mechanism ◽  
Three Dimensional ◽  
Neutral Stability ◽  
Film Stability ◽  
New Approach ◽  
Draw Resonance

In order to understand the effects of inertia and gravity on draw resonance and on the physical mechanism of draw resonance in three-dimensional Newtonian film casting, a linear stability analysis has been conducted. An eigenvalue problem resulting from the linear stability analysis is formulated and solved as a nonlinear two-point boundary value problem to determine the critical draw ratios. Neutral stability curves are plotted to separate the stable/unstable domain in different appropriate parameter spaces. Both inertia and gravity stabilize the process and the process is more unstable to two- than to three-dimensional disturbances. The effects of inertia and gravity on the physical mechanism of draw resonance have been investigated using the eigenfunctions from the eigenvalue problem. A new approach is introduced in order to evaluate the traveling times of kinematic waves from the perturbed thickness at the take-up, which satisfies the same stability criterion illustrating the general stability of the system.

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