Non-linear electrorheological instability of two streaming cylindrical fluids

Moatimid, Galal M.

doi:10.1088/0305-4470/36/44/012

Cited by 12 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More recently, nonlinear effects have been specially studied in order to explain the experimental phenomena, such as the formation of satellite droplets (e.g. López-Herrera, Gañán-Calvo & Perez-Saborid 1999;López-Herrera & Gañán-Calvo 2004;Zakaria 2000;Elhefnawy, Agoor & Elcoot 2001;Elhefnawy, Moatimid & Elcoot 2004;Moatimid 2003).…”

Section: Introductionmentioning

confidence: 99%

Instability of a viscous coflowing jet in a radial electric field

Li¹,

Yin²,

Yin³

2008

J. Fluid Mech.

View full text Add to dashboard Cite

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

show abstract

Section: Introductionmentioning

confidence: 99%

Instability of a viscous coflowing jet in a radial electric field

Li¹,

Yin²,

Yin³

2008

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Therefore, the remaining boundary condition arises from the normal component of the stress σ i j . This component is discontinuous at the interface by the amount of surface tension at the interface r = R + η(z; t) [8]. This may be written as…”

Section: The Nonlinear Boundary Conditionsmentioning

confidence: 99%

“…The perturbation analysis produces two levels of the solvability conditions, which are used to construct the Ginsburg-Landau equation. A weakly nonlinear instability of surface waves propagating through two viscoelastic cylindrical dielectric fluids is investigated by Moatimid [8]. He considered weak viscoelastic effects on the interface so that their contributions are demonstrated through the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The instability of nonlinear surface waves in an electrified liquid jet

Moatimid¹

2009

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg-Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schrödinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.

show abstract

“…In axisymmetric deformations, this result was given by Othman [41] and Moatimid [42] with different notations. The low-conductivity limit in absence of the streaming velocity was considered by Nayyar and Murty [9] and Mestel [15].…”

Section: Linear Stability Approachmentioning

confidence: 99%

Modulation instability of electrohydrodynamic waves on liquid jet

Elcoot

2006

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

Non-linear electrorheological instability of two streaming cylindrical fluids

Cited by 12 publications

References 27 publications

Instability of a viscous coflowing jet in a radial electric field

Instability of a viscous coflowing jet in a radial electric field

The instability of nonlinear surface waves in an electrified liquid jet

Modulation instability of electrohydrodynamic waves on liquid jet

Contact Info

Product

Resources

About