Linear Instability of Liquid Sheets Subjected to a Transverse Electric Field

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Xiao Cui ◽  
Qing-Fei Fu ◽  
Lijun Yang ◽  
Luo Xie ◽  
Bo-Qi Jia
Keyword(s):  
Growth Rate ◽  
Liquid Sheet ◽  
Linear Instability ◽  
Wave Number ◽  
Perfect Conductor ◽  
Liquid Density ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric ◽  
Gas To Liquid

Abstract A temporal linear instability analysis was performed for a liquid sheet moving around the inviscid gas in transverse electrical field. The fluid was described by the leaky-dielectric model, which is more complex and more comparable to the liquid electrical properties than existing models. As a result, the sinuous and the varicose modes exist, in which the dimensionless dispersion relation between wave number and temporal growth rate can be derived as a 3 × 3 matrix. According to this relationship, the effects of liquid properties on sheet instability were performed. It was concluded that, as the electrical Euler number (Eu), the ratio of gas-to-liquid density (ρ), Weber number (We), Reynolds number (Re), and the relative relaxation time (τ) increased, the instability of the sheet was enhanced. This work also compared the leaky-dielectric model with the perfect conductor model and found that the unstable growth rate in the leaky-dielectric model was higher than the one in the perfect conductor model. Moreover, as the ratio of gas-to-liquid improved, this difference decreased. Finally, an energy approach was adopted to investigate the instability mechanism for the two models.

The electrostatically forced Faraday instability: theory and experiments

2019 ◽  
Vol 862 ◽  
pp. 696-731 ◽  
Author(s):  
Kevin Ward ◽  
Satoshi Matsumoto ◽  
Ranga Narayanan
Keyword(s):  
Interfacial Instability ◽  
Perfect Conductor ◽  
Dc Voltage ◽  
Fluid Systems ◽  
Instability Theory ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric ◽  
Rigorous Model ◽  
Parametric Frequency

The onset of interfacial instability in two-fluid systems using a viscous, leaky dielectric model is studied. The instability arises as a result of resonance between the parametric frequency of an imposed electric field and the system’s natural frequency. In addition to a rigorous model that uses Floquet instability analysis, where both viscous and charge effects are considered, this study also provides convincing validating experiments. In other results, it is shown that (a) the imposition of a periodic electrostatic potential acts to counter gravity and this countering effect becomes more effective if a DC voltage is also added, (b) a critical DC voltage exists at which the interface becomes unstable such that no parametric frequency is required to completely destabilize the interface and (c) the leaky dielectric model approaches a model for a perfect dielectric/perfect conductor pair as the conductivity ratio becomes large. It is also shown via experiments that parametric resonant instability using electrostatic forcing may be reliably used to estimate interfacial tension to sufficient accuracy.

Linear Instability Analysis of an Annular Liquid Sheet With Inner and Outer Gas Flow

2009 ◽  
Author(s):  
Fathollah Ommi ◽  
Seid Askari Mahdavi ◽  
S. Mostafa Hosseinalipour ◽  
Ehsan Movahednejad
Keyword(s):  
Growth Rate ◽  
Dispersion Equation ◽  
Liquid Sheet ◽  
Linear Instability ◽  
Wave Number ◽  
Unstable Wave ◽  
Instability Analysis ◽  
Air Stream ◽  
Linear Instability Analysis ◽  
Air Streams

A linear instability analysis of an inviscid annular liquid sheet emanating from an atomizer subjected to inner and outer swirling air streams has been carried out. The dimensionless dispersion equation that governs the instability is derived. The dispersion equation solved by Numerical method to investigate the effects of the liquid-gas swirl orientation on the maximum growth rate and its corresponding unstable wave number that it produces the finest droplets. To understand the effect of air swirl orientation with respect to liquid swirl direction, four possible combinations with both swirling air streams with respect to the liquid swirl direction have been considered. Results show that at low liquid swirl Weber number a combination of co-inner air stream and counter-outer air stream has the largest most unstable wave number and shortest breakup length. The combination of inner and the outer air stream co-rotating with the liquid has the highest growth rate.

Effect of Velocity Profile on the Stability of Liquid Sheet

2014 ◽  
Vol 694 ◽  
pp. 288-291
Author(s):  
Run Ze Duan ◽  
Zhi Ying Chen ◽  
Li Jun Yang
Keyword(s):  
Growth Rate ◽  
Velocity Profile ◽  
Linear Analysis ◽  
Liquid Sheet ◽  
Wave Number ◽  
Flat Plates ◽  
Chebyshev Spectral Collocation ◽  
The Stability ◽  
The Relationship ◽  
Temporal Growth Rate

An electrified liquid sheet injected into a dielectric moving through a viscous gas bounded by two horizontal parallel flat plates of a transverse electric field is investigated with the linear analysis method. The liquid sheet velocity profile and the gas boundary layer thickness are taken into account. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The effects of the velocity profile on the stability of the electrified liquid sheet were revealed for both sinuous mode and varicose mode. The results show that the growth rate of the electrified Newtonian liquid is greater than that of corresponding Newtonian one under the same condition, and the growth rate of the sinuous mode is greater than that of the varicose mode. Keywords: instability; planar liquid sheet; velocity profile;spectral method;linear analysis

scholarly journals Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations

2017 ◽  
Vol 829 ◽  
pp. 127-152 ◽  
Author(s):  
Debasish Das ◽  
David Saintillan
Keyword(s):  
Numerical Simulations ◽  
Electric Fields ◽  
Small Deformation ◽  
Dielectric Liquid ◽  
Uniform Electric Field ◽  
Liquid Drops ◽  
Wide Range ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviours contingent on field strength and material properties. These phenomena are best described by the Melcher–Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop–fluid interface and prescribes a balance between charge relaxation, the jump in ohmic currents from the bulk and charge convection by the interfacial fluid flow. Most previous numerical simulations based on this model have either neglected interfacial charge convection or restricted themselves to axisymmetric drops. In this work, we develop a three-dimensional boundary element method for the complete leaky dielectric model to systematically study the deformation and dynamics of liquid drops in electric fields. The inclusion of charge convection in our simulations permits us to investigate drops in the Quincke regime, in which experiments have demonstrated a symmetry-breaking bifurcation leading to steady electrorotation. Our simulation results show excellent agreement with existing experimental data and small-deformation theories.

Transient Electrohydrodynamic Manipulation of Particles on the Surface of a Drop

2016 ◽  
Author(s):  
Edison C. Amah ◽  
Ian S. Fischer ◽  
Pushpendra Singh
Keyword(s):  
Electric Field ◽  
Applied Electric Field ◽  
Control Parameter ◽  
Transient Behavior ◽  
Uniform Electric Field ◽  
Electrohydrodynamic Flow ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

In our previous studies we have shown that particles adsorbed on the surface of a drop can be concentrated at its poles or equator by applying a uniform electric field. This happens even when the applied electric field is uniform; the electric field on the surface of the drop is nonuniform, and so particles adsorbed on the surface are subjected to dielectrophoretic (DEP) forces. In this study, we use leaky dielectric model to model the transient behavior of particles at low electric field frequencies. We show that the frequency of the electric field is an important control parameter that under certain conditions can be used to collect particles at the poles or the equator, and to move them from the poles to the equator. The speed with which particles move on the surface depends on the strength of the electrohydrodynamic flow which diminishes with increasing frequency.

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 “Leaky Dielectric” Model for the Suppression of Dynamic $R_{\mathrm{ON}}$ in Carbon-Doped AlGaN/GaN HEMTs

2017 ◽  
Vol 64 (7) ◽  
pp. 2826-2834 ◽  
Author(s):  
Michael J. Uren ◽  
Serge Karboyan ◽  
Indranil Chatterjee ◽  
Alexander Pooth ◽  
Peter Moens ◽  
...  
Keyword(s):  
Carbon Doped ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Gan Hemts ◽  
Leaky Dielectric

Theoretical Analysis of Surface Waves on Liquid Jets in Crossflows with Deformation

2013 ◽  
Vol 681 ◽  
pp. 152-157
Author(s):  
Shao Lin Wang ◽  
Yong Huang ◽  
Fang Wang ◽  
Zhi Lin Liu
Keyword(s):  
Growth Rate ◽  
Theoretical Analysis ◽  
Surface Waves ◽  
Cross Section ◽  
Aerodynamic Force ◽  
Linear Instability ◽  
Wave Number ◽  
Liquid Jets ◽  
Liquid Jet ◽  
The Cross

Liquid jets in cross air flows are widely used and play an important role in propulsion systems, such as ramjet combustors. Surface waves on the liquid jets in gaseous crossflows have been observed in numerous experiments. Especially for lower gas Webber number, liquid jets breaks up due to the surface waves. However compared with injecting into gas coaxial flow, liquid jet will be deformed in crossflow due to the transverse aerodynamic force. Deformation of jet is investigated by analyzing stress force equilibrium of the cross-section. Though linear instability analysis, dispersion relation and growth rate of surface waves of liquid jet with deformation were derived. According to the present theoretical analysis, the cross-section shape can be deformed to stable ellipse only if the gas velocity was lower than 9m/s for 1mm diameter jet. The maximum growth rate of disturbances takes place at wave number 0.7 approximately, and it will decrease with increasing the jet diameter. The range of instable wave number will expand and the most instable wave number will grow for the deformed jets.

Absolute and convective instability of a liquid sheet

1990 ◽  
Vol 220 ◽  
pp. 673-689 ◽  
Author(s):  
S. P. Lin ◽  
Z. W. Lian ◽  
B. J. Creighton
Keyword(s):  
Weber Number ◽  
Convective Instability ◽  
Density Ratio ◽  
Sheet Thickness ◽  
Surface Tension Force ◽  
Liquid Sheet ◽  
Inertia Force ◽  
Liquid Density ◽  
Gas To Liquid ◽  
Density Ratios

The linear stability of a viscous liquid sheet in the presence of ambient gas is investigated. It is shown that there are two independent modes of instability, sinuous and varicose. The large-time asymptotic amplitude of sinuous disturbances is found to be bounded but non-vanishing for all calculated values of Reynolds numbers and the gas-to-liquid density ratios when the Weber number is greater than one half. The Weber numberWeis defined as the ratio of the surface tension force to the inertia force per unit area of the gas–liquid interface. WhenWeis smaller than one half, the sinuous mode is stable if the gas-to-liquid density ratio is zero, otherwise it is convectively unstable. The varicose mode is always convectively unstable unless the density ratio,Q, is zero. Then it is asymptotically stable. The spatial growth rate of the varicose mode is smaller than that of the sinuous mode for the same flow parameters. The wavelength of the most amplified waves in both modes is found to scale with the product of the sheet thickness andQ/We. It is shown, by use of the energy equation, that the mechanism of instability is a capillary rupture whenWe[ges ] 0.5, and the convective instability is due to the interfacial pressure fluctuation whenWe< 0.5.

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